Improved density diffusion term for long duration wave propagation

This paper presents the applicability of a new density diffusion term recently proposed by Fourtakas et al. [Computers & Fluids, 2019] for the weakly compressible smoothed particle hydrodynamics scheme as part of the DualSPHysics solver. We show that the new density diffusion term is suitable for long duration simulations without the computationally expensive renormalized density gradient usually present in such terms. By using this formulation the higher order terms are computed locally as a hydrostatic density difference that deems the scheme computationally inexpensive. In this study, the diffusion term formulation is shown to reproduce accurately the pressure and velocity field for long duration simulations without any free-surface diffusion or pressure noise. The test cases simulated are a still water (hydrostatic) case, a regular wave generated by a paddle and finally a sloshing tank to demonstrate the applicability of the term with moving boundaries.