Two-dimensional-one-dimensional splitting scheme for the numerical solution of problems of transport of multicomponent suspensions using θ coordinates

Abstract

The work considers the spatial-three-dimensional problem of suspension transport, which takes into account many parameters and processes (multicomponent fractional composition of suspension, particle sedimentation rate, suspension distribution, intensity of sources of suspension distribution, etc.). For the basic equation of this problem, a symmetric representation of the convective terms is used, which makes it possible to ensure the unconditional skew symmetry of the convective transport operator. The methodology for constructing additive circuits (splitting circuits) is outlined, which makes it possible to reduce the solution of the original problem to a sequential (or parallel for multiprocessor computers) solution of two-dimensional and one-dimensional analogues. The feasibility of this approach is determined, first of all, by the significant differences in space-time scales for the difference operators of diffusion transfer in the horizontal and vertical directions, as well as their spectra. The constructed splitting scheme is monotonic, and each of the difference equations is non-degenerate if the grid Peclet number is less than one.