Computational Mathematics

Algorithm for numerical study of degenerate models of nonlinear diffusion and filtration with a random initial state

N. A. Manakova, N. G. Nikolaeva

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article is devoted to the numerical study of one class of stochastic models of nonlinear diffusion and filtration with a random initial condition of Showalter–Sidorov. The nonlinear diffusion model describes the process of changing the concentration potential of a viscoelastic fluid filtering in a porous medium; the nonlinear filtration model describes the dependence of the pressure of a viscoelastic incompressible fluid filtering in a porous formation on the external load. The models under consideration study within an abstract semilinear equation of Sobolev type with $p$-coercive and $s$-monotone operator. An algorithm for the numerical solution method of one class of problems of mathematical physics is constructed. An example of applying the algorithm to the stochastic model of nonlinear diffusion under study is given.

Keywords: Sobolev type equations, stochastic model of nonlinear diffusion, stochastic model of nonlinear filtration, projection method.

UDC: 517.9

MSC: 35Q99

Received: 14.01.2025

Language: English

DOI: 10.14529/jcem250103