Detailed study on the extension of the δ-SPH model to multi-phase flow

• Published in: Computer methods in applied mechanics and engineering 2020-08, Vol.368, p.113189, Article 113189
• Main Authors: Hammani, I., Marrone, S., Colagrossi, A., Oger, G., Le Touzé, D.
• Format: Article
• Language: English
• Subjects: [formula omitted]-SPH model; Air-cushion effects; Continuity equation; Engineering Sciences; Entrapment; Flow-density-speed relationships; Mathematical models; Multi-phase flows; Multiphase flow; Reactive fluid environment; Smoothed Particle Hydrodynamics; Sound; Spatial distribution; Stability; Water impact
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113189

In the present work the multi-phase SPH model presented in Grenier et al. (2009) is considered and extended through the inclusion of a diffusive term in the continuity equation. The latter based on the δ-SPH model of Antuono et al. (2012), allows to improve the evaluation of the pressure field, removing numerical noise and improving also the particles spatial distribution. The time stepping and the choice of the speeds of sound for the different phases are discussed, showing that this choice is driven not only by physical consideration but also by numerical constraints linked to the stability of the scheme. To this aim, comparisons are provided to a Riemann–SPH multi-phase model. In particular we show that the proposed δ-SPH multi-phase solver has a different stability region than its Riemann–SPH counterpart, allowing for bigger time steps for some density and speed of sound ratios, while in other conditions the Riemann–SPH multi-phase model is more convenient. A series of validating tests are carried out over different benchmarks widely used in the SPH literature. As a final test-case the water entry of a corrugated panel involving the entrapment of an air cavity is considered to show how the proposed multi-phase δ-SPH method is able to accurately treat complex water impact events. •An extension of the δ-SPH model to multi-phase flow is presented.•Its connections with previous SPH multi-phase existing model are addressed.•The proposed SPH model can handle multi-phase flow in presence of a free-surface.•Two different derivations are discussed starting from different equations.•Stability of the proposed scheme is investigated in terms of CFL number depending on the density ratio and sound speeds choice.•A series of validating tests of increasing complexities are carried out.