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The stability of Lattice Boltzmann Equations modelling Shallow WaterEquations in the special case of reduced gravity is investigated theoretically.A stability notion is defined as applied in incompressible Navier-Stokesequations in Banda, M. K., Yong, W.- A. and Klar, A: A stability notion forlattice Boltzmann equations. SIAM J. Sci. Comput. {\bf 27(6)}, 2098-2111(2006). It is found that to maintain stability a careful choice of the value ofthe reduced gravity must be made. The stability notion is employed toinvestigate different shallow water lattice Boltzmann Equations. Results aretested using the Lattice Boltzmann Method for various values of the governingparameters of the flow. It is observed that even for the discrete model thereduced gravity has a significant effect on the stability.

A Stability notion for the viscous Shallow Water Discrete-Velocity Boltzmann Equations