Publications

Articles In Preparation

  1. David Del Rey Fernández, Mark H. Carpenter, Lucas Friedrich, Lisandro Dalcin, Andrew R. Winters, Gregor J. Gassner and Matteo Parsani. “Entropy Stable Non-conforming Discretization with the Summation-by-Parts Property for the Compressible Navier-Stokes equations.” Journal Of Computational Physics (submitted).

  2. David Del Rey Fernández, Mark H. Carpenter, Lucas Friedrich, Lisandro Dalcin, Andrew R. Winters, Gregor J. Gassner and Matteo Parsani. “Entropy Stable Non-conforming Discretization with the Summation-by-Parts Property for the Compressible Euler equations.” Journal Of Computational Physics (submitted).

  3. L. Friedrichs, G. Schnücke, A. R. Winters, D. C. D. R. Fernández, G. J. Gassner, and M. H. Carpenter. “Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws.” Journal of Scientific Computing (under revision), ArXiv e-prints: arXiv:1808.08218.

 

Refereed Journal Articles

  1. M.Bohm, A. R. Winters, G. J. Gassner, D.Derigs, F. Hindenlang and J. Saur. “An Entropy Stable Nodal Discontinuous Galerkin Method for the Resistive MHD Equations. Part I: Theory and Numerical Verification.” Journal of Computational Physics doi.org/10.1016/j.jcp.2018.06.027.

  2. N. Wintermeyer, A. R. Winters, G. J. Gassner, and T. Warburton. “An Entropy Stable Discontinuous Galerkin Method for the Shallow Water Equations on Curvilinear Meshes with Wet/Dry Fronts Accelerated by GPUs.” Journal of Computational Physics 375, (2018): 447–480.

  3. A. R. Winters, R. C. Moura, G. Mengaldo, G. J. Gassner, S. Walch, J. Peiro, S. J. Sherwin. “A Comparative Study on Polynomial Dealiasing and Split Form Discontinuous Galerkin Schemes for Under-Resolved Turbulence Computations.” Journal of Computational Physics 372, (2018): 1–21.

  4. L. Friedrichs, A. R. Winters, D. C. D. R. Fernández, G. J. Gassner, M. Parsani, and M. H. Carpenter. “An Entropy Stable $h/p$ Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property.” Journal of Scientific Computing 77, 2 (2018): 689–725.

  5. G. J. Gassner, A. R. Winters, F. Hindenlang, D. A. Kopriva. “The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations.” Journal of Scientific Computing, 77, 1 (2018): 154–200.

  6. D. Derigs, A. R. Winters, G. J. Gassner, S. Walch, and M. Bohm. “Ideal GLM-MHD: About the Entropy-Consistent Nine-Wave Magnetic Field Divergence Diminishing Ideal Magnetohydrodynamic Equations.” Journal of Computational Physics 364, (2018): 420–467.

  7. D. Derigs, G. J. Gassner, S. Walch, A. R. Winters. “Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics.” Deutsche Mathematiker-Vereinigung (DMV) Jahresbericht, 120, 3 (2018): 153–219.

  8. L. Friedrichs, D. C. D. R. Fernández, A. R. Winters, G. J. Gassner, D. W. Zingg, and J. Hicken. “Conservative and Stable Degree Preserving Summation-By-Parts Finite Difference Operators for Non-Conforming Meshes.” Journal of Scientific Computing, 75, 2 (2018): 657–686.

  9. N. Wintermeyer, A. R. Winters, G. J. Gassner, and D. A. Kopriva. “An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry.” Journal of Computational Physics 340, (2017): 200–242.

  10. A. R. Winters, D. Derigs, G. J. Gassner, and S. Walch. “A Uniquely Defined Entropy Stable Matrix Dissipation Operator for High Mach Number Ideal MHD and Compressible Euler Simulations.” Journal of Computational Physics 332, (2017): 274–289.

  11. D. Derigs, A. R. Winters, G. J. Gassner, and S. Walch. “A Novel Averaging Technique for Discrete Entropy-Stable Dissipation Operators for Ideal MHD.” Journal of Computational Physics 330, (2017): 624-632.

  12. B. Schmidtmann and A. R. Winters. “Hybrid Entropy Stable HLL Type Riemann Solvers for Hyperbolic Conservation Laws.” Journal of Computational Physics 330, (2017): 556-560.

  13. G. J. Gassner, A. R. Winters, and D. A. Kopriva. “Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations.” Journal of Computational Physics 327 (2016): 39-66.

  14. D. A. Kopriva, A. R. Winters, M. Bohm, and G. J. Gassner. “A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes.” Computers & Fluids 139, (2016): 148-160.

  15. D. Derigs, A. R. Winters, G. J. Gassner, and S. Walch. “A Novel High-Order, Entropy Stable 3D AMR MHD Solver with Guaranteed Positive Pressure.” Journal of Computational Physics 317 (2016): 223-256

  16. A. R. Winters and G. J. Gassner. “Affordable, Entropy Conserving and Entropy Stable Flux Functions for the Ideal MHD Equations.” Journal of Computational Physics 304, (2016): 72-108.

  17. G. J. Gassner, A. R. Winters, and D. A. Kopriva. “A Well Balanced and Entropy Conservative Discontinuous Galerkin Spectral Element Method for the Shallow Water Equations.” Applied Mathematics and Computation 272, 2 (2016): 291-308.

  18. A. R. Winters and G. J. Gassner. “An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics.” Journal of Scientific Computing 67,2 (2016): 514-539.

  19. A. R. Winters and G. J. Gassner. “A Comparison of Two Entropy Stable Discontinuous Galerkin Spectral Element Approximations for the Shallow Water Equations with Non-Constant Topography.” Journal of Computational Physics 301, (2015): 357-376.

  20. A. R. Winters and D. A. Kopriva. “ALE-DGSEM Approximation of Wave Reflection and Transmission from a Moving Medium.” Journal of Computational Physics 263, (2014): 233-267.

  21. A. R. Winters and D. A. Kopriva. “High-Order Local Time Stepping on Moving DG Spectral Element Meshes.” Journal of Scientific Computing 58, 1 (2014): 176-202.

 

Non-Refereed Publications Completed

  1. G. J. Gassner and A. R. Winters. “Robust High-Order Discontinuous Galerkin Methods for Computational Fluid Dynamics.” GAMM-Rundbrief/Heft 1, 2017.

  2. A. R. Winters and M. J. Shashkov. “Support Operators Method for the Diffusion Equation in Multiple Materials.” Technical report, LA-UR-12-24117, Los Alamos National Laboratory, 2012.

 

Refereed Abstracts and Conference Proceedings

  1. A. R. Winters and G. J. Gassner. “Entropy Stable Approximations for Shallow Water Models.” 12th International Conference on Mathematical and Numerical Aspects of Wave Propagation: Book of Abstracts. Karlsruhe, Germany. July 2015.

  2. A. R. Winters and D. A. Kopriva. “Efficient and High-Order Explicit Local Time Stepping on Moving DG Spectral Element Meshes.” Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. (eds.) R. M. Kirby, M. Berzins, and J. S. Hesthaven. Springer International Publishing, 2015: 513-522.


Dissertation

A. R. Winters. “Discontinuous Galerkin Spectral Element Approximations for the Reflection and Transmission of Waves from Moving Material Interfaces,” 2014. http://diginole.lib.fsu.edu/etd/8916.