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The mathematical formulation, basic concept and numerical implementation of anew meshless method for solving three dimensional fluid flow and related heattransfer problems are presented in this paper. Moving least squaresapproximation is used for the spatial discretization together with an implicitscheme for time marching. The vorticity and vector potential formulation ofNavier-Stokes equations is employed to avoid the difficulties associated withpressure/velocity coupling. Two 3D problem of natural convection in adifferentially heated cubic cavity and in the annular space between a sphereand a cube are considered. Results show the flexibility of the method anddemonstrate its accuracy.

A new meshless approach for three dimensional fluid flow and related heat transfer problems