SPECTRAL SIMULATION OF THERMOCAPILLARY CONVECTION WITH DEFORMABLE FREE-SURFACE USING BOUNDARY-FITTED COORDINATES

A Chebyshev collocation spectral method has been developed to investig ate thermocapillary and buoyancy-induced flow with a deformable free s urface. The flow in a two-dimensional cavity is considered, and the eq uations of motion are solved in a generalized boundary-fitted coordina te (BFC) system to handle the free-surface deformation. The BFC grid i s generated using a finite-difference Poisson solver. The metrics of t ransformation are evaluated using a spectral approximation for the map ping of the physical grid onto the computational grid. The transformed equations are solved using the influence matrix technique in order to produce a solenoidal flow field. Results from the two-dimensional cal culations show that this method can be competitive with finite-element and spectral-element solutions previously reported in the literature.