- Title
- Analytic and numerical solution of free boundary fluid flow through porous media
- Creator
- Almalki, Faisal Muteb K.
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2024
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Free boundary problems (FBP) arise in many applications, including in the flow of porous media. They involve the solution of a partial differential equation (PDE) that has an unknown boundary. The unknown boundary is called a free boundary, and it should be determined as part of the solution. In general, the boundary conditions that are applied to the free boundary are overspecified. The Boundary Element Method (BEM) is a numerical technique used to solve PDEs that appear in mathematics, physics, and engineering. This method works by dividing the boundaries of the problem into smaller parts, which reduces the dimension of the problem and allows for the application of Green's theorem. BEM is particularly well-suited for solving Laplace's equation. BEM transforms the issue from a PDE with boundary conditions to an integral equation, resulting in a linear system that can be efficiently calculated. We can solve for the free boundary by constructing an iterative approach. This technique is thoroughly described, and some problem calculations are included. This thesis presents numerical results obtained by using the BEM to simulate fluid flow through homogeneous isotropic porous media. The governing equation for this flow is Laplace's equation, which is modeled by Darcy's law. The boundary conditions for this system include both Dirichlet and Neumann conditions, and the free surface is subject to both types of boundary conditions. The conformal mapping technique is used to make the numerical resolution of fluid flow issues easier through porous media. By transforming the intricate fluid domain into a simpler one, exact solutions can be attained for the simplified domain, which can then be used to modify the boundary element method and enhance the precision of the numerical outcomes. The two methods of conformal mapping, iterative and direct, are used to locate the free surface in fluid flow problems. These techniques involve transforming the solution from a complex shape to a simpler one, where the solution to Laplace's equation is solved using the boundary element method. The solution is then mapped back to the original geometry, allowing the free surface to be identified. Also, we have used the separation of variables method, which is a useful tool for solving mathematical models of fluid flow through porous media, which are described by PDEs. This approach simplifies complex equations, making it easier to determine solutions and gain a better understanding of the behavior of the fluid.
- Subject
- free boundary; porous media; fluid flow; partial differential equation
- Identifier
- http://hdl.handle.net/1959.13/1510881
- Identifier
- uon:56451
- Rights
- Copyright 2024 Faisal Muteb K. Almalki
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
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| View Details Download | ATTACHMENT02 | Abstract | 308 KB | Adobe Acrobat PDF | View Details Download |