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A Discontinuous Petrov-Galerkin Method for Viscous Compressible Low

March 5, 2014 10:30AM to 11:30AM
Jesse Chan, Rice University
Building 240, Room 4301
The Discontinuous Petrov-Galerkin (DPG) method is a class of novel higher order adaptive finite element methods derived from the minimization of the residual of the variational problem, and has delivered a method for convection-diffusion that is provably robust in the diffusion parameter. In this work, the DPG method is extrapolated to nonlinear systems, and applied to problems in fluid dynamics whose solutions exhibit boundary layers or singularities in viscous stresses.

In particular, the effectiveness of DPG as a numerical method for compressible flow is assessed with the application of DPG to two model problems over a range of Mach numbers and laminar Reynolds numbers using automatic adaptivity with higher order finite elements, beginning with highly under-resolved coarse initial meshes.