Mathematical Models of Groundwater Flow

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Code Completion Credits Range Language
01MMPV KZ 2 2+0 Czech
Garant předmětu:
Jiří Mikyška
Jiří Mikyška
Jiří Mikyška
Department of Mathematics

The course provides an overview of computational methods for selected groundwater flow problems. The first part of the course is devoted to mathematical formulations of these problems. The second part is aimed at selected numerical methods, emphasizing implementation issues related to these methods.


Basic course of Calculus, Linear Algebra and Ordinary Differential Equations (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01LAA2, 01NM held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Basic terminology and quantities, Darcy's law and its extensions.

2. Derivation of basic equations, classical formulation of the fluid flow problem in saturated zone.

3. Brief introduction to the theory of Sobolev spaces.

4. Weak formulation of the second-order elliptic boundary value problems.

5. Existence and uniqueness of the weak solution.

6. Finite Element Method (FEM) for steady-state flow equation in saturated domain.

7. Implementation problems related to FEM. Assembling of the equations, treatment of the boundary conditions.

8. Formulation of a non-stationary problem and its numerical solution by means of method of lines.

9. Discussion of alternative methods of time discretization, several special techniques.

10. Finite Volume Method (FVM) on dual mesh for parabolic equations.

11. Comparison of FEM with FVM, relation between these two methods.

12. Computer demonstrations of several simulation tools.

Syllabus of tutorials:
Study Objective:

Darcy's law, balance equations, formulaton of the flow problem in the saturated zone, finite element method for an elliptic boundary value problem, extension of the method to the initial-boundary value problem for a parabolic equation, assembling of the finite element systems, treatment of boundary conditions, mass lumping.

Skills: correct formulation of boundary value problems for elliptic partial differential equations, application of the finite element method including computer implementation of the method.

Study materials:

Key references:

[1] J. Bear, A. Verruijt: Modelling Groundwater Flow and Polution, D. Reidel Publishing Company, Dordrecht, Holland, 1990.

Recommended references:

[2] P.S. Huyakorn, G. F. Pinder, Computational Methods in Subsurface Flow, Academic Press, 1983

Media and tools:

A computer with OS Linux, C language compiler and UG library.

Time-table for winter semester 2023/2024:
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Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2023-11-30
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