# An efficient, open source, iterative ISPH scheme

## TL;DR

This paper introduces a simple, robust, and efficient open-source iterative ISPH scheme suitable for CPU and GPU implementation, featuring a matrix-free approach and novel boundary condition handling, demonstrated through various benchmarks.

## Contribution

The paper presents a new iterative, matrix-free ISPH method that improves boundary conditions and is easily implementable on GPUs, with open-source code and reproducible results.

## Key findings

- The method is fast and GPU-compatible.
- It maintains accuracy comparable to existing approaches.
- It demonstrates robustness across multiple benchmark problems.

## Abstract

In this paper a simple, robust, and general purpose approach to implement the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is proposed. This 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. This formulation enables the use of solid wall boundary conditions from the weakly-compressible SPH schemes. The method is fast and runs on GPUs without the need for complex integration with sparse linear solvers. We show that this approach is sufficiently accurate and yet efficient compared to other approaches. 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.