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Journal of Computational Physics 167, 277315 (2001) doi:10.1006/jcph.2000.6672, available online at http://www.idealibrary.com on

Summary: Journal of Computational Physics 167, 277­315 (2001)
doi:10.1006/jcph.2000.6672, available online at http://www.idealibrary.com on
Toward the Ultimate Conservative Scheme:
Following the Quest
R. Abgrall
Math´ematiques Appliqu´ees de Bordeaux, Universit´e Bordeaux I, 351 Cours de la Lib´eration,
33 405 Talence Cedex, France
E-mail: abgrall@math.u-bordeaux.fr
Received September 15, 1999; revised October 17, 2000
The aim of this paper is to develop a class of numerical schemes that work on
triangular finite element type meshes, and which are devoted to the computation
of steady transonic flows. The schemes are extensions of the positive streamwise
invariant scheme of Struijs and are built directly on the system of the Euler equation
for fluid mechanics. They are a blending between a first-order and a second-order
scheme, which is realized from entropy considerations. It is formally second-order
accurate at steady state. Several numerical examples are shown to demonstrate the
stability and accuracy of these schemes. c 2001 Academic Press
Key Words: compressible flow solvers; residual schemes; fluctuation splitting
schemes; unstructured meshes; multidimensional up-winding.


Source: Abgrall, Rémi - Institut de Mathematiques de Bordeaux, Université Bordeaux


Collections: Mathematics