Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: Triangular elements

Alireza Mazaheri (1) , Chi-Wang Shu (2) , Vincent Perrier (3, 4)

1 LaRC - NASA Langley Research Center [Hampton]
2 Brown University
3 CAGIRE - Computational AGility for internal flows sImulations and compaRisons with Experiments
4 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Two new classes of compact weighted essentially nonoscillatory (WENO) polynomial limiters are presented for second-, third-, fourth-, and fifth-order discontinuous Galerkin (DG) schemes on irregular simplex elements. The presented WENO-DG procedures are extensions of the high-order WENO finite-volume and finite-difference schemes of Zhu and Shu (2017) [25], (2019) [26] to high-order unstructured DG schemes. A compact positivity preserving limiter is applied to the solutions to ensure pressure and density remain within physical ranges at all time. It is then verified that the bounded WENO-DG maintains the formal order of accuracy of the underlying DG schemes in the smooth regions. The performance of the proposed WENO-DG is also demonstrated with inviscid test cases including the classical Riemann problems, shock-turbulence interaction, scramjet, blunt body flows, and the double Mach Reflection problems.

Mots clés: CWENO; Unstructured meshes; High-order DG; Positivity-preserving; Riemann problem Shu-Osher

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Alireza Mazaheri, Chi-Wang Shu, Vincent Perrier. Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: Triangular elements. Journal of Computational Physics, 2019, 395, pp.461-488. ⟨10.1016/j.jcp.2019.06.023⟩. ⟨hal-02321400⟩