Some Numerical Methods for the Computation of Capillary Free Boundaries Governed by the Navier-Stokes Equations

摘要

In section 1, the trial method, Newton's method and the total linearization method will be applied to a simple 1D free boundary (FB) problem for which the solution is known. Attention will be focused on convergence speed and computer implementation facilities of these methods. In section 2, the authors study static FB problems in 2D and 3D containers. These FBs are governed by the Laplace-Young equation. In section 3 they formulate two stationary FB problems governed by the Navier-Stokes equations and they solve these problems using the three methods introduced in section 1. A thermocapillary FB problem which is governed by the Navier-Stokes equations coupled with the heat equation is studied in section 4. In section 5, a moving FB problem governed by the Navier-Stokes equations will be considered within the context of perturbation theory. Finally, in section 6, they make some remarks on present and future research in the field of capillary FB problems governed by the Navier-Stokes equations.