Solution of thermo‐fluid problems by collocation with local pressure correction

Purpose The purpose of this paper is to explore the application of the mesh‐free local radial basis function collocation method (RBFCM) in solution of coupled heat transfer and fluid‐flow problems. Design/methodology/approach The involved temperature, velocity and pressure fields are represented on overlapping five nodded sub‐domains through collocation by using multiquadrics radial basis functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The energy and momentum equations are solved through explicit time stepping. Findings The performance of the method is assessed on the classical two dimensional de Vahl Davis steady natural convection benchmark for Rayleigh numbers from 103 to 108 and Prandtl number 0.71. The results show good agreement with other methods at a given range. Originality/value The pressure‐velocity coupling is calculated iteratively, with pressure correction, predicted from the local mass continuity equation violation. This formulation does not require solution of pressure Poisson or pressure correction Poisson equations and thus much simplifies the previous attempts in the field.