Water-balanced inlet and outlet boundary conditions of the lattice Boltzmann method for shallow water equations

Abstract

Conservation of mass or water balance is important for the simulation of shallow water projects. The traditional treatment of discharge and water level boundary conditions ignores it in the lattice Boltzmann model for shallow water equations (LABSWE). In this paper, we introduced the water balance equation at these boundary conditions and proposed a universal treatment for the straight boundary of any direction. Six schemes on the unknown particle distribution functions (PDFs) at boundary lattices for given macroscopic quantities (h,u,v) were compared in terms of accuracy and stability, and the nonequilibrium extrapolation (NEQ) scheme and full link nonequilibrium extrapolation (Ful-NEQ) scheme were finally adopted in the proposed treatment. The numerical tests show that the proposed treatment fully satisfies the specified boundary conditions and conservation of mass. Moreover, the distribution of the velocities at the boundaries is consistent along downstream which can reduce the artificial influence length of the boundary.