A Boltzmann approach to shallow water flows

The Boltzmann distribution function is employed to generate the mass, momentum, and energy, equations for shallow water flow in one- and two-dimensional systems. The expansion of this function in terms of the inverse Reynolds number is shown to allow for inclusion of frictional effects by modeling the importance of higher order terms. Equations are developed for transient and steady state systems. A numerical algorithm that can be implemented to solve the Boltzmann equations to obtain depth and velocity profiles in natural channels and reservoirs are outlined