FVM realization in Eulerian SPH: A comparative study within unified codebase

Abstract

Eulerian smoothed particle hydrodynamics (Eulerian SPH) is considered a potential meshless alternative to a traditional Eulerian mesh-based 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 following two challenges: Firstly, the Eulerian SPH framework faces a constraint related to the normal direction of interfaces in pairwise particle interactions, which prevents achieving an equivalent algorithm of FVM; Secondly, there is no unified solver available that can be applied to both Eulerian SPH and FVM methods. To address the former constraint, this paper implements a certain form of Eulerian SPH method, where a kernel gradient correction is introduced to release the constraint. To address the latter constraint, the paper realizes the mesh-based FVM within an open-source SPH library using a shared solver, i.e. single algorithm for two methods, through developing a parser that extracts necessary information from the “.msh” format file exported from a commercial pre-processing tool, ICEM (Integrated Computer Engineering and Manufacturing). Several 2D and 3D numerical simulations using both methods within a unified codebase demonstrate that compared to the mesh-based FVM, the Eulerian SPH achieves smoother results and, when using a high-order kernel, a faster convergence rate, but at the cost of lower computational efficiency.