A Hybridized Discontinuous Petrov-Galerkin scheme for compressible flows
Name
758653494-MIT.pdf
Description
Full printable version
Size
7.12 MB
Format
Adobe PDF
Checksum (MD5)
01d0e41dab2567ea8e4f7fb92df3370e
Author(s)
Moro-Ludeña, David
Advisor(s)
Jaume Peraire and Ngoc Cuong Nguyen.
Alternative Title
HDPG scheme for compressible flows
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
The Hybridized Discontinuous Petrov-Galerkin scheme (HDPG) for compressible flows is presented. The HDPG method stems from a combination of the Hybridized Discontinuous Galerkin (HDG) method and the theory of the optimal test functions, suitably modified to enforce the conservativity at the element level. The new scheme maintains the same number of globally coupled degrees of freedom as the HDG method while increasing the stability in the presence of discontinuities or under-resolved features. The new scheme has been successfully tested in several problems involving shocks such as Burgers equation and the Navier-Stokes equations and delivers solutions with reduced oscillation at the shock. When combined with artificial viscosity, the oscillation can be completely eliminated using one order of magnitude less viscosity than that required by other Finite Element methods. Also, convergence studies in the sequence of meshes proposed by Peterson [49] show that, unlike other DG methods, the HDPG method is capable of breaking the suboptimal k+1/2 rate of convergence for the convective problem and thus achieve optimal k+1 convergence.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 113-117).
Subjects
Aeronautics and Astronautics.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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