@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}
}
@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.}
}
@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.}
}
@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 {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}
}
@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 {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}
}
@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 {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}
}
@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 {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}
}
@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}
}
@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}
}
@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}
}
@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}
}
@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}
}
