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 …
[HTML][HTML] On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
We use the framework of upwind summation-by-parts (SBP) operators developed by
Mattsson (2017, doi: 10.1016/j. jcp. 2017.01. 042) and study different flux vector splittings in …
Mattsson (2017, doi: 10.1016/j. jcp. 2017.01. 042) and study different flux vector splittings in …
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
H Ranocha, GJ Gassner - Communications on Applied Mathematics and …, 2021 - Springer
Recently, it was discovered that the entropy-conserving/dissipative high-order split-form
discontinuous Galerkin discretizations have robustness issues when trying to solve the …
discontinuous Galerkin discretizations have robustness issues when trying to solve the …
Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: Applications to the Euler equations with gravity
In this work a non-conservative balance law formulation is considered that encompasses the
rotating, compressible Euler equations for dry atmospheric flows. We develop a semi …
rotating, compressible Euler equations for dry atmospheric flows. We develop a semi …
Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics
We develop error-control based time integration algorithms for compressible fluid dynamics
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
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 …
summation by parts operators and flux differencing to achieve kinetic energy preservation or …
Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics
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 …
method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto …
Energy stability of explicit Runge--Kutta methods for nonautonomous or nonlinear problems
H Ranocha, DI Ketcheson - SIAM Journal on Numerical Analysis, 2020 - SIAM
Many important initial value problems have the property that energy is nonincreasing in time.
Energy stable methods, also referred to as strongly stable methods, guarantee the same …
Energy stable methods, also referred to as strongly stable methods, guarantee the same …
Optimized filters for stabilizing high-order large eddy simulation
M Hamedi, BC Vermeire - Computers & Fluids, 2022 - Elsevier
Abstract High-order Flux Reconstruction (FR) schemes can be used to simulate unsteady
turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) …
turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) …
Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws
The paper describes the construction of entropy-stable discontinuous Galerkin difference
(DGD) discretizations for hyperbolic conservation laws on unstructured grids. The …
(DGD) discretizations for hyperbolic conservation laws on unstructured grids. The …