Multi-dimensional Limiting Process for Two-and Three-dimensional Flow Physics Analyses

Abstract

In this paper, we extend the idea of MLP to three-dimensional space and present the multi-dimensional limiting process for three-dimensional flow. 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 obtain nonoscillatory shock profile even in multiple dimension, which results in very good convergence characteristic. Furthermore, while maintaining the oscillation-free attribute, we can achieve an enhancement of solution accuracy by combining the MLP with high-order polynomial interpolation.