Enhancement of δ-SPH for ocean engineering applications through incorporation of a background mesh scheme

Abstract

The improved Smoothed Particle Hydrodynamics (SPH) method with numerical diffusive terms, which is referred to as δ-SPH, has been widely applied into the studies of engineering problems, especially in the fields of ocean and coastal engineering. Nonetheless, there are still some drawbacks associated with δ-SPH model as in case of other particle methods. These drawbacks correspond to presence of unphysical pressure noise as well as imprecise satisfaction of dynamic free-surface boundary condition in numerical simulations. Through derivation and implementation of a so-called Background Mesh (BM) scheme and enforcing the spatial continuity of calculated source term of pressure equation (Equation of State; EOS), we present enhancements for δ-SPH in providing a more accurate pressure field as well as a more precise reproduction of free-surface. The enhancing effects of the newly proposed δ-SPH+BM are portrayed through several ocean engineering-related test cases including dam break and violent sloshing flows in both two and three dimensions. The incorporation of BM scheme is shown to result in enhanced calculation of pressure field as well as improved satisfaction of dynamic free-surface boundary condition as a consequence of enhanced density and pressure fields.