Numerical Solution of a Boundary Value Inverse Problem for the Equation of Unsteady Relaxation Filtration of a Fluid in a Porous Medium

In this paper, we solve a boundary value inverse problem for the equation of unsteady relaxation fluid flow in a porous medium under elastic conditions. We applied marching methods, specifically the De Souza and Hensel-Hills methods, to solve the problem. Smoothing splines were used to obtain stable solutions, significantly reducing the error in the numerical solution of the problem. Additional data for the inverse problem are generated based on a quasi-real experiment, ensuring a more reliable reconstruction of the sought-after parameters. We also analyze the influence of smoothing parameters on the accuracy of function reconstruction. Numerical validation of the proposed algorithms using model tests demonstrates their stability in the presence of perturbations in the input data. The obtained results confirm the effectiveness of the developed approach and can be used to solve a wide range of inverse flow problems in heterogeneous porous media.

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