AN IMPLICIT SURFACE TENSION ALGORITHM FOR PICARD SOLVERS OF SURFACE–TENSION–DOMINATED FREE AND MOVING BOUNDARY PROBLEMS
✍ Scribed by P. J. SLIKKERVEER; E. P. VAN LOHUIZEN; S. B. G. O'BRIEN
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 754 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
One of the methods for solving a free or moving boundary problem is the use of Picard solvers which solve the geometry and the velocity field successively. When, however, the kinematic condition is used for updating the geometry in this technique, numerical stability problems occur for surface-tensiondominated flow. These problems are shown here to originate h m the unstable integration of the local smoothing of the surface by surface tension. By an extension of the surface tension contribution to the flow field an implicit treatment of surface tension is obtained which overcomes these stability problems. The algorithm is applicable to both free and moving boundary problems, as will be shown by examples in this paper. KEY WORDS surface tension; free boundary, moving boundary; implied algorithm 1. In the first of these methods, all unknowns, both velocity components and surface position, are combined in one ve~tor.~'''~ This algorithm enables the use of a Newton iteration scheme for free boundaries. The implementation of this linearization involves a considerable amount of work, which results in a high order of convergence but a limited r~bustness.~ 2. The second type of algorithm uses a Picard solving technique, in which the velocity components and the surface position are computed successively, This method is easier to implement since it does not require adaptation of the flow elements. It is more robust, but at the cost of a linear convergence for free surfaces.