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Influence graphs and the generalized finite difference method. (English) Zbl 1173.76376
Summary: This paper introduces directed graphs on which the evolution of a physical quantity depends only on local neighborhoods. These graphs are then used to model transfer phenomena occurring under a convective mode or a diffusive mode. The conditions under which the state associated to such graphs approaches the solution of a diffusion-convection partial differential model are established. An algorithm permitting to determine consistent neighborhoods is described and recognized as a generalization of the finite difference method. Examples of application are presented in order to illustrate the practical applicability of these concepts.

76M20 Finite difference methods applied to problems in fluid mechanics
76R99 Diffusion and convection
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