Investigations on a high order SPH scheme using WENO reconstruction

• Published in: Journal of computational physics 2023-03, Vol.477, p.111889, Article 111889
• Main Authors: Vergnaud, A., Oger, G., Le Touzé, D.
• Format: Article
• Language: English
• Subjects: Arbitrary Lagrangian Eulerian (ALE); High order convergence; Moving-Least-Squares (MLS); Riemann solvers; Smoothed Particle Hydrodynamics (SPH); Weighted Essentially Non-Oscillatory (WENO)
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.111889

Theoretically, a 2nd order convergence can be reached with the Smoothed Particle Hydrodynamics (SPH) method. However, depending on the spatial disorder of particles, the order of convergence observed in practice can be lower than one. In this paper, a methodology is proposed for the reconstruction of high order numerical fluxes in Riemann-SPH formulations for weakly-compressible flows, so as to increase the global order of convergence of the scheme. This methodology is based on the use of one-dimensional Weighted Essentially Non-Oscillatory (WENO) reconstructions applied at each pair of interacting particles, and each 1D WENO stencil is completed using Moving-Least-Squares (MLS) reconstructions. It is shown that a 6th order convergence can be reached with the proposed SPH-WENO scheme. The gain in accuracy and convergence properties of this scheme is shown and discussed through its application to various one-dimensional and two-dimensional test cases. In particular, the influence of the number of neighbor particles and of the spatial particle disorder is studied. Finally, it is shown that the proposed high-order SPH scheme provides a better accuracy to CPU time ratio than usual Riemann-SPH schemes. The treatment of boundary conditions on rigid walls with the proposed scheme is also discussed. •A new high-order method is proposed for the reconstruction of fluxes in Riemann-SPH.•A theoretical analysis is performed to determine the convergence rate of this method.•Various properties of this scheme are discussed through several test cases.