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Center for Nonlinear Studies |
Joint work with Cesar Acosta Minoli Department of Mathematics, Universidad del QuindÃo, Colombia Andrew Winters and James Custer Department of Mathematics, The Florida State University, Tallahassee, FL We present an Arbitrary Lagrangian-Eulerian (ALE) extension of the discontinuous Galerkin spectral element method (DGSEM) to approximate solutions of conservation laws with exponential accuracy in space and arbitrary order in time, while simultaneously respecting the metric identities and geometric conservation laws. The DGSEM is an efficient, nodal, quad/hex element approximation that has superior phase and dissipation properties. It is spectrally accurate even in the presence of material discontinuities, as long as element boundaries are aligned with the material boundaries. Moving boundary problems can be accommodated by introducing an ALE extension. We show that target convergence rates and free-stream preservation can be obtained with careful synchronization of the position and velocity fields. Applications will be illustrated with examples from electrodynamics, linear and nonlinear acoustics.
Host: Mikhail Shashkov, XCP-4 Methods and Algorithms, 667-4400