Energy balance in quasi-Lagrangian Riemann-based SPH schemes

Abstract

The Smoothed Particle Hydrodynamics (SPH) method suffers from the presence of irregular particle distributions inherent in its Lagrangian nature. A way to circumvent this problem is to consider a quasi-Lagrangian SPH scheme and use a Particle Shifting Technique (PST). In this framework, we include an approximate Riemann solver to represent the particle interaction and obtain two different quasi-Lagrangian Riemann-based SPH schemes: one is a mass-constant SPH model whereas the other is derived from an ALE formalism. These schemes are examined and validated by focusing on their energy balance. In particular, the energy contribution provided by the terms associated to Riemann solver and PST is studied from both a theoretical and numerical point of view. The consistency and the diffusive properties of these energy terms are investigated on test cases involving confined and free-surface flows. Albeit the investigation is performed for a specific Riemann solver and PST, the proposed methodology can be easily extended to other formulations.