A Numerical Scheme for Solving Incompressible and Low Mach Number Flows by the Finite Pointset Method

A meshfree projection method for compressible as well as incompressible flows and the coupling of two phase flows with high density and viscosity ratios is presented. The Navier-Stokes equations are considered as the basic mathematical model and are solved by the implicit projection method. The implicit projection method yields the linear second order partial differential equations. These equations are solved by the weighted least squares method and are compared with the exact solutions. A one dimensional shock tube problem is exhibited for compressible flows. Finally, two phase incompressible and quasi compressible flows are used to simulate a two phase cavity filling problem.

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