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Filtration of Viscous Fluid in Homogeneous Domain with Mixed Boundary Condition

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Abstract

A three-dimensional problem of viscous fluid filtration in domain containing homogeneous porous medium is considered. Filtration flow is described by Darcy–Brinkman law. The boundary of the medium is divided into parts with either impermeability condition or condition on velocity vector flux or pressure. Integral representation for velocity and pressure of fluid is constructed with methods of potential theory. System of integral equations satisfying boundary conditions is solved numerically with piecewise-constant approximation and collocation method. The numerical scheme is tested on problems with different boundary conditions. The effect of viscousity on the flow is also studied. The tests demonstrate high accuracy of numerical method.

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Funding

This research was funded by Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation no. 075-15-2019-1624).

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics, Russian Academy of Science (INM RAS), 119333, Moscow, Russia

    R. M. Tretiakova

  2. Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333, Moscow, Russia

    R. M. Tretiakova

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  1. R. M. Tretiakova
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Correspondence to R. M. Tretiakova.

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(Submitted by E. E. Tyrtyshnikov)

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Tretiakova, R.M. Filtration of Viscous Fluid in Homogeneous Domain with Mixed Boundary Condition. Lobachevskii J Math 42, 1465–1474 (2021). https://doi.org/10.1134/S1995080221060305

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  • DOI: https://doi.org/10.1134/S1995080221060305

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