# Mathematical Modeling and Numerical Simulation in Porous Media (MA 5332)

The objective of this lecture is to present the fundamental phenomena in the field of porous media flow. We discuss modeling aspects and state-of-the-art discretization concepts and illustrate our theoretical considerations by real-life examples. After successful completion of the module students are able to understand the significance of porous media flow simulation in engineering applications. They have a solid foundation for further studies and can choose between suitable numerical methods.Lecture | Prof. Dr. B. Wohlmuth Tue. 16:00-17:30 in MI 02.08.011 |
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Office hours | by arrangement (eMail) |

Exercises | Dr. Christian Waluga Wednesday, 16:00-17:30 in MI 03.08.011 every two weeks |

Tutorial | Christian Waluga, Lorenz John For interested students, additional training for the implementation of some methods treated in the lecture is offered based on the FEniCS finite element framework. Please see the announcements for the exact dates. |

Requirements | Numerics of Differential Equations (MA 3301) (required) |

Advanced Finite Element Methods (MA 4303) (recommended) |

## General Information

### Announcements

- the exams (oral) are planned for July 10-11.
- the sixth assignment will be discussed Wednesday, June 25 (Assignment 6)
- the fifth assignment will be discussed Wednesday, June 11 (Assignment 5)
- the second FEniCS programming tutorial will take place Wednesday, June 04, 16:00-19:00 in 'Kleine Rechnerhalle' (Tutorial 2)
- the fourth assignment will be discussed Wednesday, May 28 (Assignment 4)
- the first FEniCS programming tutorial will take place Wednesday, May 21, 16:00-19:00 in 'Kleine Rechnerhalle' (Tutorial 1)
- the third assignment will be discussed place Wednesday, May 14 (Assignment 3)
- the second assignment will be discussed Wednesday, April 30 (Assignment 2)
- the first assignment will be discussed Wednesday, April 16 (Assignment 1)

### Bonus System

- 80% of homework credits are required to obtain an extra bonus for the final exam
- Homework credits are awarded if the tutors conclude that
- 1) the students put serious effort in the solution of the exercise
- 2) the solution catches the main mathematical ideas of the exercise

- The bonus improves the final mark by one step, e.g., from 2.3 to 2.0
- The mark 1.0 can not be further improved
- The bonus is only applied, if the exam is passed without! That is, it does not improve the marks 4.3, 4.7 or 5.0
- Students should keep their homeworks to prove their eligibility for the exam bonus
- One student can submit his or her homework together with up to two other students

## Content

### Lecture

- Slides 1
- Slides 2
- Slides 3
- Slides 4
- Slides 5
- Slides 6 (incl. movies: part 1, part 2, part 3, part 4)
- Fact Sheet: Functional Analysis
- Fact Sheet: Finite Element Methods

### Assignments

- Assignment 1 (solutions), due April 22
- Assignment 2, porosity.m (solutions: porosity_solution.m, buckleyleverett.m), due May 06
- Assignment 3, (solutions: buckleyleverettplot.m), due May 20
- Assignment 4, (solutions: taylordg_naive.m), due June 3 (code due June 10; further reading here
^{}) - Assignment 5, (solutions: mcwhorter.m), due June 17
- Assignment 6, taylordg_naive.m, (solutions: taylordg_limiter.m), due July 1

### Tutorials

- Handout
- Tutorial 1 (solutions: 1, 2, 3, 4, 5, 6)
- Tutorial 2 (code template, solution)

## Literature

- Helmig. Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems (Springer, 1997)
- Chen, Huan and Ma. Computational Methods for Multiphase Flows in Porous Media (SIAM, 2005)
- Rivière. Discontinuous Galerkin Methods For Solving Elliptic And Parabolic Equations: Theory and Implementation (SIAM, 2008)
- Quarteroni and Valli. Numerical approximation of partial differential equations (Springer, 1994)

## Links

- The Python Tutorial
^{} - The FEniCS project
^{}and the FEniCS tutorial^{}