Work

Convergence Analysis of SPH Method on Irregular Particle Distributions for the Poisson Equation

Year: 2026

Type: article

Abstract: . The numerical accuracy of particle-based approximations in smoothed particle hydrodynamics (SPH) is significantly affected by the spatial uniformity of particle distributions, especially for second-order derivatives. This study aims to enhance the accuracy of the SPH method and analyze its convergence with irregular particle distributions. By establishing regularity conditions for particle distributions, we ensure that the local truncation error of traditional SPH formulations, including first and second derivatives, achieves second-order accuracy. Our proposed method, the volume reconstruction SPH method, guarantees these regularity conditions while preserving the discrete maximum principle. Benefiting from the discrete maximum principle, we conduct a rigorous global error analysis in the [Formula: see text]-norm for the Poisson equation with variable coefficients, achieving second-order convergence. Numerical examples are presented to validate the theoretical findings.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1720792

Authors: Zhonghua Qiao, Yifan Wei

Institution: Hong Kong Polytechnic University

Language: English

Topic: Fluid Dynamics Simulations and Interactions

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Chinese Academy of Sciences, Hong Kong Polytechnic University

Awards: G2348527169, G3783665241, G4717327817, G5343386188, G8041059034