Multi-Dimensional Limiting Process for Three Dimensional Compressible Flows

Abstract

In this paper, we derive a limiting condition for three-dimensional compressible flows and present the multi-dimensional limiting process for three dimensions. The basic idea of the multi-dimensional limiting condition is that the vertex values interpolated at a grid point should be within the maximum and minimum cell-average values of neighboring cells for the monotonic distribution. By applying the MLP (Multi-dimensional Limiting Process), we can achieve monotonic characteristic, which results in the substantial enhancement of solution accuracy and convergence behavior.