Andrew R. Winters

Publication Activity (10 Years)

Years Active: 2014-2024
Publications (10 Years): 44

Top Topics

Navier Stokes Equations

Numerical Simulations

Conservation Laws

Top Venues

J. Comput. Phys.

J. Sci. Comput.

Appl. Math. Comput.

Publications

David A. Kopriva, Andrew R. Winters, Jan Nordström
Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems. CoRR (2024)
Patrick Ersing, Sven Goldberg, Andrew R. Winters
Entropy stable hydrostatic reconstruction schemes for shallow water systems. CoRR (2024)
Tomas Lundquist, Andrew R. Winters, Jan Nordström
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes. J. Comput. Phys. 498 (2024)
Jan Glaubitz, Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Gregor Gassner
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods. CoRR (2024)
Patrick Ersing, Andrew R. Winters
An Entropy Stable Discontinuous Galerkin Method for the Two-Layer Shallow Water Equations on Curvilinear Meshes. J. Sci. Comput. 98 (3) (2024)
Patrick Ersing, Andrew R. Winters
An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes. CoRR (2023)
Hendrik Ranocha, Andrew R. Winters, Michael Schlottke-Lakemper, Philipp Öffner, Jan Glaubitz, Gregor J. Gassner
High-order upwind summation-by-parts methods for nonlinear conservation laws. CoRR (2023)
Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R. Winters, Florian Hindenlang, Gregor J. Gassner
Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws. ACM Trans. Math. Softw. 49 (4) (2023)
Tomas Lundquist, Andrew R. Winters, Jan Nordström
Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes. CoRR (2023)
Hendrik Ranocha, Andrew R. Winters, Hugo Guillermo Castro, Lisandro Dalcín, Michael Schlottke-Lakemper, Gregor J. Gassner, Matteo Parsani
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics. CoRR (2022)
Jan Nordström, Andrew R. Winters
A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions. J. Comput. Phys. 463 (2022)
Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan, Andrés M. Rueda-Ramírez, Andrew R. Winters, Florian Hindenlang, Gregor J. Gassner
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws. CoRR (2021)
Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha, Gregor J. Gassner
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. J. Comput. Phys. 442 (2021)
Jan Nordström, Andrew R. Winters
Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods. J. Sci. Comput. 87 (1) (2021)
Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor J. Gassner
An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing. J. Comput. Phys. 444 (2021)
Hendrik Ranocha, Michael Schlottke-Lakemper, Andrew R. Winters, Erik Faulhaber, Jesse Chan, Gregor J. Gassner
Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing. CoRR (2021)
Jan Nordström, Andrew R. Winters
Stable filtering procedures for nodal discontinuous Galerkin methods. CoRR (2020)
Andrés M. Rueda-Ramírez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor Gassner
An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing. CoRR (2020)
Andrew R. Winters, David A. Kopriva, Gregor J. Gassner, Florian Hindenlang
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations. CoRR (2020)
Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha, Gregor J. Gassner
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics. CoRR (2020)
Marvin Bohm, Andrew R. Winters, Gregor J. Gassner, Dominik Derigs, Florian Hindenlang, Joachim Saur
An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification. J. Comput. Phys. 422 (2020)
Lucas Friedrich, Gero Schnücke, Andrew R. Winters, David C. Del Rey Fernández, Gregor J. Gassner, Mark H. Carpenter
Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws. J. Sci. Comput. 80 (1) (2019)
Jan Nordström, Andrew R. Winters
Energy versus entropy estimates for nonlinear hyperbolic systems of equations. CoRR (2019)
Andrew R. Winters, Christof Czernik, Moritz B. Schily, Gregor J. Gassner
Entropy stable numerical approximations for the isothermal and polytropic Euler equations. CoRR (2019)
David C. Del Rey Fernández, Mark H. Carpenter, Lisandro Dalcín, Lucas Friedrich, Andrew R. Winters, Gregor J. Gassner, Matteo Parsani
Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Navier-Stokes Equations. CoRR (2019)
Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs
Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods. J. Sci. Comput. 81 (2) (2019)
Marvin Bohm, Sven Schermeng, Andrew R. Winters, Gregor J. Gassner, Gustaaf B. Jacobs
Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. CoRR (2019)
David C. Del Rey Fernández, Mark H. Carpenter, Lisandro Dalcín, L. Fredrich, Diego Rojas, Andrew R. Winters, Gregor J. Gassner, Stefano Zampini, Matteo Parsani
Entropy Stable p-Nonconforming Discretizations with the Summation-by-Parts Property for the Compressible Euler equations. CoRR (2019)
Lucas Friedrich, Andrew R. Winters, David C. Del Rey Fernández, Gregor J. Gassner, Matteo Parsani, Mark H. Carpenter
An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. J. Sci. Comput. 77 (2) (2018)
Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch, Marvin Bohm
Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations. J. Comput. Phys. 364 (2018)
Lucas Friedrich, David C. Del Rey Fernández, Andrew R. Winters, Gregor J. Gassner, David W. Zingg, Jason E. Hicken
Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. J. Sci. Comput. 75 (2) (2018)
Andrew R. Winters, Rodrigo Costa Moura, Gianmarco Mengaldo, Gregor J. Gassner, Stefanie Walch, Joaquim Peiró, Spencer J. Sherwin
A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. J. Comput. Phys. 372 (2018)
Gregor J. Gassner, Andrew R. Winters, Florian Hindenlang, David A. Kopriva
The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. J. Sci. Comput. 77 (1) (2018)
Niklas Wintermeyer, Andrew R. Winters, Gregor J. Gassner, Timothy Warburton
An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. J. Comput. Phys. 375 (2018)
Gregor J. Gassner, Andrew R. Winters, Florian Hindenlang, David A. Kopriva
Correction to: The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. J. Sci. Comput. 77 (1) (2018)
Niklas Wintermeyer, Andrew R. Winters, Gregor J. Gassner, David A. Kopriva
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. J. Comput. Phys. 340 (2017)
Andrew R. Winters, Dominik Derigs, Gregor J. Gassner, Stefanie Walch
A uniquely defined entropy stable matrix dissipation operator for high Mach number ideal MHD and compressible Euler simulations. J. Comput. Phys. 332 (2017)
Birte Schmidtmann, Andrew R. Winters
Hybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws. J. Comput. Phys. 330 (2017)
Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch
A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD. J. Comput. Phys. 330 (2017)
Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch
A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure. J. Comput. Phys. 317 (2016)
Gregor J. Gassner, Andrew R. Winters, David A. Kopriva
Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. J. Comput. Phys. 327 (2016)
Gregor Gassner, Andrew R. Winters, David A. Kopriva
A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. Appl. Math. Comput. 272 (2016)
Andrew R. Winters, Gregor J. Gassner
Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations. J. Comput. Phys. 304 (2016)
Andrew R. Winters, Gregor J. Gassner
An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. J. Sci. Comput. 67 (2) (2016)
Andrew R. Winters, Gregor Gassner
A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography. J. Comput. Phys. 301 (2015)
Andrew R. Winters, David A. Kopriva
ALE-DGSEM approximation of wave reflection and transmission from a moving medium. J. Comput. Phys. 263 (2014)
Andrew R. Winters, David A. Kopriva
High-Order Local Time Stepping on Moving DG Spectral Element Meshes. J. Sci. Comput. 58 (1) (2014)