Simulation of thermocapillary convection in a two-layer immiscible fluid system using a boundary element method

Abstract

A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed. The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function. Consequently, velocity gradients are eliminated and the complete formulation is written in terms of velocity. This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy. In this paper, we give the influence of different parameters (Marangoni number, Reynolds number) on thermocapillary convection in cavity with two-layer immiscible fluids. As shown by the numerical results, when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed. The influence of the free interface on thermocapillary convection is also shown.