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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…
math.NA2024
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…