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Advanced Topics in Numerical Methods in Science and Technology

In this lecture we will investigate numerical methods for the simulation of viscous flow. This applies for example to the behavior of lava or ice. We will extend the treatment to the modeling of two-phase flow, where we have a mixture of air and water, or water and oil for example. In this case, we have to consider how the two phases are represented numerically, and how physical effects like surface tension can be taken into account.

During parts of the lecture, we will work together on a software project for an example application that demonstrates the methods that we develop in the lecture.

Basic knowledge on interpolation, numerical quadrature, finite element methods for elliptic PDEs and saddle point systems will be advantageous. Since we will program demonstration programs during parts of the lecture, skills in C programming are required.

In case you were wondering what this is all about, here is the short description: We will discuss and implement techniques to simulate a so-called lava lamp. We may not get it to work completely (in fact, it's a rather difficult problem), but the different steps will be interesting regardless, and everybody will have a cute example program to take home afterwards.

The lecture takes place on Wed 8:30-10:00 and Thu 14c.t.-16 in We6 5.002.

Exams: The exams will take place on February 4, 5, and 10. I will put up the lists to sign in for the first batch on Monday, January 19., 14:30. The second batch of exams will take place on March 30 and 31.

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