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Numerical model for saturated‐unsaturated flow in deformable porous media: 2. The algorithm
Author(s) -
Narasimhan T. N.,
Witherspoon P. A.,
Edwards A. L.
Publication year - 1978
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr014i002p00255
Subject(s) - nonlinear system , algorithm , stability (learning theory) , flow (mathematics) , porous medium , convergence (economics) , mathematics , boundary (topology) , computer science , boundary value problem , mathematical optimization , mathematical analysis , geometry , porosity , physics , geotechnical engineering , quantum mechanics , machine learning , economics , economic growth , engineering
An integrated finite difference algorithm is presented for numerically solving the governing equation of saturated‐unsaturated flow in deformable porous media. In recognition that stability of the explicit equation is a local phenomenon a mixed explicit‐implicit procedure is used for marching in the time domain. In this scheme the explicit changes in potential are first computed for all elements in the system, after which implicit corrections are made only for those elements for which the stable time step is less than the time step being used. Time step sizes are automatically controlled in order to optimize the number of iterations, to control maximum change in potential during a time step, and to obtain desired outputs. Time derivatives, estimated on the basis of system behavior during two previous time steps, are used to start the iteration process and to evaluate nonlinear coefficients. Boundary conditions and sources can vary with time or with the dependent variable. Input data are organized into convenient blocks. Accuracy of solutions can be affected by modeling errors, different types of truncation errors, and convergence errors. The algorithm constitutes an efficient tool for analyzing linear and nonlinear fluid flow problems in multidimensional heterogeneous porous media with complex geometry. An important limitation is that the model cannot conveniently handle arbitrary anisotropy and other general tensorial quantities.