LATTICE BOLTZMANN METHOD FOR SHALLOW WATER EQUATIONS WITH WET - DRY INTERFACE

Abstract

This research concerns the lattice Boltzmann method (LBM) for shallow water flow problems, especially in wet-dry interfaces, where fluid flows from a wet area to a dry area or vice versa. This problem of wet-dry interfaces is known in literature that causes difficulty for numerical methods, also for the standard LBM, the lattice Boltzmann equations consist of terms that are divided by fluid depth, which is zero at dry lattice. In this study, we implement the LBM based on the idea of using the Taylor’s expansion and Chapman-Enskog procedure to handle dry lattices without any fake assumption purposed by Liu & Zhou, and combine with wet-dry tracking technique to handle this problem. The implementation of the code tested with several numerical examples, which is accurate as compared with other exact solution and results in literature.