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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.

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