Titel: Mixed explicit implicit schemes for embedded boundary geometries
Startdatum: 17 Juni
Startzeit: 17:15
Stoppzeit: 18:30Uhr
Veranstalter: Institut für Mathematik
Frau Juniorprofessorin Dr. Sandra May, Fakultät für Mathematik, Technische Universität Dortmund 
Ort: Seminarraum 1403

For flow simulations in complex geometry, the use of cut cell meshes is typically cheaper and faster than em-ploying body-fitted grids. In this approach the geometry is simply cut out of a Cartesian background grid.

This results in so called 'cut cells' around the boundary of the embedded object. These cells have irregular shape and may be very small. In the context of solving time-dependent, hyperbolic partial differential equations, probably the biggest issue caused by this approach is the so called `small cell problem' -- explicit time

stepping schemes are not stable on the arbitrarily small cut cells.

We present mixed explicit implicit finite volume schemes to overcome this problem. For simplicity, we focus on solving the time-dependent advection equation. We use an implicit timestepping scheme near the

embedded bundary for stability; and employ an explicit scheme otherwise to keep the cost low. We combine the explicit and implicit scheme by means of `flux bounding' -- this way of coupling preserves mass conservation and ensures stability in form of a TVD result [1].In this talk, we focus on our new work concerning the accuracy of the mixed scheme. One essential source of error is the transitioning from one timestepping scheme to the other. We will discuss how these errors accumulate and how to avoid their accumulation. We will present

numerical results in one and two dimensions to support our theoretical findings.


[1] S. May, M. Berger, An explicit implicit scheme for cut cells in

embedded boundary meshes, J. Sci. Comput., Vol. 71, pp. 919-943, 2017.




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