A Modified MPS Method with a Split-Pressure Poisson Equation and a Virtual Particle for Simulating Free Surface Flows

As a Lagrangian mesh-free method, the moving particle semi-implicit (MPS) method can easily handle complex incompressible flow with free surface. However, some deficiencies of MPS such as inaccurate results, unphysical pressure oscillation, and thrust near surface, still need to be further resolved. Here, we propose modified that uses following techniques: (1) scheme split-pressure Poisson equation is proposed reproduce hydrostatic stably; (2) new virtual technique developed ensure symmetrical distribution particles on surface; (3) Laplacian operator consistent original gradient introduced replace operator. In addition, two-judgment for distinguishing surface in method. Four flows were adopted verify including two problems, dam-breaking problem, violent sloshing problem. The enhancement accuracy stability by these improvements was demonstrated. Moreover, numerical results showed good agreement analytical solutions experimental results.