Speaker: Oleksii Beznosov, University of Colorado Boulder

Title: High order hybrid Hermite-discontinuous Galerkin overset grid methods for the wave equation

Abstract: We present efficient and high order hybrid Hermite-discontinuous Galerkin methods

for the scalar wave equation in complex geormeties. The hybridization combines efficient Hermite methods on Cartesian grids with geometrically flexible Galerkin methods curvilinear grids coupled through overset grid technology. It is well known that the interpolation between overset grids may cause instabilities, and more frequently so when considering hyperbolic equations. In this talk we
demonstrate that the built in dissipation of Hermite and energy based discontinuous Galerkin methods is sufficient to control such instabilities for overset grids with similar grid spacing. Additionally, for the rare cases when highly different grid spacings trigger instabilities, we show that they can always be removed by adding high orderartificial viscosity. Numerical experiments demonstrating the efficiency and accuracy of the methods of orders 5 to 11 will be presented.