colloquium

Spectral Methods in Motion

Speaker: David Kopriva (Florida State University)

Abstract: Accurate computation of wave scattering from moving, perfectly reflecting objects, or embedded objects with materialproperties that differ from the surrounding medium, requires methods that accurately represent the boundary location and motion, propagate the scattered waves with low dissipation and dispersion errors, and don't introduce errors or artifacts from the movement of a mesh. Discontinuous Galerkin spectral element methods are especially suited to problems where wave propagation accuracy is needed and the locations of material discontinuities are known. Applying the methods to an ALE (Arbitrary Lagrangian-Eulerian) formulation extends them to moving boundary problems. In this talk, we discuss the issues and choices for the development of a DGSEM-ALE approximation for the accurate approximation of wave propagation problems with moving boundaries. Examples from acoustics, fluid dynamics and electromagnetics will be presented to illustrate the application of the methods.

Bio: David Kopriva is Professor of Mathematics at The Florida State University, where he has taught since 1985. He is an expert in the development, implementation and application of high order spectral multi-domain methods for time dependent problems. In 1986 he developed the first multi-domain spectral method for hyperbolic systems, which was applied to the Euler equations of gas dynamics. Though a multi-domain or spectral element approach is common now, at that time the idea of breaking up a computation into multiple spectral approximations was considered a radical idea. That original work led to the development of new multidimensional characteristic boundary conditions, spectral multi-domain methods for the compressible Navier-Stokes equations and multi-domain spectral versions of shock fitting algorithms for high speed flows. In the 1990's Kopriva developed a robust staggered grid Chebyshev spectral method that simplified the connectivity of subdomains and simplified parallel implementations. This work included the development of a non-conforming spectral method that enables the refinement of a mesh either by increasing the spectral order or decreasing the subdomain size locally. Most recently he has concentrated on the development of a discontinuous Galerkin form of the spectral element method for the solution of time-dependent systems. Kopriva has applied multi-domain spectral methods to time dependent problems in compressible flow, aeroacoustics and electromagnetics. Spectral multi-domain methods were used to solve problems in hypersonic flows over blunt bodies, in both the inviscid and viscous limits. Most recently he has applied the techniques he has developed to problems in electromagnetic scattering, problems in particulate transport, cryogenics and computational finance.