High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
CW Shu - Journal of Computational Physics, 2016 - Elsevier
For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …
which arise frequently in computational physics, high order numerical methods, including …
An entropy-stable hybrid scheme for simulations of transcritical real-fluid flows
A finite-volume method is developed for simulating the mixing of turbulent flows at
transcritical conditions. Spurious pressure oscillations associated with fully conservative …
transcritical conditions. Spurious pressure oscillations associated with fully conservative …
On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier–Stokes equations
X Zhang - Journal of Computational Physics, 2017 - Elsevier
We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …
Second-order invariant domain preserving approximation of the Euler equations using convex limiting
A new second-order method for approximating the compressible Euler equations is
introduced. The method preserves all the known invariant domains of the Euler system …
introduced. The method preserves all the known invariant domains of the Euler system …
Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems
We introduce an approximation technique for nonlinear hyperbolic systems with sources that
is invariant domain preserving. The method is discretization-independent provided …
is invariant domain preserving. The method is discretization-independent provided …
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
K Wu, CW Shu - SIAM Review, 2023 - SIAM
Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …
example, the density and pressure are positive for equations of fluid dynamics, and in the …
[PDF][PDF] A brief survey on discontinuous Galerkin methods in computational fluid dynamics
CW Shu - Advances in mechanics, 2013 - lxjz.cstam.org.cn
Discontinuous Galerkin (DG) methods combine features in finite element methods (weak
formulation, finite dimensional solution and test function spaces) and in finite volume …
formulation, finite dimensional solution and test function spaces) and in finite volume …
Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
M Lukáčová-Medvid'ová, P Öffner - Applied Mathematics and Computation, 2023 - Elsevier
In this paper, we present convergence analysis of high-order finite element based methods,
in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts …
in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts …
A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier–Stokes equations
In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …
Stokes equations, with desired properties including high order spatial accuracy …
Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Euler equations. Part I: The one-dimensional …
EJ Ching, RF Johnson, AD Kercher - Journal of Computational Physics, 2024 - Elsevier
In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …