Shallow Water Models for Efficiently Visualizing Fluid Flow in Complex Topography Areas

Numerous serious game applications require the visualization of fluid flow that contains information about flow depth and velocity in wet/dry complex topography areas. Fluid flow visualization based on the numerical solutions of shallow water equations (SWEs) in wet/dry areas remains a challenging problem at present, because most methods are numerically unstable. In this work, we propose a stable and efficient strategy for visualizing fluid flow in various topography areas in the wet/dry domain. In the proposed framework, the visualization covers flow depth and velocity. First, we transform the commonly used conservative SWE model into the proposed non-conservative SWE model. Second, we create an algorithm based on the discretization scheme of the proposed model. The algorithm involves few numerical operations, and is stable and accurate. Finally, we verify the results by comparing them with analytical solutions and with the solutions of the conservative model. According to the numerical results, the solution of the proposed model is close to the analytical solutions, and the proposed model can successfully visualize fluids in complex topography areas in wet or wet/dry conditions.