SPHM: a MATLAB package for Smoothed Particle Hydrodynamics simulations

TL;DR

This paper introduces SPHM, a MATLAB package for Smoothed Particle Hydrodynamics simulations, providing an accessible tool for CFD problems validated through classical benchmarks.

Contribution

The paper presents a MATLAB implementation of SPH inspired by previous FORTRAN code, enabling easier CFD simulations and validation with benchmark problems.

Findings

Successfully simulates shock tube and shear cavity problems

Provides a coherent notation linking equations and code

Offers an accessible MATLAB tool for SPH simulations

Abstract

We present a MATLAB code that implements the Smoothed Particle Hydrodynamics (SPH) method. The paper reviews the continuous Navier-Stokes equations as well as their SPH approximation, adopting a coherent notation that allows to make easy reference to the code. The MATLAB implementation was heavily inspired by the earlier FORTRAN code of G. R. Liu and M. B. Liu, 2003. The code can be used for simple computational fluid dynamics simulations. Two classical benchmark problems are used to validate the algorithm: a one-dimensional shock tube and a two-dimensional shear cavity problem.