SOME NUMERICAL-METHODS FOR THE COMPUTATION OF CAPILLARY FREE BOUNDARIES GOVERNED BY THE NAVIER-STOKES EQUATIONS

The trial method, Newton's method, and the total linearization method are applied to a simple one-dimensional free boundary (FB) problem for which the solution is known. Attention is focused on convergence speed and computer implementation facilities of these methods. Static FB problems in two- and three-dimensional containers are then discussed. These FBs are governed by the Laplace-Young equation. Two stationary FB problems governed by the Navier-Stokes equations are formulated and these problems are solved using the above three methods. A thermocapillary FB problem governed by the Navier-Stokes equations coupled with the heat equation is studied. A moving FB problem governed by the Navier-Stokes equations is considered within the context of perturbation theory. Finally, some remarks are made on present and future research in the field of capillary FB problems governed by the Navier-Stokes equations.