On one effective difference scheme for the convection‐diffusion problem

Abstract

The given paper is devoted to build‐up of the special economic difference schemes for non‐stationary one and two‐dimensional problems of a convection ‐ diffusion permitting to take into account convective and diffusion terms from the uniform point of view. On the basis of a multicomponent schemes build‐up procedure, bound up with region decomposition of the cells of mesh, the economic multicomponent iterative algorithm is constructed. A series of numerical calculations on some test problems solution including Burgers problem is reduced, and the comparison with known, most spread schemes is proceeded.

Darbe pasiūlytas naujo tipo baigtiniu skirtumu schemos, aproksimuojančios konvekcijos ir difuzijos procesus. Pateikta bendra metodika, kuri apibendrina eksponentinio tipo schemas. Gerai žinoma, kad tokio tipo schemos atskirais atvejais yra tikslios. Sudaryti ekonomiški schemos realizavimo algoritmai, kuriuose panaudota daugiakomponentiniu iteraciniu metodu ideja. Pateikti apibendrinimai dvimačiams uždaviniams. Teoriniai rezultatai iliustruojami skaitinio eksperimento rezultatais.