Accession Number : ADA293626

Title :   A Well-Posed Numerical Method to Track Isolated Conformal Map Singularities in Hele-Shaw Flow.

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Baker, Gregory ; Siegel, Michael ; Tanveer, Saleh

PDF Url : ADA293626

Report Date : FEB 1995

Pagination or Media Count : 51

Abstract : We present a new numerical method for calculating an evolving 2-D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small round-off errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out. (AN)

Descriptors :   *COMPUTATIONAL FLUID DYNAMICS, *NUMERICAL METHODS AND PROCEDURES, MATHEMATICAL MODELS, ALGORITHMS, FOURIER TRANSFORMATION, COMPUTATIONS, EQUATIONS OF MOTION, SOLUTIONS(GENERAL), BOUNDARY VALUE PROBLEMS, PERTURBATIONS, TWO DIMENSIONAL FLOW, VISCOUS FLOW, VISCOSITY, CHANNEL FLOW, SURFACE TENSION, CONFORMAL MAPPING.

Subject Categories : Numerical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE