A simplified and stable lattice Boltzmann shallow water model

Abstract

In this article, a simplified and stable (S&S) lattice Boltzmann shallow water (LBMSW) model is introduced. In past articles, several types of LBMSW models based on different collision operators were studied, such as BGK-SRT, raw moments MRT, central moments MRT, or cumulants MRT, and allowed to reach interesting performances in terms of numerical stability, accuracy and execution time. But no simplified and stable model for LBMSW have been published yet, such as those for gaseous cases. In this article, such a method is introduced for shallow water problems and numerical performances are studied. For numerical performances evaluation, dam break and circular dam break benchmarks using S&S will be presented and compared to other methods.