Lattice Boltzmann methods for shallow water flow applications

Abstract

SUMMARYWe apply the lattice Boltzmann (LB) method for solving the shallow water equations with source terms such as the bed slope and bed friction. Our aim is to use a simple and accurate representation of the source terms in order to simulate practical shallow water flows without relying on upwind discretization or Riemann problem solvers. We validate the algorithm on problems where analytical solutions are available. The numerical results are in good agreement with analytical solutions. Furthermore, we test the method on a practical problem by simulating mean flow in the Strait of Gibraltar. The main focus is to examine the performance of the LB method for complex geometries with irregular bathymetry. The results demonstrate its ability to capture the main flow features.

Lattice Boltzmann Simulation for Shallow Water Flow Applications

“…A recirculating flow region is also detected on the top eastern exits of the Strait near Algeciras. Similar flow behaviours have been also reported in Almazán et al (1988); González & Sánchez-Arcilla (1995); Thömmes et al (2007).…”

“…The results for the diurnal K 1 tidal wave are presented in Thömmes et al (2007). The results at four different times using the corresponding time period of each tide are displayed.…”

“…The idea of this chapter will be to give the reader a self-contained introduction of the developments and the implementation of the shallow water lattice Boltzmann approach. In this chapter the lattice Boltzmann method will be applied to the simulation of depth-averaged models in flow hydraulics and dispersion Banda et al (2009); Klar et al (2008); ;Thömmes et al (2007). It can be pointed out that the shallow water equations referred to in this discussion are viscous and also account for the effects of bed slope, bed friction, Coriolis forces and wind stresses in two-dimensional simulations Dellar (2002); Salmon (1999a); Zhou (2002).…”

“…The LB method has been successfully adopted to simulate shallow water equations which describe wind-driven ocean circulation Salmon (1999a); Zhong et al (2005), to model three-dimensional planetary geostrophic equations Salmon (1999b), and to study atmospheric circulation of the northern hemisphere with ideal boundary conditions Feng et al (2002). In Klar et al (2008); Thömmes et al (2007), a practical study of the LBM for shallow water flows and pollutant dispersion by tidal flow problems in complex geometry and irregular bathymetry was presented. The bathymetry is given either by an analytical function or by data points in a two-dimensional domain.…”

Validation of the GPU-Accelerated CFD Solver ELBE for Free Surface Flow Problems in Civil and Environmental Engineering

“…Depth-averaged LBM was successfully applied to a variety of illustrative benchmark problems, including wave run-up on a sloping beach [34], applications featuring bed slope and friction terms [35], wind-and density-driven circulation over irregular bathymetry [36] and tank sloshing examples [37]. While the predictive agreement with traditional methods was generally good, LBM run-times were always very competitive.…”