A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta discontinuous Galerkin methods for unstructured meshes

TL;DR

This paper extends a compact subcell WENO limiting strategy for Runge-Kutta discontinuous Galerkin methods from structured to unstructured meshes, enhancing stability and accuracy in complex geometries.

Contribution

It generalizes the CSWENO limiting strategy to unstructured triangular meshes, allowing broader application in computational fluid dynamics.

Findings

Effective limiting on unstructured meshes demonstrated

High-order accuracy maintained in test cases

Improved stability in discontinuous Galerkin methods

Abstract

In this paper, we generalize the compact subcell weighted essentially non oscillatory (CSWENO) limiting strategy for Runge-Kutta discontinuous Galerkin method developed recently by us in 2021 for structured meshes to unstructured triangular meshes. The main idea of the limiting strategy is to divide the immediate neighbors of a given cell into the required stencil and to use a WENO reconstruction for limiting. This strategy can be applied for any type of WENO reconstruction. We have used the WENO reconstruction proposed by Zhu and Shu in 2019 and provided accuracy tests and results for two-dimensional Burgers' equation and two dimensional Euler equations to illustrate the performance of this limiting strategy.