Wall Boundary Potential model for incompressible smoothed particle hydrodynamics with arbitrary kernel functions

The accuracy and applicability of the wall boundary models are crucial, as they affect not only quantities at the wall boundary but also results throughout the entire computational domain. This study presents the Wall Boundary Potential (WBP) model as an accurate wall boundary model. Whereas the existing accurate wall boundary model, Wall Potential Particles (WPP) model, is only applicable to MPS (Moving Particle Semi-implicit)-type kernels which take an infinite value at the centre, the proposed WBP model is applicable to the SPH (Smoothed Particle Hydrodynamics) method, employing kernels with finite values at the centre, regardless of kernel function. Several benchmark tests have been conducted to validate WBP. By comparing the performance in the simulation of classical Hagen-Poiseuille flow among the conventional fixed particles wall boundary condition (referred to as “standard wall boundary model”) and WBP, it is found that the velocity disturbances occurring in the standard model are significantly reduced by WBP. This demonstrates that WBP is effective for accurate calculations near the wall. From the other tests involving free surface, the wide applicability of WBP is demonstrated and pressure fluctuation under the violent flow seen in the standard wall boundary model is effectively mitigated by WBP.