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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Print: 2152-5102
ISSN Online: 2152-5110

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v32.i4.30
pages 420-438

General Solution for Two-Dimensional Corner Flows Under Darcy's

Yu. A. Semenov
Institute of Hydromechanics of NAS of Ukraine, 8/4 Zhelyabov Street, Kyiv-180, MSP, 03680, Ukraine
L. J. Cummings
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK

ABSTRACT

We consider two-dimensional Darcy flow of a viscous incompressible fluid with a free boundary in a corner between two non-parallel walls. The complex potential of the flow constructed in an auxiliary parameter domain admits a general form for the flow generated by a source/sink at the corner vertex or at infinity. We present a method used to construct the flow potential, and obtain an integral equation for the velocity modulus on the free boundary. We discuss a possible numerical procedure to solve this integral equation, and present sample numerical results concerning the initial shape of the free boundary and its time evolution.


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