5 papers
Efficient Admissible Set Projection in Optimization-based Invariant-Domain-Preserving Limiters for Ideal MHD
Chen Liu, Chi-Wang Shu, Xiangxiong Zhang
Preserving the admissible set of the ideal magnetohydrodynamics (MHD) equations is important not only for producing physically meaningful numerical solutions, but more importantly…
Efficient optimization-based invariant-domain-preserving limiters in solving gas dynamics equations
Chen Liu, Dionysis Milesis, Chi-Wang Shu +1
We introduce effective splitting methods for implementing optimization-based limiters to enforce the invariant domain in gas dynamics in high order accurate numerical schemes. The…
A bound-preserving Runge--Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws
Chen Liu, Zheng Sun, Xiangxiong Zhang
In this paper, we develop bound-preserving techniques for the Runge--Kutta (RK) discontinuous Galerkin (DG) method with compact stencils (cRKDG method) for hyperbolic conservation…
An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker-Planck equations
Chen Liu, Jingwei Hu, William T. Taitano +1
For high-order accurate schemes such as discontinuous Galerkin (DG) methods solving Fokker-Planck equations, it is desired to efficiently enforce positivity without losing conserva…
An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier-Stokes equations
Chen Liu, Gregery T. Buzzard, Xiangxiong Zhang
We consider an optimization based limiter for enforcing positivity of internal energy in a semi-implicit scheme for solving gas dynamics equations. With Strang splitting, the compr…