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

The mathematical formulation, basic concept and numerical implementation of a meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. A second order moving least squares approximation is used for the spatial discretization together with an implicit scheme for time marching. The vorticity and vector potential formulation of Navier–Stokes equations is employed to avoid the difficulties associated with pressure–velocity coupling. Two three-dimensional examples of natural convection in a differentially heated cubic cavity and in the annular space between a sphere and a cube are considered and steady-state solutions are obtained for Rayleigh numbers in the range of 103–106. Results show the flexibility of the method and demonstrate its accuracy.

► A meshless method using a vorticity and vector potential formulation is presented.
► Convection problems in a cubic cavity and in the space between a sphere and a cube are treated.
► Calculations show the good accuracy of the method as compared to available results.