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.Johannes Markert, Gregor Gassner, and Stefanie Walch. A Sub-element Adaptive Shock capturing Approach for Discontinuous Galerkin Methods. Communications in Applied Mathematics and Computation (submitted).
3.Sebastian Hennemann and Gregor J. Gassner. A provably entropy stable subcell shock capturing approach for high order split form DG. Journal of Computational Physics (submitted).
4.Gregor J. Gassner and Andrew R. Winters. A Novel Robust Strategy for Discontinuous
Galerkin Methods in Computational Physics: Why? When? What? Where?
Frontiers in Physics (submitted).
5.Nico Krais, Gero Schnücke, Thomas Bolemann and Gregor J. Gassner. Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows. Journal of Computational Physics (submitted).
6.Nico Krais, Andrea Beck, Thomas Bolemann, Hannes Frank, David Flad, Gregor Gassner, Florian Hindenlang, Malte Hoffmann, Thomas Kuhn, Matthias Sonntag, Claus-Dieter Munz. FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. Computers & Mathematics with Applications (submitted).

Accepted and Published Articles

54.Andrew Winters, Christof Czernik, Moritz Schily and Gregor J. Gassner Entropy stable numerical approximations for the isothermal and polytropic Euler equations. Accepted in BIT Numerical Mathematics.
53.Gero Schnücke, Nico Krais, Thomas Bolemann and Gregor J. Gassner Entropy Stable Discontinuous Galerkin Schemes on Moving Meshes with Summation-by-Parts Property for Hyperbolic Conservation Laws. accepted in Journal of Scientific Computing.
52.Andrew R. Winters, Marvin Bohm, Sven Schermeng, Gregor J. Gassner and Gustaaf B. Jacobs. Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. Accepted in Journal of Scientific Computing.
51.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. Journal of Scientific Computing 80 (2019): pp 175–222. arXiv: 1808.08218v1.
50.Philipp Birken, Lea M. Versbach and Gregor J. Gassner. Subcell Finite Volume Multigrid Preconditioning for High Order Discontinuous Galerkin Methods. Accepted in International Journal of Computational Fluid Dynamics.
49.David Kopriva, Florian Hindenlang, Thomas Boleman and Gregor Gassner. Free-Stream Preservation for Curved Geometrically Non-Conforming Discontinuous Galerkin Spectral Elements accepted in Journal of Scientific Computing. arXiv:1809.05206v1
48.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. accepted in Journal of Computational Physics. arXiv: 1804.02221v1
47.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. Accepted in Journal of Computational Physics. arXiv:1802.07341.
46.Andrew R. Winters, Rodrigo C. Moura, Gianmarco Mengaldo, Gregor J. Gassner, Stefanie Walch,
Joaquim Peiro, Spencer J. Sherwin. A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. Accepted in Journal of Computational Physics.
45.G. J. Gassner, A. R. Winters, F. Hindenlang, D. A. Kopriva. The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations accepted in Journal of Scientific Computing, arXiv e-prints: arXiv:1704.03646.
44.D. Derigs, G.J. Gassner, S. Walch and A.R. Winters. Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics accepted in DMV. arXiv e-prints: arXiv:1708.03537.
43.Lucas Friedrich, Andrew R. Winters, David C. Del Rey Fernandez, Gregor J. Gassner, Matteo Parsani, Mark H. Carpenter An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property accepted in Journal of Scientific Computing. arXiv:1712.10234.
42.D. Derigs, A.R. Winters, G.J. Gassner and S. Walch Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations accepted in Journal of Computational Physics.
41.David Flad, Gregor J. Gassner On the use of kinetic energy preserving DG-schemes for
large eddy simulation.
Journal of Computational Physics 350 (2017): 782-795.
40.L. Friedrichs, D. C. D. R. Fernández, A. R. Winters, G. J. Gassner, D. W. Zingg, and J. Hicken Conservative and Stable Degree Preserving SBP Operators for
Non-Conforming Meshes.
Journal of Scientific Computing (2017), https://doi.org/10.1007/s10915-017-0563-z.
39.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.
38.David A. Kopriva, Jan Nordström, Gregor J. Gassner Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems. J. Sci. Comp. 72 (2017): 314-330.
37.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 Euler Simulations.Journal of Computational Physics 332, (2017): 274–289.
36.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.
35.G.J. Gassner, A.R. Winters and David 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.
34.David A. Kopriva, Andrew R. Winters, Marvin Bohm, Gregor J. Gassner, A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes.
Computers & Fluids 139, (2016): 148-160.
33.A.D. Beck, D.G. Flad, C. Tonhäuser, G.J. Gassner and C.-D. Munz On the Influence of Polynomial De-aliasing on Subgrid Scale Models Flow, Turbulence and Combustion 97: 475-511, 2016.
32.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.
31.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: 72–108, 2016.
30.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.
29.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: 357–376, 2015.
28.D.A. Kopriva and G.J. Gassner. Geometry Effects in Nodal Discontinuous Galerkin Methods on Curved Elements that are Provably Stable. Applied Mathematics and Computation, 272: 274–290, 2016.
27.G.J. Gassner, A.R. Winters and David A. Kopriva. A Well Balanced and Entropy Conservative Discontinuous Galerkin Spectral Element Method for the Shallow Water Equations. Applied Mathematics and Computation, 272: 291–308, 2016.
26.G.J. Gassner, M. Staudenmaier, F. Hindenlang, M. Atak, C.-D. Munz. A Space-Time Adaptive Discontinuous Galerkin Scheme. Computers & Fluids, 117: 247–261, 2015.
25.D.A. Kopriva, G.J. Gassner. An Energy Stable Discontinuous Galerkin Spectral Element Discretization for Variable Coefficient Advection Problems. SIAM Journal on Scientific Computing 36: A2076-A2099, 2014.
24.Th. von Larcher, A. Beck, R. Klein, I. Horenko, P. Metzner, M. Waidmann, D. Igdalov, G. Gassner and C.-D. Munz. Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation. Meteorologische Zeitschrift, 24: 313-342, 2015.
23.A.D. Beck, T. Bolemann, D. Flad, H. Frank, G.J. Gassner, F. Hindenlang, C.-D. Munz. High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations. International Journal for Numerical Methods in Fluids, 76: 522 - 548, 2014.
22.G.J. Gassner. A kinetic energy preserving nodal discontinuous Galerkin spectral element method. International Journal for Numerical Methods in Fluids, 76: 28-50, 2014.
21.F.J. Hindenlang, G.J. Gassner, C.-D. Munz. Improving the accuracy of discontinuous Galerkin schemes at boundary layers. International Journal for Numerical Methods in Fluids, 75: 385-402, 2014.
20.G. Gassner. A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods. SIAM Journal on Scientific Computing, 35: A1233-A1253, 2013.
19.P. Birken, G. Gassner, M. Haas, C.-D. Munz. Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations. Journal of Computational Physics, 240: 20-35, 2013.
18.J.P. Boyd, G. Gassner, Burhan A. Sadiq. The Nonconvergence of h-refinement in prolate elements. Journal of Scientific Computing, 57: 372-389, 2013.
17.G. Gassner. Dispersion and Dissipation Analysis of PNPM-schemes. Journal of Scientific Computing, 54: 21-44, 2013.
16.A. Stock, J. Neudorfer, M. Riedlinger, G. Pirrung, G. Gassner, R. Schneider, S. Roller, C.-D. Munz. Three-Dimensional Numerical Simulation of a 30-GHz Gyrotron Resonator With an Explicit High-Order Discontinuous-Galerkin-Based Parallel Particle-In-Cell Method. IEEE Transactions on
Plasma Science, 99: 1-11, 2012.
15.J. Neudorfer, A. Stock, J. Flamm, F. Hindenlang, G. Gassner, C.-D. Munz, R. Schneider, S. Roller Numerical Investigation of High-Order Gyrotron Mode Propagation in Launchers at 170 GHz. IEEE Transactions on Plasma Science, 40(6): 1512-1521, 2012.
14.F. Hindenlang, G. Gassner, C. Altmann, A. Beck, M. Staudenmaier, C.-D. Munz. Explicit Discontinuous Galerkin methods for unsteady problems. Computers&Fluids, 61: 86-93, 2012.
13.G. J. Gassner, A. D. Beck. On the Accuracy of High Order Discretizations for Underresolved Turbulence Simulations. Theoretical and Computational Fluid Dynamics, 27: 221-237, 2013.
12.G. Gassner, D. A. Kopriva. A Comparison of the Gauss and Gauss-Lobatto Discontinuous Galerkin Spectral Element Method for Wave Propagation Problems. SIAM J. Sci. Comp., 33(5): 2560-2576, 2011.
11.G. Gassner, M. Dumbser, F. Hindenlang, C.D. Munz. Explicit One-Step Time Discretizations for Discontinuous Galerkin and Finite Volume Schemes Based on Local Predictors. J. Comput. Phys., 230(11): 4232-4247, 2011.
10.D. A. Kopriva, G. Gassner. On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods. J. Sci. Comp., 44(2): 136-155, 2010.
9.C. Altmann, G. Gassner, M. Staudenmaier, C.-D. Munz. High Order large Scale Calculations. inSiDE, 8(23): 12-15, 2010.
8.C. Altmann, G. Gassner, F. Lörcher, C.-D. Munz. A Space-Time Expansion Discontinuous Galerkin Scheme With Local Time Stepping for the Ideal and Viscous MHD Equations. IEEE Transactions on Plasma Science, (37): 513-519, 2009.
7.M. Dumbser, G. Gassner, C.-D. Munz. Discontinuous Galerkin-Verfahren für zeitabhängige Advektions-Diffusions-Gleichungen. Jahresbericht der Deutschen Mathematiker-Vereinigung Bd. 111 (2009).
6.G. Gassner, F. Lörcher, C.-D. Munz, J. S. Hesthaven. Polymorphic nodal elements and their application in discontinuous Galerkin methods. J. Comput. Phys., (228): 1573-1590, 2009.
5.F. Lörcher, G. Gassner, C.-D. Munz. An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations. J. Comput. Phys., 227(11): 5649-5670, 2008.
4.G. Gassner, F. Lörcher, C.-D. Munz. A discontinuous Galerkin scheme based on a space-time expansion. II. Viscous flow equations in multi dimensions. J. Sci. Comp., 34(3): 260-286, 2008.
3.F. Lörcher, G. Gassner, C.-D. Munz. A discontinuous Galerkin scheme based on a space-time expansion. I. Inviscid compressible flow in one space dimension. J. Sci. Comp., 32(2): 175-199, 2007.
2.G. Gassner, F. Lörcher, C.-D. Munz. A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes. J. Comput. Phys., 224(2): 1049-1063, 2007.
1.B. Weigand, G. Gassner. The effect of wall conduction for the extended Graetz problem for laminar and turbulent flows. Int. J. Heat Mass Transfer, Vol. 50, 1097-1105, 2007.