For Zoom Link please contact ddelreyfernandez@uwaterloo.ca

## Speaker

David A. Kopriva Professor Emeritus Department of Mathematics, Florida State University and Computations Science Research Center, San Diego State University

## Title

On the Foundations of Overset Grid Methods

## Abstract

Overset grid methods were introduced forty years ago to simplify grid generation for complex geometrical configurations. The methods have their own conference series, which has been held for almost thirty years. Numerous software packages exist to implement the schemes. The methods have been used in conjunction with all major spatial approximation schemes and are used in a wide variety of application areas including aerodynamics, solid mechanics, meteorology, and electromagnetics. Over the years, robustness has been an issue, and to date no fully multidimensional stability proofs are available.

In this talk, I will look at the formulation of the overset grid problem as an overset domain problem. I will show that one-way characteristic coupling between the domains in one space dimension is well-posed, but that doesn't extend to multiple dimensions. I will then present formulations of the problem for linear and nonlinear systems that use two-way coupling. For linear problems, we can show that the new formulation is energy bounded, conservative, and that the solutions are equivalent to the original single domain problem. The formulation for nonlinear systems is entropy conserving and conservative. Numerical experiments will examine the behavior of the systems using a discontinuous Galerkin spectral element approximation.