Mathematical modeling of anisotropic physical and chemical processes

Often the proceeding of physical and chemical processes (fluid flows in nozzles, channels and shock tubes, external flow around various objects, heat and mass transfer in porous bodies, etc.) has a preferentially spatial direction. Recently $\mathrm{1D}$ models have been proposed for the mathematical description of such processes, but now more detailed $\mathrm{3D}$ models are developed. The modeling complexity increases impressively with the transfer to $\mathrm{3D}$ modeling. The article represents a computational approach based on the artificial extraction «$\mathrm{1D}$ terms» in the solution to reduce the amount of computational work in multidimensional modeling. Based on the Dirichlet boundary value problem for Poisson equation in a unit cube, the efficiency of proposed approach associated with solving $d = 2.3$ auxiliary 1D problems is demonstrated. The article represents results of the convergence analysis of the iterative methods with proposed solution decomposition for the discrete (initial-)boundary value problems. Previously, the efficiency of this approach was demonstrated for the numerical solution of saddle problems (the discrete Navier-Stokes equations).