Second-order force scheme for lattice Boltzmann model of shallow water flows

Abstract

ABSTRACTA force scheme of second-order accuracy in both time and space has been introduced into the lattice Boltzmann model for shallow water equations. The scheme is tested within the single relaxation framework by using a one-dimensional steady flow over a bump, two one-dimensional dam-break flows and a two-dimensional unsteady dam-break flow. It is found that this second-order force scheme can improve the computational accuracy in time compared with the previous force treatment in the lattice Boltzmann model for shallow water. Moreover, the scheme can be also incorporated in the multiple-relaxation-time models.