Talk on 2021-05-10: A two-dimensional stabilized discontinuous Galerkin method on curvilinear embedded boundary grids

Speaker: Dr. Andrew Giuliani, New York University
Date & time: Monday, 10th May 2021, 4pm (CEST)/10am (EDT)
Meeting link: Please request via email from Michael Schlottke-Lakemper

Abstract:
In this talk, we present a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells when explicit time steppers are used. Thus, the scheme can take time steps that are proportional to the size of cells in the background grid. The discontinuous Galerkin scheme is stabilized by postprocessing 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 prove that state redistribution is conservative and p-exact. Finally, we solve a number of test problems that demonstrate the encouraging potential of this technique for applications on curvilinear embedded geometries. Numerical experiments reveal that our scheme converges with order $p+1$ in $L_1$ and between $p$ and $p+1$ in $L_\infty$.