How to train your solver: Verification of boundary conditions for smoothed particle hydrodynamics

TL;DR

This paper verifies the convergence of boundary condition implementations in WCSPH simulations using manufactured solutions, proposing a convergent scheme and demonstrating its accuracy on flow past a cylinder.

Contribution

It introduces a systematic verification method for boundary conditions in WCSPH and proposes a convergent scheme for improved simulation accuracy.

Findings

Validated boundary condition implementations using MMS

Proposed a convergent WCSPH scheme

Demonstrated scheme accuracy with flow past a cylinder

Abstract

The weakly compressible smoothed particle hydrodynamics (WCSPH) method has been employed to simulate various physical phenomena involving fluids and solids. Various methods have been proposed to implement the solid wall, inlet/outlet, and other boundary conditions. However, error estimation and the formal rates of convergence for these methods have not been discussed or examined carefully. In this paper, we use the method of manufactured solution (MMS) to verify the convergence properties of a variety of commonly employed of various solid, inlet, and outlet boundary implementations. In order to perform this study, we propose various manufactured solutions for different domains. On the basis of the convergence offered by these methods, we systematically propose a convergent WCSPH scheme along with suitable methods for implementing the boundary conditions. We also demonstrate the accuracy of the proposed scheme by using it to solve the flow past a circular cylinder. Along with other recent developments in the use of adaptive resolution, this paves the way for accurate and efficient simulation of incompressible or weakly-compressible fluid flows using the SPH method.