Andrew R. Winters

58 papers Journal 58

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	A new class of entropy stable fluctuations for the discontinuous Galerkin method with application to the Saint-Venant-Exner model. CoRR Patrick Ersing, Andrew R. Winters
2026	J	`jnl`	Entropy analysis and entropy stable DG methods for the shallow water moment equations. CoRR Julio Careaga, Patrick Ersing, Julian Koellermeier, Andrew R. Winters
2026	J	`jnl`	Optimal boundary closures for diagonal-norm upwind SBP operators. CoRR Ken Mattsson, David Niemelä, Andrew R. Winters
2025	J	`jnl`	Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems. J. Comput. Phys. David A. Kopriva, Andrew R. Winters, Jan Nordström
2025	J	`jnl`	Entropy stable hydrostatic reconstruction schemes for shallow water systems. J. Comput. Phys. Patrick Ersing, Sven Goldberg, Andrew R. Winters
2025	J	`jnl`	Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. J. Comput. Phys. Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor Gassner
2025	J	`jnl`	Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry. CoRR David A. Kopriva, Andrew R. Winters, Jan Nordström
2025	J	`jnl`	Numerical boundary flux functions that give provable bounds for nonlinear initial boundary value problems with open boundaries. CoRR Andrew R. Winters, David A. Kopriva, Jan Nordström
2025	J	`jnl`	On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws. J. Comput. Phys. Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner
2025	J	`jnl`	Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators. CoRR Jan Glaubitz, Joshua Lampert, Andrew R. Winters, Jan Nordström
2024	J	`jnl`	An Entropy Stable Discontinuous Galerkin Method for the Two-Layer Shallow Water Equations on Curvilinear Meshes. J. Sci. Comput. Patrick Ersing, Andrew R. Winters
2024	J	`jnl`	Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes. J. Comput. Phys. Tomas Lundquist, Andrew R. Winters, Jan Nordström
2024	J	`jnl`	Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems. CoRR David A. Kopriva, Andrew R. Winters, Jan Nordström
2024	J	`jnl`	Entropy stable hydrostatic reconstruction schemes for shallow water systems. CoRR Patrick Ersing, Sven Goldberg, Andrew R. Winters
2024	J	`jnl`	Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. CoRR Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor Gassner
2024	J	`jnl`	HOHQMesh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements. J. Open Source Softw. David A. Kopriva, Andrew R. Winters, Michael Schlottke-Lakemper, Joseph A. Schoonover, Hendrik Ranocha
2023	J	`jnl`	An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes. CoRR Patrick Ersing, Andrew R. Winters
2023	J	`jnl`	Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws. ACM Trans. Math. Softw. Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R. Winters, Florian Hindenlang, Gregor J. Gassner
2023	J	`jnl`	Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes. CoRR Tomas Lundquist, Andrew R. Winters, Jan Nordström
2023	J	`jnl`	High-order upwind summation-by-parts methods for nonlinear conservation laws. CoRR Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner
2022	J	`jnl`	A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions. J. Comput. Phys. Jan Nordström, Andrew R. Winters
2022	J	`jnl`	On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics. CoRR Hendrik Ranocha, Andrew R. Winters, Hugo Guillermo Castro, Lisandro Dalcín, Michael Schlottke-Lakemper, Gregor J. Gassner, Matteo Parsani
2021	J	`jnl`	A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. J. Comput. Phys. Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha, Gregor J. Gassner
2021	J	`jnl`	Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. CoRR Hendrik Ranocha, Michael Schlottke-Lakemper, Andrew R. Winters, Erik Faulhaber, Jesse Chan, Gregor J. Gassner
2021	J	`jnl`	An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. J. Comput. Phys. Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor J. Gassner
2021	J	`jnl`	Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws. CoRR Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R. Winters, Florian Hindenlang, Gregor J. Gassner
2021	J	`jnl`	Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods. J. Sci. Comput. Jan Nordström, Andrew R. Winters
2020	J	`jnl`	A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. CoRR Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha, Gregor J. Gassner
2020	J	`jnl`	An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing. CoRR Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor Gassner
2020	J	`jnl`	An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification. J. Comput. Phys. Marvin Bohm, Andrew R. Winters, Gregor J. Gassner, Dominik Derigs, Florian Hindenlang, Joachim Saur
2020	J	`jnl`	Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations. CoRR Andrew R. Winters, David A. Kopriva, Gregor J. Gassner, Florian Hindenlang
2020	J	`jnl`	Stable filtering procedures for nodal discontinuous Galerkin methods. CoRR Jan Nordström, Andrew R. Winters
2019	J	`jnl`	Energy versus entropy estimates for nonlinear hyperbolic systems of equations. CoRR Jan Nordström, Andrew R. Winters
2019	J	`jnl`	Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. J. Sci. Comput. Lucas Friedrich, Gero Schnücke, Andrew R. Winters, David C. Del Rey Fernández, Gregor J. Gassner, Mark H. Carpenter
2019	J	`jnl`	Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Euler equations. CoRR David C. Del Rey Fernández, Mark H. Carpenter, Lisandro Dalcín, L. Fredrich, Diego Rojas, Andrew R. Winters, Gregor J. Gassner, Stefano Zampini, Matteo Parsani
2019	J	`jnl`	Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. CoRR David C. Del Rey Fernández, Mark H. Carpenter, Lisandro Dalcín, Lucas Friedrich, Andrew R. Winters, Gregor J. Gassner, Matteo Parsani
2019	J	`jnl`	Entropy stable numerical approximations for the isothermal and polytropic Euler equations. CoRR Andrew R. Winters, Christof Czernik, Moritz B. Schily, Gregor J. Gassner
2019	J	`jnl`	Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods. J. Sci. Comput. Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs
2019	J	`jnl`	Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. CoRR Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs
2018	J	`jnl`	A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. J. Comput. Phys. Andrew R. Winters, Rodrigo Costa Moura, Gianmarco Mengaldo, Gregor J. Gassner, Stefanie Walch, Joaquim Peiró, Spencer J. Sherwin
2018	J	`jnl`	An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. J. Sci. Comput. Lucas Friedrich, Andrew R. Winters, David C. Del Rey Fernández, Gregor J. Gassner, Matteo Parsani, Mark H. Carpenter
2018	J	`jnl`	An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. J. Comput. Phys. Niklas Wintermeyer, Andrew R. Winters, Gregor J. Gassner, Timothy Warburton
2018	J	`jnl`	Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. J. Sci. Comput. Lucas Friedrich, David C. Del Rey Fernández, Andrew R. Winters, Gregor J. Gassner, David W. Zingg, Jason E. Hicken
2018	J	`jnl`	Correction to: The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. J. Sci. Comput. Gregor J. Gassner, Andrew R. Winters, Florian Hindenlang, David A. Kopriva
2018	J	`jnl`	Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations. J. Comput. Phys. Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch, Marvin Bohm
2018	J	`jnl`	The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. J. Sci. Comput. Gregor J. Gassner, Andrew R. Winters, Florian Hindenlang, David A. Kopriva
2017	J	`jnl`	A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD. J. Comput. Phys. Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch
2017	J	`jnl`	A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations. J. Comput. Phys. Andrew R. Winters, Dominik Derigs, Gregor J. Gassner, Stefanie Walch
2017	J	`jnl`	An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. J. Comput. Phys. Niklas Wintermeyer, Andrew R. Winters, Gregor J. Gassner, David A. Kopriva
2017	J	`jnl`	Hybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws. J. Comput. Phys. Birte Schmidtmann, Andrew R. Winters
2016	J	`jnl`	A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure. J. Comput. Phys. Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch
2016	J	`jnl`	A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. Appl. Math. Comput. Gregor Gassner, Andrew R. Winters, David A. Kopriva
2016	J	`jnl`	Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations. J. Comput. Phys. Andrew R. Winters, Gregor J. Gassner
2016	J	`jnl`	An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. J. Sci. Comput. Andrew R. Winters, Gregor J. Gassner
2016	J	`jnl`	Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys. Gregor J. Gassner, Andrew R. Winters, David A. Kopriva
2015	J	`jnl`	A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography. J. Comput. Phys. Andrew R. Winters, Gregor Gassner
2014	J	`jnl`	ALE-DGSEM approximation of wave reflection and transmission from a moving medium. J. Comput. Phys. Andrew R. Winters, David A. Kopriva
2014	J	`jnl`	High-Order Local Time Stepping on Moving DG Spectral Element Meshes. J. Sci. Comput. Andrew R. Winters, David A. Kopriva