Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids

TL;DR

This paper introduces a modified multi-dimensional limiting process (MLP) with pressure-weighted enhancement to improve shock stability and reduce dissipation on unstructured grids, especially in hypersonic flow simulations.

Contribution

It proposes a novel pressure-weighted MLP limiter combining weak and strict conditions for better stability and accuracy on unstructured grids.

Findings

Enhanced shock stability in hypersonic simulations.

Reduced numerical dissipation in smooth regions.

Improved convergence and contact discontinuity capturing.

Abstract

The basic concept of multi-dimensional limiting process (MLP) on unstructured grids is inherited and modified for improving shock stabilities and reducing numerical dissipation on smooth regions. A relaxed version of MLP condition, simply named as weak-MLP, is proposed for reducing dissipation. Moreover, a stricter condition, that is the strict-MLP condition, is proposed to enhance the numerical stability. The maximum/minimum principle is fulfilled by both the strict- and weak-MLP condition. A differentiable pressure weight function is applied for the combination of two novel conditions, and thus the modified limiter is named as MLP-pw(pressure-weighted). A series of numerical test cases show that MLP-pw limiter has improved stability and convergence, especially in hypersonic simulations. Furthermore, the limiter also shows lower dissipation in regions without significant pressure transition. Therefore, MLP-pw limiter can capture contact discontinuity and expansion accurately.