Overcoming excessive numerical dissipation in SPH modeling of water waves

Abstract

Excessive nonphysical energy dissipation is a problem in Smoothed Particle Hydrodynamics (SPH) when modeling free surface waves, resulting in a significant decrease in wave amplitude within a few wavelengths for progressive waves. This dissipation poses a limitation to the physical scale of SPH applications involving water wave propagation. Some prior solutions to this wave decay problem rely on elaborate schemes, which require a complex, or non-straightforward, implementation. Other approaches demand large smoothing lengths that lead to longer simulation times and potential degradation of the results. In this work we present an approach based on a kernel gradient correction. Our scheme is fully 3D and solves the main known drawbacks of kernel gradient corrections, such as instabilities and lack of momentum conservation. The latter is ensured by adopting an averaged correction matrix, so as to conserve reciprocity during particle interactions. We test our model with a standing wave in a basin and a progressive wave train in a wave tank, and in both cases no nonphysical decay occurs. A comparison to an approach based on large smoothing factors shows advantages both in quality of the results and simulation time.