Simulation of Natural Convection Influenced by Magnetic Field with Explicit Local Radial Basis Function Collocation Method

摘要

The purpose of the present paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded sub-domains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and two differentially heated vertical walls with magnetic field applied in the horizontal direction. Numerical predictions are calculated for different Grashof numbers, ranging from 10~4 to 10~6, and Hartman numbers, ranging from 0 to 100, at Prandtl numbers 0.71 and 0.14. The results of the method are compared to predictions, obtained by other numerical methods, including FLUENT [Fluent (2003)]. Good agreement has been achieved. The LRBFCM has been used in this kind of problems for the first time. The main advantage of the method is its simple numerical implementation and no need for polygonisation.