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.
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Alouges, F., Le Coq, G. & Lorin, E. Two-Dimensional Extension of the Reservoir Technique for Some Linear Advection Systems. J Sci Comput 31, 419–458 (2007). https://doi.org/10.1007/s10915-006-9115-7
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DOI: https://doi.org/10.1007/s10915-006-9115-7