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  • 1
    Electronic Resource
    Electronic Resource
    Free surface seepage from nonsymmetric channels (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1547-1563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: 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.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181009
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical solutions to some free surface flows through nonhomogeneous media (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 143-167 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Steady-state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over-relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200111
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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