Moving particle semi-implicit method for fluid simulation with implicitly defined obstacles

We developed a particle-based fluid simulation method with obstacles defined in implicit form. Our fluid simulation is based on the Moving Particle Semi-implicit (MPS) method, a typical particle-based algorithm achieving incompressible flow. In general, the particle-based fluid simulation is performed with obstacles that are defined as a set of particles located along the boundaries. We employ the implicit representation for the geometric information of obstacles which requires a new formulation of particle motion at the vicinity of boundaries. The main difficulty of MPS-based simulation with implicit obstacles is the lack of boundary particles that are required for the computation of two quantities: particle number density and particle force determined by pressure field. In our formulation, new definitions of the two quantities giving good estimation of the original ones is developed and incorporated in the MPS algorithm. In addition, we provide a modified algorithm for the construction of discrete linear system specific to the implicit representation for the computation of particle pressure. Our numerical tests show that the proposed approximation techniques provide adequate particle motion at the vicinity of the implicitly defined obstacles.