@article {549,
	title = {Screened Expanding Turning Vane Concept},
	journal = {Experiments in Fluids},
	year = {In Press},
	author = {Drela, M. and Huang, A. and Darmofal, D.}
}
@mastersthesis {Huang_2020_PhD,
	title = {An Adaptive Variational Multiscale Method with Discontinuous Subscales for Aerodynamic Flows},
	year = {2020},
	school = {Massachusetts Institute of Technology},
	type = {PhD},
	address = {Department of Aeronautics and Astronautics},
	author = {Arthur C. Huang}
}
@conference {Carson_2020_MOESS_CG_DG,
	title = {Mesh optimization via error sampling and synthesis: An update},
	booktitle = {AIAA conference paper},
	number = {2020-0087},
	year = {2020},
	doi = {10.2514/6.2020-0087},
	author = {Hugh A. Carson and Arthur C. Huang and Marshall C. Galbraith and Steven R. Allmaras and David L. Darmofal}
}
@conference {Huang_2020_Variational,
	title = {A Variational multiscale method with discontinuous subscales for output-based adaptation of aerodynamic flows},
	booktitle = {AIAA conference paper},
	number = {2020-1563},
	year = {2020},
	doi = {10.2514/6.2020-1563},
	author = {Arthur C. Huang and Hugh A. Carson and Steven R. Allmaras and Marshall C. Galbraith and David L. Darmofal and Dimitry S. Kamenetskiy}
}
@article {Jayasinghe_2019_Distributed_Well_Model,
	title = {A discretization-independent distributed well model},
	journal = {Society of Petroleum Engineers Journal},
	year = {2019},
	month = {October},
	doi = {10.2118/198898-PA},
	author = {Jayasinghe, S. and Darmofal, D.L. and Dow, E. and Galbraith, M.C. and Allmaras, S.R.}
}
@conference {Frontin_2019_entropy_underresolved_DG,
	title = {Entropy behavior for underresolved discontinuous Galerkin discretization of the Navier-Stokes equations},
	booktitle = {AIAA conference paper},
	number = {2019{\textendash}1889},
	year = {2019},
	type = {AIAA Paper},
	doi = {10.2514/6.2019-1889},
	author = {Cory Frontin and David L. Darmofal and Steven R. Allmaras and Scott M. Murman}
}
@conference {Caplan_2019_Extension_of_local_cavity_operators_to_3dt_spacetime_mesh_adaptation,
	title = {{Extension of local cavity operators to 3d+t spacetime mesh adaptation}},
	booktitle = {AIAA conference paper},
	number = {2019-1992},
	year = {2019},
	doi = {10.2514/6.2019-1992},
	author = {Caplan, P.C. and Haimes, R. and Darmofal, D.L. and Galbraith, M.C.}
}
@mastersthesis {Caplan_2019_PhD,
	title = {Four-dimensional Anisotropic Mesh Adaptation for Spacetime Numerical Simulations},
	year = {2019},
	school = {Massachusetts Institute of Technology},
	type = {PhD},
	address = {Department of Aeronautics and Astronautics},
	author = {Caplan, P.C.}
}
@conference {Drela_2019_hybrid_shell_model,
	title = {Hybrid shell model for aeroelastic modeling},
	booktitle = {AIAA conference paper},
	number = {2019{\textendash}2227},
	year = {2019},
	type = {AIAA Paper},
	doi = {10.2514/6.2019-2227},
	author = {Mark Drela and Marshall Galbraith and Robert Haimes and Steven R. Allmaras and David L. Darmofal}
}
@mastersthesis {Carson_2019_PhD,
	title = {Provably Convergent Anisotropic Output-Based Adaptation for Continuous Finite Element Discretizations},
	year = {2019},
	school = {Massachusetts Institute of Technology},
	type = {PhD},
	address = {Department of Aeronautics and Astronautics},
	author = {H.A. Carson}
}
@conference {Drela_2019_screened_turning_vane,
	title = {Screened expanding turning vane concept},
	booktitle = {AIAA conference paper},
	number = {2019{\textendash}1613},
	year = {2019},
	type = {AIAA Paper},
	doi = {10.2514/6.2019-1613},
	author = {Mark Drela and Arthur C. Huang and David L. Darmofal}
}
@conference {Zhang_2019_IBL2_free_transition,
	title = {A strongly-coupled non-parametric integral boundary layer method for aerodynamic analysis with free transition},
	booktitle = {AIAA conference paper},
	number = {2019-1154},
	year = {2019},
	doi = {10.2514/6.2019-1154},
	author = {Zhang, Shun and Drela, Mark and Allmaras, Steven R. and Galbraith, Marshall C. and Darmofal, David L.}
}
@conference {Park_2019_Verification_of_Unstructured_Grid_Adaptation_Components,
	title = {Verification of unstructured grid adaptation components},
	booktitle = {AIAA conference paper},
	number = {2019{\textendash}1723},
	year = {2019},
	type = {AIAA Paper},
	doi = {10.2514/6.2019-1723},
	author = {Michael A. Park and Aravind Balan and W. Kyle Anderson and Marshall C. Galbraith and Philip Claude Caplan and Hugh A. Carson and Todd Michal and Joshua A. Krakos and Dmitry S. Kamenetskiy and Adrien Loseille and Fr{\'e}d{\'e}ric Alauzet and Lo{\"\i}c Frazza and Nicolas Barral}
}
@mastersthesis {Jayasinghe_2018_PhD,
	title = {An Adaptive Space-Time Discontinuous Galerkin Method for Reservoir Flows},
	year = {2018},
	month = {06/2018},
	school = {Massachusetts Institute of Technology},
	type = {PhD},
	address = {Department of Aeronautics and Astronautics},
	author = {Savithru Jayasinghe}
}
@article {Jayasinghe_2018_Adjoint_Analysis_BuckleyLeverett_TwoPhase,
	title = {Adjoint analysis of Buckley-Leverett and two-phase flow equations},
	journal = {Computational Geosciences},
	volume = {22},
	number = {2},
	year = {2018},
	month = {April},
	pages = {527{\textendash}542},
	author = {Jayasinghe, Savithru and Darmofal, David L. and Galbraith, Marshall C. and Burgess, Nicholas K. and Allmaras, Steven R.}
}
@mastersthesis {Couchman_2018_SM,
	title = {On the Convergence of Higher-Order Finite Element Methods to Weak Solutions},
	year = {2018},
	month = {02/2018},
	school = {Massachusetts Institute of Technology},
	type = {Masters},
	url = {http://hdl.handle.net/1721.1/115685},
	author = {Benjamin L. Couchman}
}
@mastersthesis {Frontin_2018_SM,
	title = {Entropy Behavior for Underresolved Discontinuous Galerkin Discretizations of the Navier-Stokes Equations},
	volume = {Masters},
	year = {2018},
	month = {06/2018},
	school = {Massachusetts Institute of Technology},
	type = {Masters},
	url = {http://hdl.handle.net/1721.1/119299},
	author = {Cory Frontin}
}
@mastersthesis {Zhang_2018_SM,
	title = {A Non-parametric Discontinuous Galerkin Formulation of the Integral Boundary Layer Equations with Strong Viscous-inviscid Coupling},
	year = {2018},
	month = {02/2018},
	school = {Massachusetts Institute of Technology},
	type = {Masters},
	url = {http://hdl.handle.net/1721.1/119272},
	author = {Shun Zhang}
}
@conference {Galbraith_2018_SANS_RANS_3D_Benchmark,
	title = {SANS RANS solutions for 3D benchmark configurations},
	booktitle = {AIAA conference paper},
	number = {2018{\textendash}1570},
	year = {2018},
	type = {AIAA Paper},
	doi = {10.2514/6.2018-1570},
	author = {Marshall C. Galbraith and Steven R. Allmaras and David L. Darmofal}
}
@article {Jayasinghe_2017_Spacetime_Adaptive_Method_Reservoir_Flows_Formulation,
	title = {A space-time adaptive method for reservoir flows: Formulation and one-dimensional application},
	journal = {Computational Geosciences},
	volume = {22},
	year = {2018},
	month = {02/2018},
	pages = {107-123},
	chapter = {107},
	abstract = {<p>This paper presents a space-time adaptive framework for solving porous media flow problems, with specific application to reservoir simulation. A fully unstructured mesh discretization of space and time is used instead of a conventional time-marching approach. A space-time discontinuous Galerkin finite element method is employed to achieve a high-order discretization on the anisotropic, unstructured meshes. Anisotropic mesh adaptation is performed to reduce the error of a specified output of interest, by using a posteriori error estimates from the dual-weighted residual method to drive a metric-based mesh optimization algorithm. The space-time adaptive method is tested on a one-dimensional two-phase flow problem, and is found to be more efficient in terms of computational cost (degrees-of-freedom and total runtime) required to achieve a specified output error level, when compared to a conventional first-order time-marching finite volume method and the space-time discontinuous Galerkin method on structured meshes.</p>
},
	issn = {1573-1499},
	doi = {10.1007/s10596-017-9673-9},
	url = {http://dx.doi.org/10.1007/s10596-017-9673-9},
	author = {Jayasinghe, Y S and Darmofal, D L and Burgess, N K and Galbraith, M C and Allmaras, S R}
}
@conference {Huang_2019_Wellposed_NS_BCs,
	title = {Well-posed subsonic inflow/outflow boundary conditions for the Navier-Stokes equations},
	booktitle = {AIAA conference paper},
	number = {2018{\textendash}0361},
	year = {2018},
	type = {AIAA Paper},
	doi = {10.2514/6.2018-0361},
	author = {Arthur C. Huang and Steven R. Allmaras and Marshall C. Galbraith and David L. Darmofal}
}
@article {Ojeda_2017_AdaptiveCutCellConjugateHT,
	title = {An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of conjugate heat transfer problems},
	journal = {International Journal for Numerical Methods in Engineering},
	volume = {110},
	number = {4},
	year = {2017},
	pages = {350{\textendash}378},
	abstract = {In this paper, we present a solution framework for high-order discretizations of conjugate heat transfer problems on non-body-conforming meshes. The framework consists of and leverages recent developments in discontinuous Galerkin discretization, simplex cut-cell techniques, and anisotropic output-based adaptation. With the cut-cell technique, the mesh generation process is completely decoupled from the interface definitions. In addition, the adaptive scheme combined with the discontinuous Galerkin discretization automatically adjusts the mesh in each sub-domain and achieves high-order accuracy in outputs of interest. We demonstrate the solution framework through several multi-domained conjugate heat transfer problems consisting of laminar and turbulent flows, curved geometry, and highly coupled heat transfer regions. The combination of these attributes yield nonintuitive coupled interactions between fluid and solid domains, which can be difficult to capture with user-generated meshes. Copyright {\textcopyright} 2016 John Wiley \& Sons, Ltd.},
	keywords = {adaptation, conjugate heat transfer, cut cells, high-order},
	issn = {1097-0207},
	doi = {10.1002/nme.5362},
	url = {http://dx.doi.org/10.1002/nme.5362},
	author = {Ojeda, S M and Sun, H and Allmaras, S R and Darmofal, D L}
}
@article {Carson_2017_ErrorEstimation,
	title = {Analysis of output-based error estimation for finite element methods},
	journal = {Applied Numerical Mathematics},
	volume = {118},
	year = {2017},
	pages = {182 - 202},
	abstract = {Abstract In this paper, we develop a priori estimates for the convergence of outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Output error estimates for order p finite element solutions are constructed using the Dual-Weighted Residual (DWR) method with a higher-order p ' \&gt; p dual solution. Specifically, we analyze these \{DWR\} estimates for Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized \{DG\} (HDG) methods applied to the Poisson problem. For all discretizations, as h {\textrightarrow} 0 , we prove that the output and output error estimate converge at order 2p and 2 p ' (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2 p + d and p + p ' + d . For DG, the results use a new post processing for the error associated with the lifting operator. For HDG, these rates improve an additional order when the stabilization is based upon an O ( 1 ) length scale.},
	keywords = {Hybridizable Discontinuous Galerkin},
	issn = {0168-9274},
	doi = {http://dx.doi.org/10.1016/j.apnum.2017.03.004},
	url = {http://www.sciencedirect.com/science/article/pii/S0168927417300648},
	author = {Carson, H A and Darmofal, D L and Galbraith, M C and Allmaras, S R}
}
@article {Caplan_2017_Anisotropic_geometryconforming_dsimplicial_meshing_via_isometric_embeddings,
	title = {Anisotropic Geometry-Conforming d-simplicial Meshing via Isometric Embeddings},
	journal = {Procedia Engineering},
	volume = {203},
	year = {2017},
	note = {26th International Meshing Roundtable},
	pages = {141-153},
	publisher = {Springer Berlin Heidelberg},
	author = {Caplan, P.C. and Haimes, R. and Darmofal, D.L. and Galbraith, M.C.}
}
@conference {Couchman_2017_FEMweakconvergence,
	title = {On the convergence of higher-order finite element methods to weak solutions},
	booktitle = {AIAA conference paper},
	number = {2017-4274},
	year = {2017},
	keywords = {finite element methods},
	doi = {10.2514/6.2017-4274},
	author = {Couchman, B L and Darmofal, D L and Allmaras, S R and Galbraith, M C}
}
@conference {Zhang_2017_IBL_DG,
	title = {A non-parametric discontinuous Galerkin formulation of the integral boundary layer equations with strong viscous/inviscid coupling},
	booktitle = {AIAA conference paper},
	number = {2017-4278},
	year = {2017},
	keywords = {finite element methods, integral boundary layer methods},
	doi = {10.2514/6.2017-4278},
	author = {Zhang, S and Galbraith, M C and Allmaras, S R and Drela, M and Darmofal, D L}
}
@article {Hu_2016_turbmodelcases_AIAAJ,
	title = {Application of Higher-order Adaptive Method to Reynolds-Averaged Navier{\textendash}Stokes Test Cases},
	journal = {AIAA Journal},
	volume = {54},
	number = {9},
	year = {2016},
	doi = {10.2514/1.J054558},
	author = {Hu, Y and Wagner, C F and Allmaras, S R and Galbraith, M C and Darmofal, D L}
}
@mastersthesis {Hu_2016_SM,
	title = {Investigation of a Space-Time Adaptive Method for Bluff Body Flows},
	year = {2016},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/107018},
	author = {Hu, Y}
}
@mastersthesis {Carson_2016_SM,
	title = {A Priori Analysis of Global and Local Output Error Estimates for CG, DG and HDG Finite Element Discretizations},
	year = {2016},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/105608},
	author = {Carson, H A}
}
@mastersthesis {Wagner_2015_SM,
	title = {Improving Shock-capturing Robustness for Higher-order Finite Element Solvers},
	year = {2015},
	month = {September},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/101498},
	author = {Wagner, C F}
}
@conference {Darmofal_2015_Aerodynamics_MOOC,
	title = {A massive open online course in aerodynamics},
	booktitle = {AIAA conference paper},
	number = {2015-1514},
	year = {2015},
	month = {jan},
	keywords = {education},
	author = {Darmofal, D L}
}
@mastersthesis {Jayasinghe_2015_SM,
	title = {A Space-time Adaptive Method for Flows in Oil Reservoirs},
	year = {2015},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/101495},
	author = {Jayasinghe, Y S}
}
@conference {Galbraith_2015_Verification_CFD_Development,
	title = {A verification driver process for rapid development of CFD software},
	booktitle = {AIAA conference paper},
	number = {2015-0818},
	year = {2015},
	doi = {10.2514/6.2015-0818},
	author = {Galbraith, M C, and Allmaras, S R, and Darmofal, D L}
}
@mastersthesis {Caplan_2014_SM,
	title = {An Adaptive Framework for High-Order, Mixed-Element Numerical Simulations},
	year = {2014},
	month = {June},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/90654},
	author = {Caplan, P C D}
}
@article {Sun_2014_HODG_Interface,
	title = {An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems},
	journal = {Journal of Computational Physics},
	volume = {278},
	year = {2014},
	pages = {445 - 468},
	abstract = {In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.},
	keywords = {adaptation},
	issn = {0021-9991},
	doi = {10.1016/j.jcp.2014.08.035},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999114006032},
	author = {Sun, H and Darmofal, D L}
}
@booklet {Vision_2030_Final_Report_CRDL,
	title = {CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences},
	journal = {NASA Technical Report},
	number = {NASA/CR-2014-218178},
	year = {2014},
	author = {Slotnick, J P and Khodadoust, A and Alonso, J J and Darmofal, D L and Gropp, W D and Lurie, E A and Mavriplis, D J}
}
@mastersthesis {Ojeda_2014_SM,
	title = {A Cut-Cell Method for Adaptive High-Order Discretizations of Conjugate Heat Transfer Problems},
	year = {2014},
	month = {June},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/90783},
	author = {Ojeda, S M}
}
@article {Slotnick_2014_EnivornmentCFD,
	title = {Enabling the environmentally clean air transportation of the future: a vision of computational fluid dynamics in 2030},
	journal = {Philosophical transactions. Series A, Mathematical, physical, and engineering sciences},
	volume = {372},
	number = {2022},
	year = {2014},
	month = {08},
	pages = {20130317},
	abstract = {As global air travel expands rapidly to meet demand generated by economic growth, it is essential to continue to improve the efficiency of air transportation to reduce its carbon emissions and address concerns about climate change. Future transports must be {\textquoteleft}cleaner{\textquoteright}and designed to include technologies that will continue to lower engine emissions and reduce community noise. The use of computational fluid dynamics (CFD) will be critical to enable the design of these new concepts. In general, the ability to simulate aerodynamic and reactive flows using CFD has progressed rapidly during the past several decades and has fundamentally changed the aerospace design process. Advanced simulation capabilities not only enable reductions in ground-based and flight-testing requirements, but also provide added physical insight, and enable superior designs at reduced cost and risk. In spite of considerable success, reliable use of CFD has remained confined to a small region of the operating envelope due, in part, to the inability of current methods to reliably predict turbulent, separated flows. Fortunately, the advent of much more powerful computing platforms provides an opportunity to overcome a number of these challenges. This paper summarizes the findings and recommendations from a recent NASA-funded study that provides a vision for CFD in the year 2030, including an assessment of critical technology gaps and needed development, and identifies the key CFD technology advancements that will enable the design and development of much cleaner aircraft in the future.},
	isbn = {1364-503X; 1471-2962},
	doi = {10.1098/rsta.2013.0317},
	url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4095895/},
	author = {Slotnick, J P and Khodadoust, A and Alonso, J J and Darmofal, D L and Gropp, W D and Lurie, E A and Mavriplis, D J and Venkatakrishnan, V}
}
@mastersthesis {Kudo_2014_SM,
	title = {Robust Adaptive High-Order {RANS} Methods},
	year = {2014},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {CDO},
	url = {http://hdl.handle.net/1721.1/95563},
	author = {Kudo, J}
}
@conference {Darmofal_2013_PXOverview,
	title = {An adaptive, higher-order discontinuous Galerkin finite element method for aerodynamics},
	booktitle = {AIAA conference paper},
	number = {2013-2871},
	year = {2013},
	author = {Darmofal, D L and Allmaras, S R and Yano, M and Kudo, J}
}
@conference {Sun_2013_Interface,
	title = {An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of multi-material and multi-physics problems},
	booktitle = {AIAA conference paper},
	number = {2013{\textendash}2443},
	year = {2013},
	author = {Sun, H and Darmofal, D L}
}
@conference {Krakos_2013_Anisotropic_Output-Based_Mesh_Optimization_Unsteady,
	title = {Anisotropic output-based mesh optimization for unsteady flows},
	booktitle = {AIAA conference paper},
	number = {2013-3083},
	year = {2013},
	author = {Krakos, J A and Darmofal, D L}
}
@mastersthesis {Sun_2013_PhD,
	title = {A Robust Simplex Cut-Cell Method for Adaptive High-Order Finite Element Discretizations of Aerodynamics and Multi-Physics Problems},
	year = {2013},
	month = {August},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/85764},
	author = {Sun, H}
}
@conference {Sun_2013_Robust3DCutCells,
	title = {A robust simplex cut-cell method for high-order discontinuous Galerkin discretizations of three-dimensional aerodynamic problems},
	booktitle = {AIAA conference paper},
	number = {2013{\textendash}3082},
	year = {2013},
	month = {June},
	author = {Sun, H and Darmofal, D L and Haimes, R}
}
@article {Sun_TriangleShapeImpact_JCP_2012,
	title = {On the impact of triangle shapes for boundary layer problems using high-order finite element discretization},
	journal = {Journal of Computational Physics},
	volume = {231},
	number = {2},
	year = {2012},
	pages = {541{\textendash}557},
	doi = {10.1016/j.jcp.2011.09.018},
	author = {Sun, H and Darmofal, D L and Haimes, R}
}
@mastersthesis {Yano_2012_PhD,
	title = {An Optimization Framework for Adaptive Higher-Order Discretizations of Partial Differential Equations on Anisotropic Simplex Meshes},
	year = {2012},
	month = {06/2012},
	school = {Massachusetts Institute of Technology},
	type = {PhD},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/96928},
	author = {Yano, M}
}
@conference {Yano_2012_Mesh_Optimization_Aerodynamics,
	title = {An optimization framework for anisotropic simplex mesh adaptation: {A}pplication to aerodynamic flows},
	booktitle = {AIAA conference paper},
	number = {2012{\textendash}0079},
	year = {2012},
	month = {jan},
	author = {Yano, M and Darmofal, D L}
}
@article {Yano_2012_Mesh_Optimization,
	title = {An optimization-based framework for anisotropic simplex mesh adaptation},
	journal = {Journal of Computational Physics},
	volume = {231},
	number = {22},
	year = {2012},
	pages = {7626{\textendash}7649},
	doi = {10.1016/j.jcp.2012.06.040},
	author = {Yano, M and Darmofal, D L}
}
@article {Krakos_2012_Sensitivity_analysis_LCO,
	title = {Sensitivity analysis of limit cycle oscillations},
	journal = {Journal of Computational Physics},
	volume = {231},
	number = {8},
	year = {2012},
	pages = {3228 - 3245},
	abstract = {Many unsteady problems equilibrate to periodic behavior. For these problems the sensitivity of periodic outputs to system parameters are often desired, and must be estimated from a finite time span or frequency domain calculation. Sensitivities computed in the time domain over a finite time span can take excessive time to converge, or fail altogether to converge to the periodic value. Additionally, finite span outputs can exhibit local extrema in parameter space which the periodic outputs they approximate do not, hindering their use in optimization. We derive a theoretical basis for this error and demonstrate it using two examples, a van der Pol oscillator and vortex shedding from a low Reynolds number airfoil. We show that output windowing enables the accurate computation of periodic output sensitivities and may allow for decreased simulation time to compute both time-averaged outputs and sensitivities. We classify two distinct window types: long-time, over a large, not necessarily integer number of periods; and short-time, over a small, integer number of periods. Finally, from these two classes we investigate several examples of window shape and demonstrate their convergence with window size and error in the period approximation, respectively.},
	keywords = {Limit cycles, Periodic, Sensitivity analysis, Unsteady},
	issn = {0021-9991},
	doi = {10.1016/j.jcp.2012.01.001},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999112000071},
	author = {Krakos, J A and Wang, Q and Hall, S R and Darmofal, D L}
}
@article {Diosady_2012_Unified_BDDC_DG,
	title = {A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {50},
	number = {3},
	year = {2012},
	pages = {1695-1712},
	doi = {10.1137/100812434},
	author = {Diosady, L T and Darmofal, D L}
}
@mastersthesis {Krakos_2012_PhD,
	title = {Unsteady Adjoint Analysis for Output Sensitivity and Mesh Adaptation},
	year = {2012},
	month = {September},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/77133},
	author = {Krakos, J A}
}
@mastersthesis {Modisette_2011_PhD,
	title = {An Automated Reliable Method for Two-Dimensional Reynolds-averaged Navier-Stokes Simulations},
	year = {2011},
	month = {September},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/68406},
	author = {Modisette, J M}
}
@mastersthesis {Diosady_2011_Phd,
	title = {Domain Decomposition Preconditioners for Higher-Order Discontinuous Galerkin Discretizations},
	year = {2011},
	month = {September},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	url = {http://hdl.handle.net/1721.1/71454},
	author = {Diosady, L T}
}
@booklet {Yano_2011_DWR_pDependent,
	title = {On dual-weighted residual error estimates for p-dependent discretizations},
	journal = {ACDL Report},
	number = {TR-11-1},
	year = {2011},
	publisher = {Massachusetts Institute of Technology},
	author = {Yano, M and Darmofal, D L}
}
@conference {Yano_2011_Mesh_Adaptation_Higher_Order_Discretization,
	title = {The importance of mesh adaptation for higher-order discretizations of aerodynamic flows},
	booktitle = {AIAA conference paper},
	number = {2011{\textendash}3852},
	year = {2011},
	month = {jun},
	author = {Yano, M and Modisette, J M and Darmofal, D L}
}
@inbook {Diosady_2011_Massively_Parallel_Solution_for_Higher-Order_FEM_CFD,
	title = {Massively parallel solution techniques for higher-order finite-element discretizations in CFD},
	booktitle = {Adaptive High-Order Methods in Computational Fluid Dynamics},
	year = {2011},
	pages = {33{\textendash}65},
	publisher = {World Scientific},
	organization = {World Scientific},
	author = {Diosady, L T and Darmofal, D L},
	editor = {Wang, Z J}
}
@mastersthesis {Liu_2011_Masters_Thesis,
	title = {Optimization and validation of discontinuous {G}alerkin code for the {3D} {Navier-Stokes} equations},
	year = {2011},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/62879},
	author = {Liu, E H}
}
@article {Fidkowski_2011_Output_Error_Estimate_CFD_Review,
	title = {Review of output-based error estimation and mesh adaptation in computational fluid dynamics},
	journal = {AIAA Journal},
	volume = {49},
	number = {4},
	year = {2011},
	pages = {673{\textendash}694},
	doi = {10.2514/1.J050073},
	author = {Fidkowski, K J and Darmofal, D L}
}
@article {Yano_2010_BDDC_for_High-Order_GLS,
	title = {BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	volume = {199},
	number = {45},
	year = {2010},
	pages = {2958{\textendash}2969},
	doi = {10.1016/j.cma.2010.06.006},
	author = {Yano, M and Darmofal, D L}
}
@article {Krakos_2010_Effect_of_Small-Scale_Output_Unsteadiness_on_Adjoint-Based_Sensitivity,
	title = {Effect of small-scale output unsteadiness on adjoint-based sensitivity},
	journal = {AIAA Journal},
	volume = {48},
	number = {11},
	year = {2010},
	pages = {2611{\textendash}2623},
	doi = {10.2514/1.J050412},
	author = {Krakos, J A and Darmofal, D L}
}
@article {Barter_2010_Shock_Capturing_PDE_Based_Artificial_Viscosity_for_DGFEM,
	title = {Shock capturing with PDE-based artificial viscosity for DGFEM: Part I, Formulation},
	journal = {Journal of Computational Physics},
	volume = {229},
	number = {5},
	year = {2010},
	pages = {1810{\textendash}1827},
	doi = {10.1016/j.jcp.2009.11.010},
	author = {Barter, G E and Darmofal, D L}
}
@conference {Modisette_2008_Toward_Robust_CutCell_Method_Viscous_Flows,
	title = {Toward a robust, higher-order cut-cell method for viscous flows},
	booktitle = {AIAA conference paper},
	number = {2010-721},
	year = {2010},
	author = {Modisette, J M and Darmofal, D L}
}
@article {Park_2010_Validation_Sonic_Boom_Prediction,
	title = {Validation of an output-adaptive, tetrahedral cut-cell method for sonic boom prediction},
	journal = {AIAA Journal},
	volume = {48},
	number = {9},
	year = {2010},
	pages = {1928{\textendash}1945},
	doi = {10.2514/1.J050111},
	author = {Park, M A and Darmofal, D L}
}
@article {Oliver_2009_Analysis_Dual_Consistency_DG_Source_Terms,
	title = {Analysis of dual consistency for discontinuous Galerkin discretizations of source terms},
	journal = {SIAM Journal of Numerical Analysis},
	volume = {47},
	number = {5},
	year = {2009},
	pages = {3507{\textendash}3525},
	doi = {10.1137/080721467},
	author = {Oliver, T A and Darmofal, D L}
}
@mastersthesis {Sun_2009_Adaptation,
	title = {Impact of Triangle Shapes Using High-order Discretizations and Direct Mesh Adaptation for Output Error},
	year = {2009},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Computation for Design and Optimization Program},
	url = {http://hdl.handle.net/1721.1/54215},
	author = {Sun, H}
}
@conference {Oliver_2009_Impact_Turbulence_Model_Irregularity_High_Order_Discretizations,
	title = {Impact of turbulence model irregularity on high-order discretizations},
	booktitle = {AIAA conference paper},
	number = {2009-953},
	year = {2009},
	author = {Oliver, T A and Darmofal, D L}
}
@mastersthesis {Yano_2009_SM,
	title = {Massively Parallel Solver for the High-Order Galerkin Least-Squares Method},
	year = {2009},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {CDO},
	url = {http://hdl.handle.net/1721.1/57610},
	author = {Yano, M}
}
@article {Diosady_2009_Preconditioning_Methods_for_DG_NS,
	title = {Preconditioning methods for discontinuous {Galerkin} solutions of the {Navier-Stokes} equations},
	journal = {Journal of Computational Physics},
	volume = {228},
	year = {2009},
	pages = {3917{\textendash}3935},
	doi = {10.1016/j.jcp.2009.02.035},
	author = {Diosady, L T and Darmofal, D L}
}
@mastersthesis {Park_2008_Anisotropic_Output-Based_Adaptation_with_Tet_Cut_Cells_for_Compressible_Flows,
	title = {Anisotropic Output-Based Adaptation with Tetrahedral Cut Cells for Compressible Flows},
	year = {2008},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/46363},
	author = {Park, M A}
}
@mastersthesis {Duffner_2008_SM,
	title = {The Effects of Manufacturing Variability on Turbine Vane Performance},
	year = {2008},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/57599},
	author = {Duffner, J D}
}
@mastersthesis {Oliver_2008_A_Higher-Order_Adaptive_DGFEM_for_RANS,
	title = {A Higher-Order, Adaptive, Discontinuous {Galerkin} Finite Element Method for the {Reynolds-averaged Navier-Stokes} Equations},
	year = {2008},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/46818},
	author = {Oliver, T A}
}
@conference {Modisette_2008_Output_Based_Adaptive_Rotor_Hover,
	title = {An output-based adaptive and higher-order method for a rotor in hover},
	booktitle = {AIAA conference paper},
	number = {2008-7343},
	year = {2008},
	author = {Modisette, J M and Darmofal, D L}
}
@mastersthesis {Modisette_2008_Adaptive_High-Order_Rotor_Hover_Masters,
	title = {An Output-based Adaptive and Higher-Order Method for a Rotor in Hover},
	year = {2008},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/43078},
	author = {Modisette, J M}
}
@conference {Park_2008_Parallel_Anisotropic_Tet_Adaptation,
	title = {Parallel anisotropic tetrahedral adaptation},
	booktitle = {AIAA conference paper},
	number = {2008-917},
	year = {2008},
	author = {Park, M A and Darmofal, D L}
}
@mastersthesis {Barter_2008_Shock_Capturing_with_PDE-Based_Artificial_Viscosity,
	title = {Shock Capturing with {PDE}-Based Artificial Viscosity for an Adaptive, Higher-Order, Discontinuous {Galerkin} Finite Element Method},
	year = {2008},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/44931},
	author = {Barter, G E}
}
@conference {Fidkowski_2007_Adaptive_Simplex_Cut-Cell_Method_for_DG,
	title = {An adaptive simplex cut-cell method for discontinuous {Galerkin} discretizations of the {Navier-Stokes} equations},
	booktitle = {AIAA conference paper},
	number = {2007-3941},
	year = {2007},
	author = {Fidkowski, K J and Darmofal, D L}
}
@conference {Diosady_2007_Discontinuous_Galerkin_Linear_Multigrid_Preconditioning,
	title = {Discontinuous {Galerkin} solutions of the {Navier-Stokes} equations using linear multigrid preconditioning},
	booktitle = {AIAA conference paper},
	number = {2007-3942},
	year = {2007},
	author = {Diosady, L T and Darmofal, D L}
}
@mastersthesis {Diosady_2007_SM,
	title = {A Linear Multigrid Preconditioner for the Solution of the {Navier-Stokes} Equations Using a Discontinuous Galerkin Discretization},
	year = {2007},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {CDO},
	url = {http://hdl.handle.net/1721.1/39326},
	author = {Diosady, L T}
}
@conference {Mavriplis_2007_Petaflop_Opportunities_for_NASA,
	title = {Petaflops opportunities for the {NASA} fundamental aeronautics program},
	booktitle = {AIAA conference paper},
	number = {2007-4084},
	year = {2007},
	author = {Mavriplis, D J and Darmofal, D L and Keyes, D E and Turner, M G}
}
@mastersthesis {Fidkowski_2007_Simplex_CutCell_Adaptive_Method_for_DG,
	title = {A Simplex Cut-Cell Adaptive Method for High-Order Discretizations of the Compressible {Navier-Stokes} Equations},
	year = {2007},
	month = {jun},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/39701},
	author = {Fidkowski, K J}
}
@article {Fidkowski_2007_Triangular_Cut_Cell_Method_for_DG,
	title = {A triangular cut-cell adaptive method for higher-order discretizations of the compressible {N}avier-{S}tokes equations},
	journal = {Journal of Computational Physics},
	volume = {225},
	year = {2007},
	pages = {1653{\textendash}1672},
	doi = {10.1016/j.jcp.2007.02.007},
	author = {Fidkowski, K J and Darmofal, D L}
}
@conference {Oliver_2007_Unsteady_Adaptation_Algorithm_for_DG_RANS,
	title = {An unsteady adaptation algorithm for discontinuous {Galerkin} discretizations of the {RANS} equations},
	booktitle = {AIAA conference paper},
	number = {2007-3940},
	year = {2007},
	author = {Oliver, T A and Darmofal, D L}
}
@mastersthesis {Quattrochi_Hypersonic_heat_transfer_and_anisotropic_visualization_DG,
	title = {Hypersonic Heat Transfer and Anisotropic Visualization with a Higher-order Discontinuous {G}alerkin Finite Element Method},
	year = {2006},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/35567},
	author = {Quattrochi, D J}
}
@mastersthesis {Moeckel_2006_SM,
	title = {Probabilistic Turbine Blade Thermal Analysis of Manufacturing Variability and Toleranced Designs},
	year = {2006},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/35570},
	author = {Moeckel, C W}
}
@booklet {Darmofal_2005_ChangingPedagogyStudents,
	title = {Changing pedagogy: What students say},
	journal = {M.I.T. Aero/Astro Annual},
	year = {2005},
	keywords = {education},
	author = {Darmofal, D L}
}
@inbook {Darmofal_2006_EducatingFuture,
	title = {Educating the future: the impact of pedagogical reform in aerodynamics},
	booktitle = {Frontiers of Computational Fluid Dynamics 2006},
	year = {2005},
	publisher = {World Scientific Publishing Co.},
	organization = {World Scientific Publishing Co.},
	keywords = {education},
	author = {Darmofal, D L},
	editor = {Caughey, D A and Hafez, M}
}
@article {Sidwell_2005_ImpactBladetoBladeVariabilityCooling,
	title = {The impact of blade-to-blade flow variability on turbine blade cooling performance},
	journal = {Journal of Turbomachinery},
	volume = {127},
	number = {4},
	year = {2005},
	pages = {763{\textendash}770},
	abstract = {The focus of this paper is the impact of manufacturing variability on turbine blade cooling flow and, subsequently, its impact on oxidation life. A simplified flow network model of the cooling air supply system and a row of blades is proposed. Using this simplified model, the controlling parameters which affect the distribution of cooling flow in a blade row are identified. Small changes in the blade flow tolerances (prior to assembly of the blades into a row) are shown to have a significant impact on the minimum flow observed in a row of blades resulting in substantial increases in the life of a blade row. A selective assembly method is described in which blades are classified into a low-flow and a high-flow group based on passage flow capability (effective areas) in life-limiting regions and assembled into rows from within the groups. Since assembling rows from only high-flow blades is equivalent to raising the low-flow tolerance limit, high-flow blade rows will have the same improvements in minimum flow and life that would result from more stringent tolerances. Furthermore, low-flow blade rows are shown to have minimum blade flows which are the same or somewhat better than a low-flow blade that is isolated in a row of otherwise higher-flowing blades. As a result, low-flow blade rows are shown to have lives that are no worse than random assembly from the full population. Using a higher fidelity model for the auxiliary air system of an existing jet engine, the impact of selective assembly on minimum blade flow and life of a row is estimated and shown to be in qualitative and quantitative agreement with the simplified model analysis.},
	isbn = {0889-504X},
	doi = {10.1115/1.2019247},
	author = {Sidwell, V and Darmofal, D L}
}
@article {Fidkowski_2005_pMultigrid_Higher-Order_DG_Navier-Stokes,
	title = {p-{Multigrid} solution of high-order discontiunous {Galerkin} discretizations of the compressible {Navier-Stokes} equations},
	journal = {Journal of Computational Physics},
	volume = {207},
	number = {1},
	year = {2005},
	pages = {92{\textendash}113},
	doi = {10.1016/j.jcp.2005.01.005},
	author = {Fidkowski, K J and Oliver, T A and Lu, J and Darmofal, D L}
}
@mastersthesis {Lu_2005_An_a_Posteriori_Error_Control_Framework_Using_DG,
	title = {An a Posteriori Error Control Framework for Adaptive Precision Optimization Using Discontinuous Galerkin Finite Element Method},
	year = {2005},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	url = {http://hdl.handle.net/1721.1/34134},
	author = {Lu, J}
}
@mastersthesis {Lamb_2005_SM,
	title = {Probabilistic Performance-Based Geometric Tolerancing of Compressor Blades},
	year = {2005},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/32459},
	author = {Lamb, C M}
}
@conference {Darmofal_2005_nextgenCFD,
	title = {Towards the next-generation in CFD},
	booktitle = {AIAA conference paper},
	number = {2005-0087},
	year = {2005},
	author = {Darmofal, D L and Haimes, R}
}
@conference {Lu_2004_Adaptive_Precision,
	title = {Adaptive precision methodology for flow optimization via output error control},
	booktitle = {AIAA conference paper},
	number = {2004-1096},
	year = {2004},
	author = {Lu, J and Darmofal, D L}
}
@article {Okusanya_2004_Algebraic_Multigrid_for_Stabilized_FEM,
	title = {Algebraic multigrid for stabilized finite element discretizations of the Navier{\textendash}Stokes equations},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	volume = {193},
	number = {33},
	year = {2004},
	pages = {3667{\textendash}3686},
	doi = {10.1016/j.cma.2004.01.025},
	author = {Okusanya, T and Darmofal, D L and Peraire, J}
}
@conference {Fidkowski_2004_Development_of_a_higher-order_solver,
	title = {Development of a higher-order solver for aerodynamic applications},
	booktitle = {AIAA conference paper},
	number = {2004-0436},
	year = {2004},
	author = {Fidkowski, K J and Darmofal, D L}
}
@article {Lu_2004_HighDIntegration_GaussianWeight,
	title = {Higher-dimensional integration with Gaussian weight for applications in probabilistic design},
	journal = {SIAM Journal on Scientific Computing},
	volume = {26},
	number = {2},
	year = {2004},
	pages = {613-624},
	doi = {10.1137/S1064827503426863},
	author = {Lu, J and Darmofal, D L}
}
@mastersthesis {Fidkowski_2004_High-Order_DG_Multigrid_Solver,
	title = {A High-Order Discontinuous {Galerkin} Multigrid Solver for Aerodynamic Applications},
	year = {2004},
	month = {jun},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/16657},
	author = {Fidkowski, K J}
}
@mastersthesis {Collin_2004_SM,
	title = {Impact of Aerothermal Modeling on the Estimation of Turbine Blade Life},
	year = {2004},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/30301},
	author = {Collin, J E}
}
@mastersthesis {Sidwell_2004_Phd,
	title = {On the Impact of Variability and Assembly on Turbine Blade Cooling Flow and Oxidation Life},
	year = {2004},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/17814},
	author = {Sidwell, V}
}
@article {Nielsen_2004_An_Implicit_Exact_Dual_Adjoint_Solution_Method,
	title = {An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids},
	journal = {Computers and Fluids},
	volume = {33},
	year = {2004},
	pages = {1131{\textendash}1155},
	doi = {10.1016/j.compfluid.2003.09.005},
	author = {Nielsen, E J and Lu, J and Park, M A and Darmofal, D L}
}
@mastersthesis {Oliver_2004_Multigrid_Solution_for_High-Order_DG,
	title = {Multigrid Solution for High-order Discontinuous {Galerkin} Discretizations of the Compressible {Navier-Stokes} Equations},
	year = {2004},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/28886},
	author = {Oliver, T A}
}
@mastersthesis {Kountras_2004_SM,
	title = {Probabilistic Analysis of Turbine Blade Durability},
	year = {2004},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/28893},
	author = {Kountras, A}
}
@article {Venditti_2003_Anisotropic_Grid_Adaptation,
	title = {Anisotropic grid adaptation for functional outputs: Application to two-dimensional viscous flows},
	journal = {Journal of Computational Physics},
	volume = {187},
	number = {1},
	year = {2003},
	pages = {22{\textendash}46},
	doi = {10.1016/S0021-9991(03)00074-3},
	author = {Venditti, D A and Darmofal, D L}
}
@article {Garzon_2003_ImpactGeometricVariabilityCompressor,
	title = {Impact of geometric variability on axial compressor performance},
	journal = {Journal of Turbomachinery},
	volume = {125},
	number = {4},
	year = {2003},
	pages = {692{\textendash}703},
	abstract = {A probabilistic methodology to quantify the impact of geometric variability on compressor aerodynamic performance is presented. High-fidelity probabilistic models of geometric variability are derived using a principal-component analysis of blade surface measurements. This probabilistic blade geometry model is then combined with a compressible, viscous blade-passage analysis to estimate the impact on the passage loss and turning using a Monte Carlo simulation. Finally, a mean-line multistage compressor model, with probabilistic loss and turning models from the blade-passage analysis, is developed to quantify the impact of the blade variability on overall compressor efficiency and pressure ratio. The methodology is applied to a flank-milled integrally bladed rotor. Results demonstrate that overall compressor efficiency can be reduced by approximately 1{\%} due to blade-passage effects arising from representative manufacturing variability.},
	isbn = {0889-504X},
	doi = {10.1115/1.1622715},
	author = {Garzon, V E and Darmofal, D L}
}
@mastersthesis {Garzon_2003_Phd,
	title = {Probabilistic Aerothermal Design of Compressor Airfoils},
	year = {2003},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/16995},
	author = {Garzon, V E}
}
@article {Lu_2003_SuperconvergentQMR,
	title = {A Quasi-Minimal Residual Method for Simultaneous Primal-Dual Solutions and Superconvergent Functional Estimates},
	journal = {SIAM Journal on Scientific Computing},
	volume = {24},
	number = {5},
	year = {2003},
	pages = {1693-1709},
	doi = {10.1137/S1064827501390625},
	author = {Lu, J and Darmofal, D L}
}
@mastersthesis {Lavainne_2003_SM,
	title = {Sensitivity of a Compressor Repeating-stage to Geometry Variation},
	year = {2003},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/82797},
	author = {Lavainne, J}
}
@mastersthesis {Okusanya_2002_Phd,
	title = {Algebraic Multigrid for Stabilized Finite Element Discretizations of the Navier-Stokes Equations},
	year = {2002},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/8098},
	author = {Okusanya, T}
}
@booklet {Darmofal_2002_EnhancingConceptualUnderstanding,
	title = {Enhancing conceptual understanding},
	journal = {M.I.T. Faculty Newsletter},
	volume = {XV},
	number = {2},
	year = {2002},
	keywords = {education},
	author = {Darmofal, D L}
}
@article {Venditti_2002_Grid_Adaptation_for_Functional_Outputs_Isotropic,
	title = {Grid adaptation for functional outputs: Application to two-dimensional inviscid flows},
	journal = {Journal of Computational Physics},
	volume = {176},
	number = {1},
	year = {2002},
	pages = {40{\textendash}69},
	doi = {10.1006/jcph.2001.6967},
	author = {Venditti, D A and Darmofal, D L}
}
@mastersthesis {Venditti_2002_Grid_Adaptation_for_Functional_Outputs,
	title = {Grid Adaptation for Functional Outputs of Compressible Flow Simulations},
	year = {2002},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	url = {http://hdl.handle.net/1721.1/29246},
	author = {Venditti, D A}
}
@mastersthesis {Powell_2002_SM,
	title = {Impact of Aerothermal Performance Variability on Jet Engine Cost},
	year = {2002},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/82257},
	author = {Powell, R F}
}
@mastersthesis {Lu_2002_SM,
	title = {Krylov Subspace Methods for Simultaneous Primal-dual Solutions and Superconvergent Functional Estimates},
	year = {2002},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/82253},
	author = {Lu, J}
}
@mastersthesis {Bradshaw_2002_SM,
	title = {Physics-based, Reduced-order Combustor Flow Modeling},
	year = {2002},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	address = {Department of Aeronautics and Astronautics},
	url = {http://hdl.handle.net/1721.1/82215},
	author = {Bradshaw, S D}
}
@conference {Darmofal_2002_ConceptMaps,
	title = {Using concept maps and concept questions to enhance conceptual understanding},
	booktitle = {Proceedings of the 2002 American Society for Engineering Education Annual Conference \& Exposition},
	year = {2002},
	keywords = {education},
	author = {Darmofal, D L and Soderholm, D H and Brodeur, D R}
}
@conference {Darmofal_2001_ReengineeringAerodynamicEducation,
	title = {Re-engineering aerodynamics education},
	booktitle = {AIAA conference paper},
	number = {2001-0870},
	year = {2001},
	keywords = {education},
	author = {Darmofal, D L and Murman, E M and Love, M}
}
@article {Wong_2001_LowMachSUPG,
	title = {The solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	volume = {190},
	number = {43},
	year = {2001},
	pages = {5719 - 5737},
	abstract = {We present a streamline-upwind/Petrov{\textendash}Galerkin (SUPG) algorithm for the solution of the compressible Euler equations at low Mach numbers. The Euler equations are written in terms of entropy variables which result in Jacobian matrices which are symmetric. We note that, in the low Mach number limit, the SUPG method with the standard choices for the stabilization matrix fail to provide adequate stabilization. This results in a degradation of the solution accuracy. We propose a stabilization matrix which incorporates dimensional-scaling arguments and which exhibits the appropriate behavior for low Mach numbers. To guide in the derivation of the new stabilization matrix, the non-dimensionalized equations are transformed to a new set of variables that converge, when the characteristic Mach number tends to zero, to the incompressible velocity and pressure variables. The resulting algorithm is capable of accurately computing external flows with free stream Mach numbers as low as 10-3.},
	keywords = {Entropy variables},
	issn = {0045-7825},
	doi = {10.1016/S0045-7825(01)00193-1},
	url = {http://www.sciencedirect.com/science/article/pii/S0045782501001931},
	author = {Wong, J S and Darmofal, D L and Peraire, J}
}
@article {Darmofal_2001_VortexCore1DModel,
	title = {Vortex core behaviour in confined and unconfined geometries: A quasi-one-dimensional model},
	journal = {Journal of Fluid Mechanics},
	volume = {449},
	year = {2001},
	pages = {61{\textendash}84},
	doi = {10.1017/S0022112001006103},
	author = {Darmofal, D L and Khan, R and Greitzer, E M and Tan, C S}
}
@article {Venditti_2000_Adjoint_Error_Estimation_1D,
	title = {Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow},
	journal = {Journal of Computational Physics},
	volume = {164},
	number = {1},
	year = {2000},
	pages = {204{\textendash}227},
	doi = {10.1006/jcph.2000.6600},
	author = {Venditti, D A and Darmofal, D L}
}
@article {Darmofal_2000_BC_1DPCEuler,
	title = {Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations},
	journal = {Journal of Computational Physics},
	volume = {160},
	number = {1},
	year = {2000},
	pages = {369 - 384},
	abstract = {The effect of local preconditioning on boundary conditions is analyzed for the subsonic, one-dimensional Euler equations. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions and different preconditioners whose intent is to accelerate low Mach number computations. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective when used with preconditioning, and asymptotically, at low Mach numbers, initial disturbances do not decay. Other boundary conditions are shown to be perfectly nonreflective in conjunction with preconditioning. Two-dimensional numerical results confirm the trends predicted by the one-dimensional analysis.},
	issn = {0021-9991},
	doi = {10.1006/jcph.2000.6472},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999100964726},
	author = {Darmofal, D L and Moinier, P and Giles, M B}
}
@mastersthesis {Cain_1999_SM,
	title = {A Robust, Locally Preconditioned Multigrid Algorithm for the Navier-Stokes Equations},
	year = {1999},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Cain, M}
}
@article {Darmofal_1999_RobustMultigrid_LPC_SC,
	title = {A Robust Multigrid Algorithm for the Euler Equations with Local Preconditioning and Semi-coarsening},
	journal = {Journal of Computational Physics},
	volume = {151},
	number = {2},
	year = {1999},
	pages = {728 - 756},
	abstract = {A semi-coarsened multigrid algorithm with a point block Jacobi, multi-stage smoother for second-order upwind discretizations of the two-dimensional Euler equations which produces convergence rates independent of grid size for moderate subsonic Mach numbers is presented. By modification of this base algorithm to include local preconditioning for low Mach number flows, the convergence becomes largely independent of grid size and Mach number over a range of flow conditions from nearly incompressible to transonic flows, including internal and external flows. A local limiting technique is introduced to increase the robustness of preconditioning in the presence of stagnation points. Computational timings are made showing that the semi-coarsening algorithm requiresO(N) time to lower the fine grid residual six orders of magnitude, whereNis the number of cells. By comparison, the same algorithm applied to a full-coarsening approach requiresO(N3/2) time, and, in nearly all cases, the semi-coarsening algorithm is faster than full coarsening with the computational savings being greatest on the finest grids.},
	issn = {0021-9991},
	doi = {10.1006/jcph.1999.6216},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999199962162},
	author = {Darmofal, D L and Siu, K}
}
@mastersthesis {Raghunathan_1998_SM,
	title = {An Adaptive Cycling Multigrid Algorithm for Two-dimensional Convection-dominated Flows},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Raghunathan, S}
}
@mastersthesis {Kim_1998_SM,
	title = {An Adaptive Mesh Method for the Simulation of Blade Vortex Interaction},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Kim, K}
}
@mastersthesis {delaGarza_1998_SM,
	title = {An All-at-Once Approach for Multidisciplinary Preliminary Aircraft Design},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {de~la~Garza, A}
}
@inbook {Darmofal_1998_LocalPCreview,
	title = {Local preconditioning: {M}anipulating {M}other {N}ature to fool {F}ather {T}ime},
	booktitle = {Computing the Future II: Advances and Prospects in Computational Aerodynamics},
	year = {1998},
	publisher = {John Wiley and Sons},
	organization = {John Wiley and Sons},
	author = {Darmofal, D L and Van Leer, B},
	editor = {Caughey, D A and Hafez, M}
}
@mastersthesis {Srinivasan_1998_SM,
	title = {Multidiscipinary Simulation of a Flexible Hydrofoil},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Srinivasan, V}
}
@mastersthesis {Siu_1998_SM,
	title = {A Robust, Locally Preconditioned Multigrid Algorithm for the Euler Equations},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Siu, K}
}
@mastersthesis {Singh_1998_SM,
	title = {Software Development for an Improved Particle Image Velocimetry},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Singh, K D}
}
@mastersthesis {Cary_1997_Phd,
	title = {Non-axisymmetric Effects in Vortex Breakdown},
	year = {1997},
	school = {University of Michigan},
	type = {phd},
	address = {Department of Aerospace Engineering},
	author = {Cary, A}
}
@article {Darmofal_1996_ParticlePaths,
	title = {An Analysis of 3D Particle Path Integration Algorithms},
	journal = {Journal of Computational Physics},
	volume = {123},
	number = {1},
	year = {1996},
	pages = {182 - 195},
	abstract = {Several techniques for the numerical integration of particle paths in steady and unsteady vector (velocity) fields are analyzed. Most of the analysis applies to unsteady vector fields, however, some results apply to steady vector field integration. Multistep, multistage, and some hybrid schemes are considered. It is shown that due to initialization errors, many unsteady particle path integration schemes are limited to third-order accuracy in time. Multistage schemes require at least three times more internal data storage than multistep schemes of equal order. However, for timesteps within the stability bounds, multistage schemes are generally more accurate. A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor. Thus, the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory. This paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed. For steady velocity fields, we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors. From this analysis, guidelines for accurate timestep sizing are suggested for both steady and unsteady flows. In particular, using simulation data for the unsteady flow around a tapered cylinder, we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow.},
	issn = {0021-9991},
	doi = {10.1006/jcph.1996.0015},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999196900157},
	author = {Darmofal, D L and Haimes, R}
}
@article {Darmofal_1996_ComparisonsAxisymmetricVBD,
	title = {Comparisons of experimental and numerical results for axisymmetric vortex breakdown in pipes},
	journal = {Computers \& Fluids},
	volume = {25},
	number = {4},
	year = {1996},
	pages = {353 - 371},
	abstract = {Experimental data for the bubble mode of breakdown in pipe flows is compared with calculations of the axisymmetric form of the Navier-Stokes equations. The location of breakdown in the calculations is found to be extremely sensitive to the inlet conditions; however, generally good agreement between the experimental and numerical breakdown locations is obtained. Detailed comparisons of the velocity distributions show that the bubble form of breakdown is well approximated by the axisymmetric Navier-Stokes equations for the flow upstream of the middle of the recirculation region. In the bubble tail, larger discrepancies exist between the experiment and calculation suggesting that the bubble form of breakdown is unstable to non-axisymmetric disturbances in the tail. Also, high Reynolds number bubble structures are found to exhibit periodic vortex ring shedding from the tail of the breakdown bubble.},
	issn = {0045-7930},
	doi = {10.1016/0045-7930(95)00041-0},
	url = {http://www.sciencedirect.com/science/article/pii/0045793095000410},
	author = {Darmofal, D L}
}
@mastersthesis {McCann_1996_SM,
	title = {Evaluation of Local Preconditioners for Multigrid Solutions of the Compressible Euler Equations},
	year = {1996},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {McCann, B}
}
@article {Darmofal_1996_LocalPreconditioningEigenvectors,
	title = {The Importance of Eigenvectors for Local Preconditioners of the Euler Equations},
	journal = {Journal of Computational Physics},
	volume = {127},
	number = {2},
	year = {1996},
	pages = {346 - 362},
	abstract = {The design of local preconditioners to accelerate the convergence to a steady state for the compressible Euler equations has so far been solely based on eigenvalue analysis. However, numerical evidence exists that the eigenvector structure also has an influence on the performance of preconditioners and should therefore be included in the design process. In this paper, we present the mathematical framework for the eigenvector analysis of local preconditioners for the multi-dimensional Euler equations. The non-normality of the preconditioned system is crucial in determining the potential for transient amplification of perturbations. Several existing local preconditioners are shown to possess a highly non-normal structure for low Mach numbers. This non-normality leads to significant robustness problems at stagnation points. A modification to these preconditioners which eliminates the non-normality is suggested, and numerical results are presented showing the marked improvement in robustness.},
	issn = {0021-9991},
	doi = {10.1006/jcph.1996.0180},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999196901801},
	author = {Darmofal, D L and Schmid, P J}
}
@conference {Darmofal_1995_Wave_propagation_vortical_flows,
	title = {Wave propagation characteristics of vortical flows in varying-area pipes},
	booktitle = {AIAA conference paper},
	number = {AIAA-95-2307},
	year = {1995},
	keywords = {vortex breakdown},
	author = {Darmofal, D L and Cary, A W and Powell, K G}
}
@conference {Darmofal_1994_trappedwaveavbd,
	title = {On the trapped wave nature of axisymmetric vortex breakdown},
	booktitle = {AIAA conference paper},
	number = {AIAA-94-2318},
	year = {1994},
	keywords = {vortex breakdown},
	author = {Darmofal, D L and Murman, E M}
}
@conference {Darmofal_1993_VorticityDynamics_VBD,
	title = {The role of vorticity dynamics in vortex breakdown},
	booktitle = {AIAA conference paper},
	number = {AIAA-93-3036},
	year = {1993},
	keywords = {vortex breakdown},
	author = {Darmofal, D L}
}
@mastersthesis {Darmofal_1993_PhD,
	title = {A Study of the Mechanisms of Axisymmetric Vortex Breakdown},
	year = {1993},
	month = {December},
	school = {Massachusetts Institute of Technology},
	type = {phd},
	url = {http://hdl.handle.net/1721.1/12208},
	author = {Darmofal, D L}
}
@conference {darmofal_1992_stream,
	title = {Visualization of 3-d vector fields : Variations on a stream},
	booktitle = {AIAA conference paper},
	number = {AIAA-92-0074},
	year = {1992},
	keywords = {scientific visualization},
	author = {Darmofal, D L and Haimes, R}
}
@mastersthesis {Darmofal_1991_SM,
	title = {Hierarchal Visualization of Three-dimensional Vortical Flow Calculations},
	year = {1991},
	month = {March},
	school = {Massachusetts Institute of Technology},
	type = {masters},
	keywords = {scientific visualization},
	url = {http://hdl.handle.net/1721.1/44269},
	author = {Darmofal, D L}
}
@conference {darmofal_1991_Visual_feature_identification,
	title = {Visual feature identification for 3-d data sets},
	booktitle = {AIAA conference paper},
	number = {AIAA-91-1583},
	year = {1991},
	keywords = {scientific visualization},
	author = {Darmofal, D L and Haimes, R}
}
@booklet {Haimes_1991_VKI,
	title = {Visual3 - A software environment for flow visualization},
	journal = {VKI Lecture Series on Computer Graphics and Flow Visualization in CFD},
	year = {1991},
	keywords = {scientific visualization},
	author = {Haimes, R and Giles, M B and Darmofal, D L}
}
@conference {haimes_1991_viz_case_study,
	title = {Visualization in computational fluid dynamics: A case study},
	booktitle = {IEEE Visualization Conference Proceedings},
	year = {1991},
	keywords = {scientific visualization},
	author = {Haimes, R and Darmofal, D L}
}
@article {Murman_1990_CFD_LEVortex,
	title = {Computation and visualization of leading edge vortex flows},
	journal = {Computing Systems in Engineering},
	volume = {1},
	number = {2-4},
	year = {1990},
	pages = {341-348},
	doi = {10.1016/0956-0521(90)90020-L},
	author = {Murman, E M, and Becker, T M and Darmofal, D L}
}
