# Seminar WS 17/18 Graduate Seminar on Scientific Computing

In this seminar 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.

Basic knowledge on interpolation, numerical quadrature, finite element methods for elliptic PDEs and saddle point systems will be advantageous.

The seminar takes place on Tuesdays at 14 o'clock (c.t.) in room 5.002, Wegelerstr. 6.

The presentations will be on November 14th and 28th and on December 7th and 12th, 2017. They should last roughly 75 minutes. The first 45 minutes are to be done on the blackboard. The format of the remaining 30 is up to you.

Please turn in a four-page summary (LaTex, 11pt, geometry[margin=30mm]) of the most relevant mathematical content of your talk by December 22th, 2017. Email is fine, but please make sure that I receive it.

- Review of multigrid preconditioning
- The algebraic multigrid method
- Block preconditioners for saddle point systems
- The least-squares commutator preconditioner
- Time integration of parabolic PDEs
- Numerical methods for the advection-diffusion equation
- The level set method for tracking interfaces
- Gradient augmented level set methods
- Numerical modeling of surface tension
- Volume-of-fluid methods for two-phase flow
- The arbitrary Lagrangian-Eulerian (ALE) method

Notes on scientific writing