Simple Iterative Incompressible Smoothed Particle Hydrodynamics

In this paper a simple, robust, and general purpose approach to implement the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is proposed. The new approach is well suited for implementation on CPUs and GPUs. The method is matrix-free and uses an iterative formulation to setup and solve the pressure Poisson equation. A novel approach is used to ensure homogeneous particle distributions and improved boundary conditions. The new formulation enables the use of solid wall boundary conditions from the weakly-compressible SPH schemes. The new method is fast and runs on GPUs without the need for complex integration with sparse linear solvers. Several benchmark problems that illustrate the robustness, performance, and wide range of applicability of the new scheme are demonstrated. An open source implementation is provided and the manuscript is fully reproducible.