A Second-Order, Variable-Resolution, Weakly-Compressible Smoothed Particle Hydrodynamics Scheme

TL;DR

This paper introduces a novel second-order convergent adaptive refinement scheme for weakly-compressible SPH, enabling more accurate and efficient fluid flow simulations with dynamic resolution adjustments.

Contribution

It presents the first second-order convergent adaptive refinement strategy combined with a weakly-compressible SPH scheme, validated through systematic testing.

Findings

Achieved second-order convergence in SPH simulations.

Validated the scheme with Taylor-Green vortex and flow past a cylinder.

Demonstrated improved accuracy and adaptability in fluid flow modeling.

Abstract

The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp gradients in the flow have also been developed. However, most of the SPH schemes in the literature are not second-order convergent (SOC). Both second-order convergence and adaptive resolution are considered grand challenge problems in the SPH community. In this paper, we propose, for the first time, a second-order convergent (SOC) adaptive refinement strategy along with a SOC weakly-compressible SPH scheme. We employ the method of manufactured solutions to systematically develop the scheme and validate the solver. We demonstrate the order of convergence of the entire scheme using the Taylor-Green vortex problem and then go on to demonstrate the applicability of the method to simulate flow past a circular cylinder.