350 citations · 1.2k across the 53 of their papers we have counts for
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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 +2
The second paper of this series presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible m…
Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps
David A. Kopriva, Gregor J. Gassner, Jan Nordström
We use the behavior of the norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous G…
A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods
Johannes Markert, Gregor Gassner, Stefanie Walch
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collec…
A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems
David A. Kopriva, Gregor J. Gassner
We present a hybrid continuous and discontinuous Galerkin spectral element approximation that leverages the advantages of each approach. The continuous Galerkin approximation is us…
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
Hendrik Ranocha, Gregor J Gassner
Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim…
A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler Equations
Sebastian Hennemann, Andrés M. Rueda-Ramírez, Florian J. Hindenlang +1
The main result in this paper is a provably entropy stable shock capturing approach for the high order entropy stable DGSEM based on a hybrid blending with a subcell low order vari…
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha +1
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravit…
Stability issues of entropy-stable and/or split-form high-order schemes
Gregor J. Gassner, Magnus Svärd, Florian J. Hindenlang
The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conservi…
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 +1
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order…
Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows
Nico Krais, Gero Schnücke, Thomas Bolemann +1
The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volum…