Computational Methods for Complex Physical Systems Governed by PDEs (virtual)

In this talk, I will present robust and high-performance computational methods for complex physical systems governed by PDEs.  In particular, we will focus on the approximation of solutions to PDEs on complicated domains using embedded boundary grids, that is, grids containing cut cells.  

I will discuss a novel approach, called the state redistribution method, that relaxes the overly restrictive time step that results from arbitrarily small cut cells with explicit time stepping methods.  

I will show how to stabilize both finite volume and discontinuous Galerkin spatial discretizations so that time steps proportional to the size of a full Cartesian cell can be taken.  

This approach uses only basic mesh information that is already available in many cut cell codes and does not require complex geometric manipulations.  Using state redistribution, we solve a number of problems with smooth and shocked solutions that demonstrate the potential of this technique in several applications.