Energy balance in the δ-SPH scheme

• Published in: Computer methods in applied mechanics and engineering 2015-06, Vol.289, p.209-226
• Main Authors: Antuono, M., Marrone, S., Colagrossi, A., Bouscasse, B.
• Format: Article
• Language: English
• Subjects: Balancing; Computational fluid dynamics; Computer simulation; Dissipation; Energy balance; Engineering Sciences; Fluid flow; Mathematical analysis; Mathematical models; Meshless methods; Numerical dissipation; Particle methods; Smoothed particle hydrodynamics; Validation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2015.02.004

An in-depth analysis of the energy balance in the δ-SPH model has been carried on. In comparison to the standard SPH scheme, the mechanical energy equation of the δ-SPH variant is characterized by a further term that is generally dissipative and is related to the diffusive operator inside the continuity equation. The behaviour and the structure of such a term have been studied in detail and a number of specifically conceived test cases have been considered, highlighting that the dissipative term is generally small and it mainly acts when spurious high-frequency acoustic components are excited. In spite of such a dissipation mechanism, the δ-SPH appears more accurate than the standard SPH scheme even in simulating inviscid fluids. •The theoretical analysis of the energy balance in the δ-SPH model has been carried on.•Inviscid free-surface problems have been used to study the model dissipation.•δ-SPH numerical dissipation mainly acts on spurious high-frequency acoustic components.•Higher accuracy of the solutions with respect to the standard SPH model is observed.•δ-SPH prevents numerical accumulation from mechanical energy to compressible energy.