Abstract
From the previous works, we found that the stability of the pressure solution obtained by using particle-based method can be improved by solving the pressure equation on a stationary Eulerian grid. In this study, the Multiquadric Radial Basis Function (RBF-MQ) interpolation technique is applied for the data transfer between Lagrangian particles and Eulerian grids in solving the incompressible Navier-Stokes equations. Also, the argument on selecting the optimal shape parameter (for MQ kernel) is resolved in the current work as well by using the information of the surrounding nodes. In order to preserve the continuity constraint on the particle level, the divergence-free interpolation scheme is proposed to interpolate the velocity from grid to particle. For validation purpose, a series of flow cases are solved by using the current Moving Particle with Pressure Mesh (MPPM) method and good agreement has been found between the current and the benchmark solutions. Also, we found that the current method is more accurate than our previous MPPM method.
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