  This report summarises the results for the numerical simulation of
thermocapillary convection in a two-fluid system with a deformable interface.
An explicit technique with 3rd order Runge-Kutta method in time, 2nd order ENO
for the advection terms, and 2nd order central-differencing for the diffusion
terms are employed in the momentum equations for simulating the flow on a
staggered grid using a Marker and Cell method. An energy equation is solved
numerically and a level-set method is used to implicitly capture the interface.
A constant contact angle condition is assumed between the end walls and the
interface. The domain is enclosed with adiabatic walls on the top and bottom
and a temperature gradient is imposed along the horizontal walls. A Continuum
Surface Force model is used for surface tension to numerically simulate the
thermo-capillary effect. A Successive Over-Relaxation (SOR) technique is used
to solve the pressure equations iteratively. The level set method and the
energy equation are tested with a few test-cases before implementing in the
solver. The imposed temperature difference along the horizontal direction
produces a surface tension gradient along the liquid-liquid interface resulting
in the flow of the interface fluid from the region of lower surface tension
(Higher temperature) to higher surface tension (Lower temperature). The end
walls cause recirculation by imposing a horizontal pressure gradient in each
fluid layer.
