Improvement of Stability of Free-Molecular Type LBM by Using Median Filter

Abstract

The free-molecular type LBM (FMT-LBM) is a new lattice Boltzmann model which can simulate supersonic flows described by the compressible Euler equations. FMT-LBM is superior to the existing LBM and other shock capturing schemes in the following three points: (I) advection term is linear, (II) supersonic flows and non-viscosity flows can be simulated, (III) small oscillations like sound waves can be captured with high resolution. We improve this scheme by using median filter, which is one of the image processing filters, to reduce peculiar numerical oscillations generated in expansion waves of high speed flows. Numerical results agree well with the corresponding theories and other numerical methods and show that this scheme can capture shock waves sharply like various shock capturing methods.