Enhancement of the LABSWE for shallow water flows

In the lattice Boltzmann method for the shallow water equations (LABSWE), the force term involves the first order derivative related to a bed slope, which has to be determined using the centred scheme for an accurate solution. However, such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice Boltzmann method. This paper shows how to remove this drawback from the LABSWE by incorporating the bed level into the lattice Boltzmann equation in a consistent manner with the lattice Boltzmann approach. Three numerical tests have been presented to verify the proposed method.