Localized kernel gradient correction for SPH simulations of water wave propagation

Basic Smoothed Particle Hydrodynamics (SPH) models exhibit excessive, numerical dissipation in the simulation of water wave propagation. This can be remedied using higher-order approaches such as kernel gradient correction, which introduce additional computational effort. The present work demonstrates, that the higher-order scheme is only required in a limited part of the water wave in order to obtain satisfying results. The criterion for distinguishing particles in need of special treatment from those that do not is motivated by water wave mechanics. Especially for deep water waves, the approach potentially spares large amounts of computational effort. The present paper also proposes a remedy for issues of the kernel gradient correction occurring at the free surface. Satisfying results for the proposed approach are shown for a standing wave in a basin and a progressive wave train in a long wave tank.