Approaches To Solving A Free Boundary
Porous Medium Flow Problem
Author(s)
J. Zhang, B. Jiang & J. C. Bruch, Jr.
Abstract
The free boundary problem considered is that of a steady, two-dimensional flow
through a porous dam sitting on an impervious foundation with reservoirs on
both sides of different heights of water. Several methods will be used to solve
this problem and comparisons will be made of the results. The first method to be
implemented will be the classical variational inequality approach. This technique
yields a fixed domain formulation which is very efficient from both a
computational and a theoretical point of view. The second method is a new
non-overlapping domain decomposition approach. The seepage problem is
broken up into two problems on non-overlapping regions. In one region the
problem is treated as a partial differential equation formulation, while in the
second region which contains the free boundary part, a variational inequality
formulation is considered. A robin boundary condition is utilized on the
common boundary between the two sub-domains. The third method to be used
is the generalized Stefan velocity method for a class of free boundary problems
including the seepage model. It is an iteration method, where a non-physical
velocity on the free interface is specified for updating and locating the new
interface at the next iteration step. The advantage of this method is that the
convergence rate does not depend on the size of the numerical discretization
whenever the non-physical velocity is properly chosen.
Keywords: porous media flow, free boundary, variational inequality, domain
decomposition, generalized Stefan velocity method.
Keywords
porous media flow, free boundary, variational inequality, domain
decomposition, generalized Stefan velocity method.
Related Book
Other papers in this volume
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