A Moving Particle Method with Embedded Pressure Mesh (MPPM) for Incompressible Flow Calculations

An accurate moving particle method for incompressible flow calculations is presented in this article. The major distinctive feature in this proposition is the insertion of a pressure mesh within the particle cloud to handle the continuity constraint. It is motivated by the thought that pressure should be a field variable rather than a material one moving with fluid flow. Both the diffusion and convection operators are executed on the particle locations, while the projection operator to retain a convergence-free velocity field is manipulated on the inserted pressure mesh. It will yield a diagonally dominant and constant-coefficient matrix equation to update the pressure field. Besides the advantages gained to enforce the continuity constraint, the auxiliary mesh can significantly enhance the particle searching efficiency in the particle smoothing process. Numerical verifications on some benchmark problems indicate that the present proposition will provide accurate results for incompressible flow calculations.