On the consistency of MPS

TL;DR

This paper analyzes the consistency of the MPS method in reproducing differential operators, compares it with SPH, identifies inconsistency issues in pressure Poisson solutions, and proposes a corrected method with boundary terms, demonstrated on flow problems.

Contribution

It rigorously establishes the relation between MPS and SPH, identifies inconsistency problems, and introduces a corrected MPS method with boundary terms for improved accuracy.

Findings

Identified inconsistency issues in the original MPS method.

Proposed a corrected MPS method with boundary terms.

Validated the corrected method on flow problems.

Abstract

The consistency of Moving Particle Semi-implicit (MPS) method in reproducing the gradient, divergence and Laplacian differential operators is discussed in the present paper. Its relation to the Smoothed Particle Hydrodynamics (SPH) method is rigorously established. The application of the MPS method to solve the Navier-Stokes equations using a fractional step approach is treated, unveiling inconsistency problems when solving the Poisson equation for the pressure. A new corrected MPS method incorporating boundary terms is proposed. Applications to one dimensional boundary value Dirichlet and mixed Neumann-Dirichlet problems and to two-dimensional free-surface flows are presented.