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 …
Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
Abstract Fisher and Carpenter (2013)[12] found a remarkable equivalence of general
diagonal norm high-order summation-by-parts operators to a subcell based high-order finite …
diagonal norm high-order summation-by-parts operators to a subcell based high-order finite …
Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy
cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and …
cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and …
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
J Chan - Journal of Computational Physics, 2018 - Elsevier
High order methods based on diagonal-norm summation by parts operators can be shown
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …
[HTML][HTML] A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics
We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …
On thermodynamically compatible finite volume schemes for continuum mechanics
In this paper we present a new family of semidiscrete and fully discrete finite volume
schemes for overdetermined, hyperbolic, and thermodynamically compatible PDE systems …
schemes for overdetermined, hyperbolic, and thermodynamically compatible PDE systems …
[HTML][HTML] A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
This work focuses on the accuracy and stability of high-order nodal discontinuous Galerkin
(DG) methods for under-resolved turbulence computations. In particular we consider the …
(DG) methods for under-resolved turbulence computations. In particular we consider the …
High order entropy preserving ADER-DG schemes
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …
Summation-by-parts operators for correction procedure via reconstruction
The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is
a framework of high order methods for conservation laws, unifying some discontinuous …
a framework of high order methods for conservation laws, unifying some discontinuous …
On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows
In this paper we propose a new reformulation of the first order hyperbolic model for unsteady
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …