A dynamic δ-SPH model: How to get rid of diffusive parameter tuning

• Published in: Computers & fluids Vol. 179; pp. 334 - 355
• Main Authors: Meringolo, Domenico D., Marrone, Salvatore, Colagrossi, Andrea, Liu, Yong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 30.01.2019; Elsevier BV; Elsevier
• Subjects: Compressibility; Computational fluid dynamics; Dam-break flows; Energy dissipation; Energy measurement; Engineering Sciences; Fluids mechanics; Free-surface flows; Large Eddy Simulation; Mathematical models; Mechanics; Parameters; Smoothed Particle Hydrodynamics; Water impacts; δ-SPH; Water impacts; Energy dissipation; δ-SPH; Smoothed Particle Hydrodynamics; Dam-break flows; Large Eddy Simulation; Free-surface flows
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2018.11.012

•Single components of the energy dissipation terms of the δ-SPH scheme are analyzed.•Dissipations related to delta and alpha terms are found to be strictly interdependent.•When parameters are chosen inside a certain range the total dissipation is not affected.•Results are compared with a dynamic δ-SPH which needs no parameter tuning.•The dynamic δ-SPH allows for a good compromise between dissipation and stability. This work aims to clarify some of the dissipation properties observed in the weakly compressible SPH model with artificial diffusive terms, by specifically considering the δ-SPH formulation. The main features of the δ-SPH formulation are the use of two diffusive terms added in the continuity and momentum equations in order to stabilise the scheme. The action of the two artificial diffusive terms can be, in principle, arbitrarily tuned by two coefficients, namely δ and α. Thanks to the particular structure of the weakly-compressible SPH scheme it is possible to measure the energy dissipated by each term separately. Therefore, the effects on the dissipation process when changing δ and α are analysed. It is found that the two components are strictly related and, surprisingly, different sets of coefficients lead in most of the cases to similar amount of total dissipated energy. Further, the results obtained by the δ-SPH formulation are compared with those obtained by a δ-LES-SPH. In the latter δ and α parameters are determined through a turbulence closure model and are, therefore, different for each particle. Within this new scheme the two parameters dynamically change depending on the local and instantaneous flow conditions and are no longer to be regarded as tunable parameters.