Performance analysis of high accuracy multi-dimensional limiting process

The conventional limiting process is mostly based on one-dimensional structure, which cannot keep monotonic features of quantities under conditions of multi-dimensional discontinuities, leading to non-physical oscillations. In order to overcome the structure defects of the conventional methods, multi-dimensional limiting process (MLP) is a high accuracy limiter whose basic idea is that the vertex values interpolated at a grid point should be within the maximum and minimum cell-average values of neighboring cells through multi-dimensional correction. The major advantage of MLP is to avoid multi-dimensional oscillatory effectively and ensure solving accuracy. According to a set of test cases including one-dimensional shock tube, non-viscous vortex flow and shock boundary-layer interaction, the performance of MLP with high accuracy was analyzed, it is verified that third-order MLP can avoid multi-dimensional oscillatory effectively both in continuous and discontinuous area. Compared with higher-order WENO (weighted essentially non-oscillatory) schemes, the third-order MLP maintains several desirable characteristics, such as simple algorithm, simple implementation, improving the solving accuracy, monotonicity and convergence. For these properties, MLP can be applied to study complicated flow in engineering and scientific research, and is expected to have a bright application future.