An adaptive multi-resolution SPH approach for three-dimensional free-surface flow with fluid impacting

Abstract

This paper presents a new adaptive multi-resolution smoothed particle hydrodynamics (SPH) approach for simulating three-dimensional free surface flows with fluid impacting. The governing equations for multi-resolution SPH are derived based on the finite particle method (FPM) particle interpolation, which is an alternative SPH formulation for improving interpolation accuracy in the non-uniform particle distribution. A variable kernel length related to the volume of neighbor particles is proposed to control the numerical instability due to the multi-resolution scheme. In adaptive particle refinement (APR), a concept named as continuously-variable characteristic length (CCL) for each particle is defined to determine the splitting or merging scheme and then build a smoothing non-uniform particle distribution. Three-dimensional examples are conducted to validate the presented new APR approach, and the capability and numerical efficiency of the proposed numerical model are verified through solving free-surface flow problems with middle and low Weber numbers. After validation, a refined simulation of droplet impacting is conducted using the proposed adaptive multi-resolution SPH approach. The results show that the proposed SPH could well adapt to the large deformation of three-dimensional free-surface flow, and only provide a refinement near the free-surface domain.