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. We will have an initial meeting (Vorbesprechung) on October 17, 2017, at 14 o'clock, in which we will discuss the topics and the literature.
|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|