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Speaker: Marsha Berger, Group Leader, Modeling and Simulation, CCM, Flatiron Institute
Title: Cartesian Cut-cell Methods for Flows in Complicated Geometries
Abstract: Cut-cell methods are popular for inviscid flow simulations since they handle complicated geometry in a robust and automatic way. These methods use regular Cartesian meshes except at cells that intersect the geometry surface. Discretization has been a challenge with cut cells because their irregularity can lead to loss of accuracy. For time dependent problems and explicit difference schemes, instability at the small cut cells becomes an issue.
We review some popular approaches to the `small cell' problem, and describe our new approach called State Redistribution, which stabilizes finite volume schemes in a practical post-processing step. It can be generalized to high-order accuracy, and has provably monotone weights. Computations in two and three space dimensions are shown. We end with a discussion of open problems.