29 citations · 134 across the 14 of their papers we have counts for
14 papers
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
F. Fambri, E. Zampa, S. Busto +4
We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 sp…
Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics
Andrés M Rueda-Ramírez, Florian J Hindenlang, Jesse Chan +1
In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto-hydrod…
JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators
Nikita Nikulsin, Rohan Ramasamy, Matthias Hoelzl +4
Although the basic concept of a stellarator was known since the early days of fusion research, advances in computational technology have enabled the modelling of increasingly compl…
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan +4
Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entro…
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 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…
A locally field-aligned discontinuous Galerkin method for anisotropic wave equations
Benedict Dingfelder, Florian J. Hindenlang
In magnetized plasmas of fusion devices the strong magnetic field leads to highly anisotropic physics where solution scales along field lines are much larger than perpendicular to…
FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws
Nico Krais, Andrea Beck, Thomas Bolemann +8
High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization…
On the order reduction of entropy stable DGSEM for the compressible Euler equations
Florian J. Hindenlang, Gregor J. Gassner
Is the experimental order of convergence lower when using the entropy stable DGSEM-LGL variant? Recently, a debate on the question of the convergence behavior of the entropy stable…
Stability of Wall Boundary Condition Procedures for Discontinuous Galerkin Spectral Element Approximations of the Compressible Euler Equations
Florian J. Hindenlang, Gregor J. Gassner, David A. Kopriva
We perform a linear and entropy stability analysis for wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equat…
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 +3
The first paper of this series presents a discretely entropy stable discontinuous Galerkin (DG) method for the resistive magnetohydrodynamics (MHD) equations on three-dimensional c…
Stability of Overintegration Methods for Nodal Discontinuous Galerkin Spectral Element Methods
David A. Kopriva
We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved…
The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations
Gregor J. Gassner, Andrew R. Winters, Florian J. Hindenlang +1
We show how to modify the original Bassi and Rebay scheme (BR1) [F. Bassi and S. Rebay, A High Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the…