The problem of the end-to-end calculation of the flow of a weakly compressible fluid flowing in a porous body–free flow system is considered. This problem is relevant to the design of hydrocarbon processing systems, pollution purification plants, etc. As an example, the problem of the flow of an aqueous fluid through a cylindrical region containing a porous insert formed by spherical sorbent granules is chosen. This model problem is analyzed by two mathematical methods. The first method is based on direct mathematical modeling of a flow in a medium with discontinuous porosity determined by a system of granules. The second method involves the introduction of a continuous porous medium and consists of averaging the flow parameters over a representative volume under the specified fluid velocity and filtration rate. Within the framework of each method, the basic model is a quasi-hydrodynamic system of equations. Approximation of the proposed systems is based on the finite volume method for unstructured three-dimensional grids. The constructed computational algorithm is programmatically implemented using geometric parallelism. Based on the results obtained in direct mathematical modeling, permeability coefficients for the averaged model are selected. Computational experiments carried out within the framework of the averaged representation of porosity demonstrated the correctness of the used model, computational algorithm, and its software realization.
Kudryashova et al. (2026) studied this question.