Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows: Part II: Multi-dimensional limiting process

Abstract

Through the analysis of conventional TVD limiters, a new multi-dimensional limiting function is derived for an oscillation control in multi-dimensional flows. And, multi-dimensional limiting process (MLP) is developed with the multi-dimensional limiting function. The major advantage of MLP is to prevent oscillations across a multi-dimensional discontinuity, and it is readily compatible with more than third order spatial interpolation. Moreover, compared with other higher order interpolation schemes such as ENO type schemes, MLP shows a good convergence characteristic in a steady problem and it is very simple to be implemented. In the present paper, third and fifth order interpolation schemes with MLP, named MLP3 and MLP5, are developed and tested for several real applications. Through extensive numerous test cases including an oblique stationary contact discontinuity, an expansion fan, a vortex flow, a shock wave/vortex interaction and a viscous shock tube problem, it is verified that MLP combined with M-AUSMPW+ numerical flux substantially improves accuracy, efficiency and robustness both in continuous and discontinuous flows. By extending the current approach to three-dimensional flows, MLP is expected to reduce computational cost and enhance accuracy even further.