Comparative Study of a Boltzmann-based Finite Volume and a Lattice Boltzmann Model for Shallow Water Flows in Complex Domains

The Lattice Boltzmann method (LBM) has proved to yield results with accuracy comparable to approaches based on 2D multilayer shallow water equations (MSWE) aimed at simulating gravity currents. The rapid diffusion of the LBM stems from the reduced computational burden required. The handling of complex boundaries is a crucial capability that a numerical method solving the MSWE must exhibit. In this work we show that an approach employing a Finite Volume scheme to solve the Lattice Boltzmann equation (FV-LBE) provides the desired ability for boundary representation at the expense of a reasonable increase in complexity with respect to the LBM approach. In a “time to result” technical framework, the FV-LBE is far superior, this feature being more important for cases where the smallest-to-highest spatial scale ratio to be represented in the simulation decreases.