3 papers
math.NA2025
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…
math.NA2024
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…
math.NA2024
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…