Title: State redistribution methods for hyperbolic problems on cut cells grids
Abstract: In this talk, we present state redistribution methods for hyperbolic problems on embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells when explicit time steppers are used. We show how to stabilize both finite volume and discontinuous Galerkin spatial discretizations so that time steps proportional to the size of Cartesian cells in the background grid can be taken. State redistribution works by post-processing the numerical solution after each stage or step of an explicit time stepping method. The advantage of this approach is that it uses only basic mesh information that is already available in many cut cell codes and does not require complex geometric manipulations. We solve a number of test problems with smooth and shocked solutions that demonstrate the encouraging potential of this technique for applications on embedded boundary grids.
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