Enhancement of stabilization of MPS to arbitrary geometries with a generic wall boundary condition

Abstract

As a Lagrangian meshless method, moving particle semi-implicit (MPS) method has been proven useful in the analysis of the free-surface flow, especially accompanied by the large deformation and fragmentation of fluids. The improvement of pressure distribution in three dimensions is an important aspect to verify the effectiveness of MPS. The accurate representation of 3-D geometries especially complex geometries is the premise of obtaining convincing pressure distribution. However, most of MPS applications cannot accurately represent complex wall geometries, which highly affects the reliability of MPS. For this reason, the triangle meshes are used to accurately represent the complex wall geometries in this research. The polygon wall boundary condition (PW) is adopted to enforce the wall boundary condition to the triangle meshes. The pressure of the wall boundaries is derived from the Neumann boundary condition to improve the velocity distribution of fluid particles near the wall boundaries. A first-order gradient model is presented to improve the accuracy and stability of the PW. Our approach can enhance the numerical stabilization to arbitrary geometries. We simulate several 3-D examples such as the classic hydrostatic simulation and the complex 3-D geometries with sharp angles and curved surfaces to demonstrate the general applicability of our new model.