Particle-based shallow water simulation for irregular and sparse simulation domains

Abstract

We propose a shallow water simulation using a Lagrangian technique. Smoothed particle hydrodynamics are used to solve the shallow water equation, so we avoid discretization of the entire simulation domain and easily handle sparse and irregular simulation domains. In the context of shallow water equations, much less attention has been paid to Lagrangian simulation methods than to Eulerian methods. Therefore, many problems remained unsolved, which prevents the practical use of Lagrangian shallow water simulations in computer graphics. We concentrate on several issues associated with the simulation. First, we increase the accuracy of the smoothed particle hydrodynamics approximation by applying a correction to the kernel function that is used in the simulation. Second, we introduce a novel boundary handling algorithm that can handle arbitrary boundary domains; even irregular and complicated boundaries do not pose a problem and introduce only small computational overhead. Third, with the increased accuracy, we use the fluid height to generate a flat fluid surface. All the proposed methods can easily be integrated into the smoothed particle hydrodynamics framework.