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 …
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 …
Second-order invariant domain preserving approximation of the compressible Navier–Stokes equations
We present a fully discrete approximation technique for the compressible Navier–Stokes
equations that is second-order accurate in time and space, semi-implicit, and guaranteed to …
equations that is second-order accurate in time and space, semi-implicit, and guaranteed to …
Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes
K Wu, CW Shu - Numerische Mathematik, 2019 - Springer
This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and
finite volume methods which provably preserve the positivity of density and pressure for the …
finite volume methods which provably preserve the positivity of density and pressure for the …
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and
Navier-Stokes equations require the positivity of thermodynamic quantities in order to …
Navier-Stokes equations require the positivity of thermodynamic quantities in order to …
A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
We consider a class of time-dependent second order partial differential equations governed
by a decaying entropy. The solution usually corresponds to a density distribution, hence …
by a decaying entropy. The solution usually corresponds to a density distribution, hence …
A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws
We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for
solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes …
solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes …
Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations
K Wu, H Jiang, CW Shu - SIAM Journal on Numerical Analysis, 2023 - SIAM
In the numerical simulation of ideal magnetohydrodynamics (MHD), keeping the pressure
and density always positive is essential for both physical considerations and numerical …
and density always positive is essential for both physical considerations and numerical …
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn–Hilliard–Navier–Stokes system
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving
without losing conservation and accuracy by a postprocessing procedure of solving a …
without losing conservation and accuracy by a postprocessing procedure of solving a …
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 …