A central moments-based lattice Boltzmann scheme for shallow water equations

In this paper, we explore the possibility to derive an original lattice Boltzmann scheme for solving shallow water equations. Specifically, it is proposed to decompose the collision operator by means of a non-orthogonal basis of central moments which relax independently to a discrete equilibrium. Our method is strictly consistent with the BGK operator, as the latter is recovered exactly if all the moments relax with a common frequency. The methodology is validated against five well-consolidated established benchmark problems, showing very good agreement. Moreover, it possesses very high properties in terms of stability.