|
|||||
|
|
On the reservoir technique convergence for nonlinear hyperbolic conservation laws - Part I |
|
| Authors: | Stéphane Labbé |
| Institution: | a Département de Mathématiques, Université Joseph Fourier, 38041 Grenoble Cedex 9, France b Faculty of Science, University of Ontario Institute of Technology, Oshawa, ON, L1H 7K4, Canada c Centre de Recherches Mathématiques, Montréal, Québec, H3T 1J4, Canada |
| Abstract: | This paper is devoted to the analysis of flux schemes coupled with the reservoir technique for approximating hyperbolic equations and linear hyperbolic systems of conservation laws F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, The reservoir scheme for systems of conservation laws, in: Finite Volumes for Complex Applications, III, Porquerolles, 2002, Lab. Anal. Topol. Probab. CNRS, Marseille, 2002, pp. 247-254 (electronic); F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, Un procédé de réduction de la diffusion numérique des schémas à différence de flux d'ordre un pour les systèmes hyperboliques non linéaires, C. R. Math. Acad. Sci. Paris 335 (7) (2002) 627-632; F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, The reservoir technique: A way to make Godunov-type schemes zero or very low diffusive. Application to Colella-Glaz, Eur. J. Mech. B Fluids 27 (6) (2008)]. We prove the long time convergence of the reservoir technique and its TVD property for some specific but still general configurations. Proofs are based on a precise study of the treatment by the reservoir technique of shock and rarefaction waves. |
| Keywords: | Finite volume scheme Numerical diffusion Convergence Hyperbolic systems |
| 本文献已被 ScienceDirect 等数据库收录！ | |