On the use of Mühlbach expansions in the recovery step of ENO methods |
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Authors: | Rémi Abgrall Thomas Sonar |
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Institution: | INRIA Sophia Antipolis 2004, route des Lucioles, B.P.93, F-09902 Sophia Antipolis Cedex, France; e-mail: abgrall@sophia.inria.fr, FR Institut für Str?mungsmechanik, DLR G?ttingen, Bunsenstra?e 10, D-37073 G?ttingen, Germany; e-mail: Thomas.Sonar@ts.go.dlr.de, DE
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Abstract: | Summary. The recovery step is the most expensive algorithmic ingredient in modern essentially non-oscillatory (ENO) shock capturing
methods on triangular meshes for the numerical simulation of compressible fluid flow. While recovery polynomials in Newton
form are used in one-dimensional ENO schemes it is a priori not clear whether such useful as well as numerically stable form of polynomials exists in multiple dimensions. As was observed
in 1] a very general answer to this question was provided by Mühlbach in two subsequent papers 15] and 16]. We generalise
his interpolation theory further to the general recovery problem and outline the use of Mühlbach's expansion in ENO schemes.
Numerical examples show the usefulness of this approach in the problem of recovery from cell average data.
Received August 24, 1995 / Revised version received December 14, 1995 |
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Keywords: | Mathematics Subject Classification (1991): 65M20 65M60 65D05 76M25 |
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