Two-Dimensional Extension of the Reservoir Technique for Some Linear Advection Systems

  • Authors:

  • François Alouges;Gérard Coq;Emmanuel Lorin

  • Affiliations:

  • Département de Mathématiques, Université d'Orsay, Orsay, France 91405;Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, Cachan, France 94235;Département de Mathématiques, Université d'Orsay, Orsay, France 91405 and Centre de Recherche en Mathématiques, Université de Montréal, Montreal, Canada H3T 1J4

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2007

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Abstract

In this paper we present an extension of the reservoir technique (see, [Alouges et al., Submitted; Alouges et al.(2002a), In: Finite volumes for complex applications, III, pp. 247---254, Marseille; Alouges et al.(2002b), C. R. Math. Acad. Sci. Paris, 335(7), 627---632.]) for two-dimensional advection equations with non-constant velocities. The purpose of this work is to make decrease the numerical diffusion of finite volume schemes, correcting the numerical directions of propagation, using a so-called corrector vector combined with the reservoirs. We then introduce an object called velocities rose in order to minimize the algorithmic complexity of this method.