Asymmetric lattice Boltzmann model for shallow water flows

•Definition of an asymmetric lattice Boltzmann scheme based on a Galilean transformation.•Proofs for the convergence and order of convergence.•Stability analysis for the asymmetric scheme.•Numerical validations for the sub-critical/super-critical transition. We consider a Galilean transformation of the lattice Boltzmann model for shallow water flows. In this new reference frame, the velocity lattice is asymmetrical but it is possible to simulate flows with Froude number larger than 1 and to model the transition from a torrential to a fluvial regime.