A numerical study of the effect of free surface deformation on buoyancy and thermocapillary convection

In this paper an improved formulation of the equilibrium equation for the free surface is presented which eliminates the need to evalu- proposed the constant pressure effect. This has then been used in conjunction with a vorticity-velocity formulation discretized using a curvilinear coordinate system in two dimensions. The system of non-linear equations resulting from the discretization of field equations, the free surface displacement, and mesh description are solved simultaneously using Newton’s method. This method has been validated using a number of previously reported test cases. The techniques presented have been used to study the effects of free surface deformation and fluid/solid contact angle on combined buoyancy and thermocapillary convection in a steel container filled with water.