Shallow water simulation based on SPH with irregular simulation domains

Abstract

We propose a shallow water simulation in a Lagrangian way. Smoothed particle hydrodynamic (SPH) is used to solve shallow water equation by which we avoid discretization of the whole simulation domain and get an easy handling of sparse and irregular simulation domains. In contrast to the Eulerian methods in the context of shallow water equations much less attention has been paid to the Lagrangian simulation methods. Therefore many problems remained unsolved and prevented a practical use of Lagrangian shallow water simulation in computer graphics. We concentrate on several issues connected to the simulation. First, we increase the accuracy of the smoothed particle hydrodynamics approximation by applying a correction to the kernel function used in the simulation. Second, we introduce a novel boundary handling algorithm which can handle arbitrary boundary domains. Even irregular and complicated boundaries pose no 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 be easily integrated into the smoothed particle hydrodynamics framework.Computational fluid dynamics has been a popular research area in computer graphics for many years. The most work has been done in the field of 3-dimensional fluid simulation. One of the most widely used approaches is the use of shallow water equations (SWE), which are the simplified version of Navier-Stokes equations for an inviscid 2D fluid flow.The SWE are usually solved in Eulerian way using a grid, but they are not suitable for irregular domains which are not aligned with the grid. In this paper we propose the shallow water simulation in Lagrangian way to avoid discretization of the whole simulation domain and get an easier handling of complicated boundary domains. The novelty is that we utilize smoothed particle hydrodynamics (SPH) to solve the SWE. There is the list of problems to which the proposed solution provides answers:• The use of SPH results in inaccurate evaluation of quantities, especially in areas near boundaries because of particle deficiency. We increase the accuracy by applying a correction to the kernel functions used in the simulation.• The existing methods for boundary handling are difficult to set up correctly. Their use in the handling of irregular boundaries is also problematic because of computational complexity. We propose a novel boundary handling for SPH-based shallow water simulation handling boundary domains with arbitrary complexity.• Achieving flat fluid surface is problematic because of irregular fluid sampling. We propose a new method producing flat fluid surface using the fluid height.