A Sharp Interface and Fully Conservative Scheme for Computing Nonclassical Shocks

B. Boutin (), C. Chalons (), F. Lagoutière () and P. G. LeFloch ()
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B. Boutin: Université Pierre et Marie Curie Paris 6, Laboratoire J.L. Lions
C. Chalons: DEN/DANS/DM2S/SFME/LETR CEA-Saclay
F. Lagoutière: Laboratoire J.L. Lions & Université Paris Diderot (Paris 7)
P. G. LeFloch: Université Pierre et Marie Curie Paris 6, Laboratoire J.L. Lions, Centre National de la Recherche Scientifique

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 217-224 from Springer

Abstract: Abstract We present a sharp interface and fully conservative numerical strategy for computing nonclassical solutions of scalar conservation laws. The difficult point is to impose at the discrete level a prescribed kinetic relation along each nonclassical discontinuity. Our method is based on a relevant reconstruction technique operating on each cell which is expected to contain a nonclassical shock. To prove the validity of our approach, we state some important stability properties and numerical tests are proposed. The convergence is also illustrated numerically.

Keywords: Conservative Scheme; Riemann Problem; Sharp Interface; Kinetic Function; Riemann Solution (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_25

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DOI: 10.1007/978-3-540-69777-0_25

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