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

Abstract

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.