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

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    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
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