Extended Eulerian SPH and its realization of FVM

TL;DR

This paper extends Eulerian SPH with new techniques to match the accuracy and efficiency of finite volume methods, enabling rigorous comparison and potential meshless CFD solutions.

Contribution

It introduces extensions to Eulerian SPH, including particle relaxation, kernel correction, and dissipation limiters, making it equivalent to FVM for accurate CFD simulations.

Findings

Eulerian SPH extensions improve numerical accuracy.

The method achieves equivalence with FVM.

Implementation within SPHinXsys enables direct comparison.

Abstract

Eulerian smoothed particle hydrodynamics (Eulerian SPH) is considered as a potential meshless alternative to a traditional Eulerian mesh-based method, i.e. finite volume method (FVM), in computational fluid dynamics (CFD). While researchers have analyzed the differences between these two methods, a rigorous comparison of their performance and computational efficiency is hindered by the constraint related to the normal direction of interfaces in pairwise particle interactions within Eulerian SPH framework. To address this constraint and improve numerical accuracy, we introduce Eulerian SPH extensions, including particle relaxation to satisfy zero-order consistency, kernel correction matrix to ensure first-order consistency and release the constraint associated with the normal direction of interfaces, as well as dissipation limiters to enhance numerical accuracy and these extensions make Eulerian SPH rigorously equivalent to FVM. Furthermore, we implement mesh-based FVM within SPHinXsys, an open-source SPH library, through developing a parser to extract necessary information from the mesh file which is exported in the MESH format using the commercial software ICEM. Therefore, these comprehensive approaches enable a rigorous comparison between these two methods.