Abstract
The article discusses elementary solutions of problems of nonlinear filtration with a piece-wise-linear resistance law, and analyzes their behavior with a relative increase in the resistance in the region of small velocities, and a transition to the law of filtration with a limiting gradient. The results obtained are applied to a determination of the dimensions of the stagnant zones in stratified strata. The law of filtration with a limiting gradient
describes motion in some intermediate range of velocities w, but its satisfaction in the region of the smallest velocities, as a rule, remains unverified. It is natural to pose the problem of the degree to which a divergence between the true filtration law and its approximation (0.1) affects the accuracy of calculation of the flow fields, and the significance of a determination of the dimensions of the stagnant zones under such conditions. To answer this problem to some measure, there are considered below several simple exact (elementary) solutions obtained for a more general nonlinear filtration law
going over into (0.1) with w0→ 0. The solutions obtained are applied also to an evaluation of the dimensions of stagnant zones, forming in stratified strata when the effects of the limiting gradient in one of the intercalations are considerable.
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V. M. Entov, “Two-dimensional problems in the theory of filtration with a limiting gradient,” Prikl. Mat. Mekhan.,31, No. 5 (1967).
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V. M. Entov, “Paired integral equations arising in problems of filtration with a limiting gradient,” Prikl. Mat Mekhan.,34, No. 3 (1970).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 40–45, March–April, 1974.
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Entov, V.M., Malakhova, T.A. Filtration problems with a piecewise-linear resistance law. Fluid Dyn 9, 194–198 (1974). https://doi.org/10.1007/BF01092649
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DOI: https://doi.org/10.1007/BF01092649