Improving efficiency of incompressible SPH method using a hybrid kernel function for simulation of free surface flows

Abstract

In this study, a hybrid kernel function including a flat and steep function is introduced to improve efficiency of incompressible SPH method for simulation of free surface flows. The governing equations including the mass and momentum conservations are solved in a Lagrangian form using a two-step fractional method. The solid boundary conditions in which water penetration across the walls is avoided can be imposed in the computations by solving a pressure Poisson equation on the wall particles. This treatment exerts a force on inner fluid particles to repulse these particles accumulating in the vicinity of the walls. Several lines of dummy particles are also placed outside the walls in the conventional SPH method. Arrangement of these particles can be difficult for complex boundary shapes and 3-D problems. Here, the steeper kernel function is employed for SPH approximation of the particles in the vicinity of the walls that models accurately the wall conditions without requiring to the dummy particles. Function approximation of the particles with larger distances from the walls is also performed by employing the flatter kernel function requiring lower computational times. This strategy based on the hybrid kernel function has both advantages of simpler modeling the wall conditions without penetration in the absence of dummy particles and lower computational times. The efficiency of the hybrid kernel function is verified for two benchmark free surface problems.