Computational Mathematics and Scientific Computing Seminar

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Recent Discontinuous Galerkin developments at ONERA

Speaker: Juliet Ryan, ONERA & Paris 13 University

Location: Warren Weaver Hall 1302

Date: Feb. 18, 2011, 10 a.m.

Synopsis:

Discontinuous Galerkin (DG) methods have become the subject of considerable research over the last decade due to their ability to give high order solutions in complex applications whether geometrical or physical. Also, they are, because of their locality, eminently well adapted to nowadays supercomputers whether vectorial, parallel or GPUs.

In our talk we shall first present some variants of the space time DG approach useful to control numerical diffusion. Another part of our talk will be new techniques to compute the viscous flux. Although well suited to the discretization of first order hyperbolic problems, extension to elliptic problems such as diffusion, is far less natural and still an up-to-date subject. The first technnique is based on local reconstruction of the solution to smooth the discontinuities similar to Van Leer's recovery method, and is relevant to any type of geometrical discretization ( structured, unstructured, non conforming) The second one aims at reducing costs for implicit parabolic DG schemes. An iterative algorithm has been devised by partial uncoupling in space between low-order and high-order degrees of freedom. The performance of this method will be shown in terms of CPU time and compared to a fully implicit method.

BIO A research Engineer at ONERA, France since 1986 and associate professor at Paris 13 University since 1998, my first studies were on Boundary and Spectral Element Methods. My work has mostly delved in Applied Mathematics with an emphasis on parallel and Time-Space Domain Decomposition methods, and since 2006, on Discontinuous Galerkin discretizations. All these methods have been applied to fluid mechanics, solid mechanics and sometimes optics.