Abstract
Hele-Shaw flow with suction for an incompressible fluid in a porous medium is introduced as a nontrivial model problem for two-dimensional transient free boundary problems. In this model an initially smooth free boundary can move with unbounded velocities and develop cusps. Two analytic solutions are worked out for a special geometry with which numerical results can be compared. It is then shown that the method of lines can reasonably well reproduce the analytic solutions, although at the expense of long computer times. Some strategies for improving the efficiency of the method of lines, including a multi-grid method, are described.
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