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Exact solutions of boundary-value problems for nonlinear flow in porous media

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Abstract

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 [1] are known only for two models of the resistance law [2–6]. 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 in [1]. It should be noted that the characteristics of the flow are determined without additional quadratures.

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  1. Tomsk

    S. V. Pan'ko

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  1. S. V. Pan'ko
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 107–112, May–June, 1985.

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Pan'ko, S.V. Exact solutions of boundary-value problems for nonlinear flow in porous media. Fluid Dyn 20, 427–432 (1985). https://doi.org/10.1007/BF01049997

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  • DOI: https://doi.org/10.1007/BF01049997

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