A regularized high-order diffusive smoothed particle hydrodynamics scheme without tensile instability

Author:

Michel J.12ORCID,Colagrossi A.12ORCID,Antuono M.1ORCID,Marrone S.1ORCID

Affiliation:

1. CNR-INM, Institute of Marine Engineering, National Research Council of Italy 1 , via di Vallerano 139, Rome 00128, Italy

2. LHEEA Research Department (ECN and CNRS), Ecole Centrale Nantes 2 , 1 Rue de la Noë, BP 92101, Nantes Cedex 3 44321, France

Abstract

In the present work, we derive a novel high-order weakly compressible smoothed particle hydrodynamics scheme based on an accurate approximation of the pressure gradient and on the use of numerical Riemann fluxes. Specifically, a switch between non-conservative and conservative formulations of the pressure gradient is adopted close to the free surface, in order to fulfill the dynamic free-surface boundary condition and, at the same time, prevent the onset of the tensile instability in inner regions of the fluid domain. The numerical diffusion is obtained using Riemann solvers, with reconstruction/limitation of the left and right states derived from the Monotonic Upstream-centered Scheme for Conservation Laws technique. These allow for a high-order convergence rate of the diffusive terms that, for increasing spatial resolutions, results in a low numerical dissipation without tuning parameters. Regular particle distributions, which are crucial for the model accuracy, are obtained thanks to recent improvements in Particle Shifting Techniques. These are taken into account within the constitutive equations through a quasi-Lagrangian formalism. The energy balance of such a non-conservative formulation is derived, and an in-depth analysis of the term contributing to numerical dissipation is performed. The numerical investigation is carried out on several problems, illustrating the advantages of the present scheme with respect to conservative formulations. Since the proposed formulation does not intrinsically guarantee momenta conservation, the latter are monitored showing that the overall errors are generally small.

Funder

Siemens Digital Industries Software Chair

Publisher

AIP Publishing

Subject

Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Incompressible δ-SPH via artificial compressibility;Computer Methods in Applied Mechanics and Engineering;2024-02

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