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Pan’ko, S. V.

Exact solutions of boundary-value problems for nonlinear flow in porous media. (English. Russian original) Zbl 0603.76097

Fluid Dyn. 20, 427-432 (1985); translation from Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1985, No. 3, 107-112 (1985).
Exact solutions for flow problems in porous media with a limiting gradient in the case when the flow region in the hodograph plane is a half-strip with a longitudinal cut are known only for two models of the resistance law. The present study gives a one-parameter family of flow laws, and argues the possibility of effective determination of exact and approximate analytical solutions on the basis of successive reduction to boundary-value problems for the Laplace equation or for the equation studied in detail by M. G. Bernadiner and V. M. Entov, The hydrodynamic theory of flow of anomalous fluids in porous media, Nauka, Moscow (1975). It should be noted that the characteristics of the flow are determined without additional quadratures.

Cited in 1 Document

MSC:

76S05 Flows in porous media; filtration; seepage
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

plane steady flow; nonlinear flow law; Exact solutions; limiting gradient; hodograph plane; resistance law; one-parameter family of flow laws; approximate analytical solutions; successive reduction; boundary- value problems; Laplace equation; characteristics of the flow
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References:

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