ALE-DGSEM approximation of wave reflection and transmission from a moving medium. - Andrew R. Winters; David A. Kopriva (J. Comput. Phys., 2014)

High-Order Local Time Stepping on Moving DG Spectral Element Meshes. - Andrew R. Winters; David A. Kopriva (J. Sci. Comput., 2014)

A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography. - Andrew R. Winters; Gregor Gassner (J. Comput. Phys., 2015)

A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. - Gregor Gassner; Andrew R. Winters; David A. Kopriva (Appl. Math. Comput., 2016)

A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2016)

Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. - Gregor J. Gassner; Andrew R. Winters; David A. Kopriva (J. Comput. Phys., 2016)

Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations. - Andrew R. Winters; Gregor J. Gassner (J. Comput. Phys., 2016)

An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. - Andrew R. Winters; Gregor J. Gassner (J. Sci. Comput., 2016)

A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2017)

Hybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws. - Birte Schmidtmann; Andrew R. Winters (J. Comput. Phys., 2017)

An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. - Niklas Wintermeyer; Andrew R. Winters; Gregor J. Gassner; David A. Kopriva (J. Comput. Phys., 2017)

A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations. - Andrew R. Winters; Dominik Derigs; Gregor J. Gassner; Stefanie Walch (J. Comput. Phys., 2017)

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations. - Dominik Derigs; Andrew R. Winters; Gregor J. Gassner; Stefanie Walch; Marvin Bohm (J. Comput. Phys., 2018)

An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. - Niklas Wintermeyer; Andrew R. Winters; Gregor J. Gassner; Timothy Warburton (J. Comput. Phys., 2018)

A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. - Andrew R. Winters; Rodrigo Costa Moura; Gianmarco Mengaldo; Gregor J. Gassner; Stefanie Walch; Joaquim Peiró; Spencer J. Sherwin (J. Comput. Phys., 2018)

Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. - Lucas Friedrich; David C. Del Rey Fernández; Andrew R. Winters; Gregor J. Gassner; David W. Zingg; Jason E. Hicken (J. Sci. Comput., 2018)

An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. - Lucas Friedrich; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Matteo Parsani; Mark H. Carpenter (J. Sci. Comput., 2018)

The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. - Gregor J. Gassner; Andrew R. Winters; Florian Hindenlang; David A. Kopriva (J. Sci. Comput., 2018)

Correction to: The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. - Gregor J. Gassner; Andrew R. Winters; Florian Hindenlang; David A. Kopriva (J. Sci. Comput., 2018)

Entropy stable numerical approximations for the isothermal and polytropic Euler equations. - Andrew R. Winters; Christof Czernik; Moritz B. Schily; Gregor J. Gassner (CoRR, 2019)

Energy versus entropy estimates for nonlinear hyperbolic systems of equations. - Jan Nordström; Andrew R. Winters (CoRR, 2019)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Euler equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; L. Fredrich; Diego Rojas; Andrew R. Winters; Gregor J. Gassner; Stefano Zampini; Matteo Parsani (CoRR, 2019)

Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. - David C. Del Rey Fernández; Mark H. Carpenter; Lisandro Dalcín; Lucas Friedrich; Andrew R. Winters; Gregor J. Gassner; Matteo Parsani (CoRR, 2019)

Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods. - Marvin Bohm; Sven Schermeng; Andrew R. Winters; Gregor J. Gassner; Gustaaf B. Jacobs (J. Sci. Comput., 2019)

Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. - Lucas Friedrich; Gero Schnücke; Andrew R. Winters; David C. Del Rey Fernández; Gregor J. Gassner; Mark H. Carpenter (J. Sci. Comput., 2019)

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations. - Andrew R. Winters; David A. Kopriva; Gregor J. Gassner; Florian Hindenlang (CoRR, 2020)

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification. - Marvin Bohm; Andrew R. Winters; Gregor J. Gassner; Dominik Derigs; Florian Hindenlang; Joachim Saur (J. Comput. Phys., 2020)

Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. - Hendrik Ranocha; Michael Schlottke-Lakemper; Andrew R. Winters; Erik Faulhaber; Jesse Chan; Gregor J. Gassner (CoRR, 2021)

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. - Andrés M. Rueda-Ramírez; Sebastian Hennemann; Florian J. Hindenlang; Andrew R. Winters; Gregor J. Gassner (J. Comput. Phys., 2021)

A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. - Michael Schlottke-Lakemper; Andrew R. Winters; Hendrik Ranocha; Gregor J. Gassner (J. Comput. Phys., 2021)

Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods. - Jan Nordström; Andrew R. Winters (J. Sci. Comput., 2021)

On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics. - Hendrik Ranocha; Andrew R. Winters; Hugo Guillermo Castro; Lisandro Dalcín; Michael Schlottke-Lakemper; Gregor J. Gassner; Matteo Parsani (CoRR, 2022)

A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions. - Jan Nordström; Andrew R. Winters (J. Comput. Phys., 2022)

High-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (CoRR, 2023)

Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws. - Hendrik Ranocha; Michael Schlottke-Lakemper; Jesse Chan; Andrés M. Rueda-Ramírez; Andrew R. Winters; Florian Hindenlang; Gregor J. Gassner (ACM Trans. Math. Softw., 2023)

Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes. - Tomas Lundquist; Andrew R. Winters; Jan Nordström (J. Comput. Phys., 2024)

An Entropy Stable Discontinuous Galerkin Method for the Two-Layer Shallow Water Equations on Curvilinear Meshes. - Patrick Ersing; Andrew R. Winters (J. Sci. Comput., 2024)

HOHQMesh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements. - David A. Kopriva; Andrew R. Winters; Michael Schlottke-Lakemper; Joseph A. Schoonover; Hendrik Ranocha (J. Open Source Softw., 2024)

Entropy stable hydrostatic reconstruction schemes for shallow water systems. - Patrick Ersing; Sven Goldberg; Andrew R. Winters (J. Comput. Phys., 2025)

Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. - Jan Glaubitz; Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Gregor Gassner (J. Comput. Phys., 2025)

Energy bounds for discontinuous Galerkin spectral element approximations of well-posed overset grid problems for hyperbolic systems. - David A. Kopriva; Andrew R. Winters; Jan Nordström (J. Comput. Phys., 2025)

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws. - Hendrik Ranocha; Andrew R. Winters; Michael Schlottke-Lakemper; Philipp Öffner; Jan Glaubitz; Gregor J. Gassner (J. Comput. Phys., 2025)

Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry. - David A. Kopriva; Andrew R. Winters; Jan Nordström (CoRR, 2025)