Author(s): M. D. Green; J. Peiro; R. Vacondio

Linked Author(s):

Keywords: Smoothed particle hydrodynamics; Godunov methods; δ-SPH formulation; Riemann solver; Free-surface flows

Abstract: A novel formulation for the diffusive term in the continuity equation is proposed to improve the consistency of Smoothed Particle Hydrodynamic (SPH) weakly compressible scheme avoiding the introduction of empirical parameters. The diffusive term is derived using an approximate Riemann solver with MUSCL reconstruction. In SPH numerical schemes based on the so-called weakly compressible approach stability is obtained by means of a diffusive term in the momentum equation, which has to be tuned by means of an artificial viscosity parameter. This approach has been extensively used in literature also for practical engineering applications, but it is affected by spurious oscillations that appears in the pressure field. Different authors have suggested to introduce an additional diffusive term in the continuity equation to improve the accuracy, Antuono et al. proposed the so-called δ-SPH formulation which can guarantee consistency also near the free surface. In this approach however, the amount of diffusion introduced in the continuity equation is controlled by means of a coefficient which is unique for all particles and has to be adjusted by the user. In Godunov SPH (GSPH) methods each particle to particle interaction is treated as a Riemann problem to intrinsically introduce diffusion avoiding empirical parameters. However, GSPH formulations applied to free-surface flow, and adopting the weakly compressible assumption, are too dissipative and do not allow to accurately simulate problems with strong free-surface deformation. In the present work we start from the discretization of the continuity equation proposed in the framework of GSPH approach and we demonstrate that it is equivalent to the δ-SPH formulation of Antuono et al. avoiding the introduction of any additional empirical parameters. Results also demonstrate that the proposed method is able to guarantee consistency both inside the fluid and close to the free surface. Furthermore an analysis on several flux limiter functions has been conducted, assessing that the choice of this function is a critical point to guarantee the accuracy of the method.

DOI: https://doi.org/10.3850/978-981-11-2731-1_280-cd

Year: 2018