A novel robust strategy for discontinuous Galerkin methods in computational fluid mechanics: Why? When? What? Where?
GJ Gassner, AR Winters - Frontiers in Physics, 2021 - frontiersin.org
In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods
DS Balsara - Living reviews in computational astrophysics, 2017 - Springer
As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …
is an increasing need to move to high accuracy schemes for computational astrophysics …
Relaxation Runge--Kutta methods: Fully discrete explicit entropy-stable schemes for the compressible Euler and Navier--Stokes equations
The framework of inner product norm preserving relaxation Runge--Kutta methods [DI
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …
Ideal GLM-MHD: about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
The paper presents two contributions in the context of the numerical simulation of
magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics …
magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics …
An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification
The first paper of this series presents a discretely entropy stable discontinuous Galerkin
(DG) method for the resistive magnetohydrodynamics (MHD) equations on three …
(DG) method for the resistive magnetohydrodynamics (MHD) equations on three …
An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part II: Subcell finite volume shock capturing
AM Rueda-Ramírez, S Hennemann… - Journal of …, 2021 - Elsevier
The second paper of this series presents two robust entropy stable shock-capturing methods
for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible …
for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible …
Entropy–stable discontinuous Galerkin approximation with summation–by–parts property for the incompressible Navier–Stokes/Cahn–Hilliard system
We develop an entropy–stable two–phase incompressible Navier–Stokes/Cahn–Hilliard
discontinuous Galerkin (DG) flow solver method. The model poses the Cahn–Hilliard …
discontinuous Galerkin (DG) flow solver method. The model poses the Cahn–Hilliard …
Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D
special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume …
special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume …
Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes
We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for
ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi …
ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi …
High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics
This paper develops the high-order accurate entropy stable (ES) finite difference schemes
for the shallow water magnetohydrodynamic (SWMHD) equations. They are built on the …
for the shallow water magnetohydrodynamic (SWMHD) equations. They are built on the …