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A technique in using integrodifferential equations for model simulation of multiaquifer systems
Author(s) -
Premchitt Jerasak
Publication year - 1981
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/wr017i001p00162
Subject(s) - curse of dimensionality , convolution (computer science) , exponential function , mathematics , flow (mathematics) , aquifer , basis (linear algebra) , mathematical analysis , computer science , geology , geometry , geotechnical engineering , groundwater , statistics , machine learning , artificial neural network
A numerical technique for modeling a multiaquifer system is developed on the basis of a quasi three‐dimensional flow model. The model consists of many horizontal aquifers interconnected by leakage flux from aquitards. The direct flow across aquitards and yield from aquitard storage are taken into account in leakage flux terms in the form of convolution integrals. Mathematical formulation results in flow functions which diminish with time and can be approximated by few exponential terms. They have been proved to be very convenient in a numerical solution scheme involving the convolution integrals. The approach reduces the dimensionality of the problem and uncouples the equations corresponding to each of the aquifers. The technique is flexible and can be used for any basin geometry with an arbitrary pumping scheme. The validity of the technique is demonstrated by comparing the model results with available analytical solutions. In general, it appears that this technique is more economical than the full three‐dimensional model or even the quasi three‐dimensional models that use one‐dimensional elements to represent the aquitards.