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Free surface seepage from nonsymmetric channels
Author(s) -
Remar J.,
Bruch J. C.,
Sloss J. M.
Publication year - 1982
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620181009
Subject(s) - mathematics , free surface , nonlinear system , compatibility (geochemistry) , projection method , mathematical analysis , intersection (aeronautics) , boundary value problem , homogeneous , variable (mathematics) , domain (mathematical analysis) , surface (topology) , geometry , mathematical optimization , mechanics , engineering , dykstra's projection algorithm , physics , quantum mechanics , combinatorics , chemical engineering , aerospace engineering
The problem of steady, two‐dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions—one for the flowrate and one for the value of the new dependent variable at the left‐hand side free surface‐channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the literature.