Boundary integral based polygon wall representation in the MPS method

Abstract

The particle methods are suited to simulate fluid flow problems with large boundary deformation. The moving particle semi-implicit (MPS) method is one of the representative particle methods for incompressible flow. In recent years, the MPS method has received a great deal of attention in various fields of science and engineering. However, the numerical treatment of complicated wall geometry is still an open question. The conventional approaches have severe issues in handling arbitrary shape or calculation accuracy. In these circumstances, this study has been done to propose a novel numerical treatment of solid wall boundary in the MPS method. In this approach, the wall contribution in the discretization scheme is described in a form of volume integral over object domain. Thus, arbitrary-shaped boundaries represented by a polygon mesh can faithfully be considered. Moreover, since the distribution of physical quantity inside object is given by linear extrapolation, it satisfies the prescribed boundary condition with high accuracy. While the volume integral cannot be numerically evaluated with affordable computational cost, it can be transformed into a boundary integral form based on the divergence theorem. The derived boundary integral can be calculated with reasonable cost and acceptable accuracy using a projection technique and the Gaussian quadrature. The proposed method has been examined through several numerical test cases in 2D and 3D. As a result of the numerical tests, the present method is shown to have considerably higher accuracy compared to conventional methods, and its validity is verified.

Keywords

• computational fluid dynamics
• particle method
• mps method
• wall boundary condition
• polygon boundary representation
• boundary integral
• gaussian quadrature