Vortrag im Oberseminar Numerik und Optimierung am 12. Juni 2020
Im Rahmen des Oberseminares "Numerik und Optimierung" hielt
Frau Jun.-Prof. Dr. Sandra May (TU Dortmund)
am Freitag, 12. Juni 2020,
einen Vortrag mit dem Titel
"Time-dependent conservation laws on cut cell meshes and the small cell problem"
Beginn: 15:00 Uhr, der Vortrag fand online statt.
Cut cells methods have been developed in recent years for computing
flow around bodies with complicated geometries. Cut cell methods cut
the flow body out of a regular Cartesian grid resulting in so called
cut cells. Cut cells can have irregular shape and may be very small.
For solving time-dependent conservation laws on cut cell meshes,
probably the biggest problem one has to face is the small cell problem:
standard explicit schemes are not stable if the time step is chosen
based on the size of the background cells. Therefore, special schemes
must be developed.
In the first part of this talk, we discuss the small cell problem in
detail and summarize several existing solution approaches in the
context of both finite volume (FV) schemes and discontinuous Galerkin
(DG) schemes. In the second part, we present our two fundamentally
different solution approaches for overcoming the small cell problem:
the FV based mixed explicit implicit scheme, developed in collaboration
with Berger (J. Sci. Comput. 71, pp. 919-943, 2017), and the DG based
Domain-of-Dependence (DoD) stabilization, joint work with Engwer,
Nuessing, and Streitbuerger (arXiv:1906.05642).