An application of GSMAC–FEM to coupled natural and Marangoni convection in a square cavity

Abstract

This paper presents an efficient numerical scheme for the analysis of coupled natural and Marangoni convection encouraged by the thermal radiation. The novel feature of the proposed algorithm is the introduction of the jump quantity on the free surface into the boundary integration term in the Navier–Stokes equation discretized by the finite element method (FEM). In addition, the generalized simplified marker and cell (GSMAC) method is applied to the solution of the velocity field, which realizes high-speed computation. In order to verify the validity of the present scheme, two-dimensional (2D) and three-dimensional (3D) numerical simulation of coupled natural and Marangoni convection in a square cavity is performed for a wide range of Marangoni number and Grashof number: Numerical results obtained here are in good agreement with the experimental data, and the dominance of Marangoni convection is clearly shown with the increase of Marangoni number.