Two-dimensional extension of the reservoir technique for some linear advection systems

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.