Some numerical methods for the computation of capillary free boundaries governed by the NavierStokes equations
Abstract
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 dimensional and three dimensional containers are studied. These FBs are governed by the LaplaceYoung equation. Two stationary FB problems governed by the NavierStokes equations are formulated and these problems are solved using the three methods. A thermocapillary FB problem which is governed by the NavierStokes equations coupled with the heat equation is studied. A moving FB problem governed by the NavierStokes equations is considered within the context of perturbation theory. Present and future research in the field of capillary FB problems governed by the NavierStokes equations are discussed.
 Publication:

Presented at the Dutch Mathematical Congress
 Pub Date:
 1990
 Bibcode:
 1990duma.cong.....C
 Keywords:

 Free Boundaries;
 Laplace Equation;
 Marangoni Convection;
 NavierStokes Equation;
 Finite Element Method;
 Linearization;
 Newton Methods;
 Partial Differential Equations;
 Vibration;
 Fluid Mechanics and Heat Transfer