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 …

Relaxation Runge--Kutta methods: Fully discrete explicit entropy-stable schemes for the compressible Euler and Navier--Stokes equations

H Ranocha, M Sayyari, L Dalcin, M Parsani… - SIAM Journal on …, 2020 - SIAM
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 …

High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: Scalable …

M Parsani, R Boukharfane, IR Nolasco… - Journal of …, 2021 - Elsevier
This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …

On the robustness and performance of entropy stable collocated discontinuous Galerkin methods

D Rojas, R Boukharfane, L Dalcin… - Journal of …, 2021 - Elsevier
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable
simulations, for both analysis and design optimization purposes, requires transformational …

Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations

H Ranocha, L Dalcin, M Parsani - Computers & Mathematics with …, 2020 - Elsevier
Recently, relaxation methods have been developed to guarantee the preservation of a
single global functional of the solution of an ordinary differential equation. Here, we …

[HTML][HTML] Nonlinear boundary conditions for initial boundary value problems with applications in computational fluid dynamics

J Nordström - Journal of Computational Physics, 2024 - Elsevier
We derive new boundary conditions and implementation procedures for nonlinear initial
boundary value problems (IBVPs) with non-zero boundary data that lead to bounded …

Entropy stable h/p-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier–Stokes equations

DCDR Fernández, MH Carpenter, L Dalcin… - SN Partial Differential …, 2020 - Springer
In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey
Fernández et al.(2019) for the compressible Euler and Navier–Stokes equations on …

High order discontinuous Galerkin simulation of hypersonic shock-boundary layer interaction using subcell limiting approach

VD Potluri, BP Puranik, KVR Bodi - Journal of Computational Physics, 2023 - Elsevier
Numerical simulation of shock-boundary layer interactions in the hypersonic regime has for
long been a challenge, plagued by high sensitivity of the surface predictions to grid and …

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

J Chan, Y Lin, T Warburton - Journal of Computational Physics, 2022 - Elsevier
Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a
semi-discrete entropy inequality under appropriate boundary conditions. In this work, we …

Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier–Stokes equations

AR Winters, DA Kopriva, GJ Gassner… - Efficient High-Order …, 2021 - Springer
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 …