Multi-Dimensional Limiting Process for Two-Dimensional Compressible Flows

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 3rd 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, 3rd and 5th order interpolation schemes with MLP, named MLP3 and MLP5, are developed and tested for several real applications, and it is verified that MLP combined with M-AUSMPW+ numerical flux substantially improves accuracy, efficiency and robustness both in continuous and discontinuous flows.