A new approach of a limiting process for multi-dimensional flows

An enhanced Multi-dimensional Limiting Process (e-MLP) is developed for the accurate and efficient computation of multi-dimensional flows based on the Multi-dimensional Limiting Process (MLP). The new limiting process includes a distinguishing step and an enhanced multi-dimensional limiting process. First, the distinguishing step, which is independent of high order interpolation and flux evaluation, is newly introduced. It performs a multi-dimensional search of a discontinuity. The entire computational domain is then divided into continuous, linear discontinuous and nonlinear discontinuous regions. Second, limiting functions are appropriately switched according to the type of each region; in a continuous region, there are no limiting processes and only higher order accurate interpolation is performed. In linear discontinuous and nonlinear discontinuous regions, TVD criterion and MLP limiter are respectively used to remove oscillation. Hence, e-MLP has a number of advantages, as it incorporates useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. This new limiting process was applied to numerous test cases including one-dimensional shock/sine wave interaction problem, oblique stationary contact discontinuity, isentropic vortex flow, high speed flow in a blunt body, planar shock/density bubble interaction, shock wave/vortex interaction and, particularly, magnetohydrodynamic (MHD) cloud-shock interaction problems. Through these tests, it was verified that e-MLP substantially enhances the accuracy and efficiency with both continuous and discontinuous multi-dimensional flows.