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

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.