A Modified Lax-Friedrichs Method for the Shallow Water Equations

Abstract

In this paper, we present a simple modified Lax-Friedrichs method for the numerical solution of shallow water equations. In the proposed method, we approximate the next-step value by applying the Lax-Friedrichs method at the half grid of space. The method was applied to simulate the wave propagation at a resting pool for non-flat topography. Based on the simulation, the proposed method is more accurate in terms of fulfilling the conservation law than the Lax-Friedrichs method and it shows good agreement with the steady analytical solution.