- Title
- Analytic solution of the free boundary problem for porous media flow using a conformal map validated by the boundary element method
- Creator
- Almalki, Faisal Muteb K.; Meylan, Michael H.
- Relation
- ARC.IC170100006 https://purl.org/au-research/grants/arc/IC170100006
- Relation
- Engineering Analysis with Boundary Elements Vol. 166, Issue September 2024, no. 105806
- Publisher Link
- http://dx.doi.org/10.1016/j.enganabound.2024.105806
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2024
- Description
- This paper presents an analytic approach to solving the classical problem of free boundary porous media flow. The solution is found by constructing an operator, derived from a conformal map, which is then reduced to a matrix and inverted. This matrix is then used to solve a system of linear equations with all terms in the matrix calculated exactly. To confirm the solution, we made a comparison with an iterative boundary element solution, which shows good agreement. Visual representations of the flow are also provided.
- Subject
- free boundary problems; Darcy’s law; Laplace’s equation; boundary element method; conformal map; separation of variables
- Identifier
- http://hdl.handle.net/1959.13/1515894
- Identifier
- uon:56920
- Identifier
- ISSN:0955-7997
- Rights
- © 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
- Language
- eng
- Full Text
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