An algorithm is presented in this article for the numerical study of the problem of filtration of compressible fluids and for solving the problem posed using the component splitting method and the data-driven sweep. The developed algorithm was first applied to solve a model problem in a rectangular domain with sources located symmetrically at the four edges and the center of the domain. Due to the symmetry of the results obtained, the result obtained for the quarter of the domain is presented. The developed algorithm is also used to solve a problem set in an arbitrary area and sources arbitrarily located in it. The solution results are shown in the form of graphs.