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12.06.2020 Sandra May

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).