Development of a cascaded lattice Boltzmann model for two-layer shallow water flows

Abstract

Many environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multi-layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi-layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi-layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two-layered liquid Lattice-Boltzmann model (CaLB-2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.