A numerical scheme for transport equations with spatially distributed coefficients based on locally exact difference method
A numerical difference scheme to solve stationary transport equations with spatially distributed coefficients is presented. The scheme SDCLENS (spatially distributed coefficients locally exact numerical scheme) for the convection term in the transport equation is presented in which the difference coefficients are determined such that the resulting equation interpolating numerical flux satisfies any locally exact solution of the transport equation with absorption and source terms. The spatial distribution of the coefficients of the transport equation is taken into consideration based on a four-region model among three adjacent volumes in which continuity conditions of the solutions are imposed on each boundary between two adjacent regions. The SDCLENS scheme is examined through numerical experiments using the one-dimensional transport equation with spatially distributed coefficients and the two-dimensional cavity flow problem.
spatially distributed coefficients locally exact numerical scheme
scientific article; zbMATH DE number 1067829
scientific article