Abstract
The eigenvalues method provides an explicit continuous-in-time solution for groundwater flow equations. Only space is discretized and a vector differential equation is obtained. Both finite differences and finite elements can be used to approximate partial derivatives of space. The eigenvalues and eigenvectors of a matrix, which is a function of the coefficients of the linear equations of the vector differential equation, are the key to the solution. The state of the aquifer can be expressed on the orthonormal basis provided by the eigenvectors.
Hydraulic head or flow at specific points can be explicitly obtained for particular times of interest. Also, in most real cases, external actions can be expressed as a linear combination of a reduced set of stresses, allowing there to be an important reductions in computation. Other important reduction in computation can be achieved owing to the rapid approximation to the steady state solution of many of the orthogonal components.
The approach is most useful when the simulation to be made for various alternatives is of considerable accumulative length.
Other possibilities of the method for the solution of the mass-transport equation are described.
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© 1988 D. Reidel Publishing Company
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Sahuquillo, A., Andreu, J. (1988). The Eigenvalues Approach for Solving Linear Groundwater Flow Problems. In: Custodio, E., Gurgui, A., Ferreira, J.P.L. (eds) Groundwater Flow and Quality Modelling. NATO ASI Series, vol 224. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2889-3_9
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DOI: https://doi.org/10.1007/978-94-009-2889-3_9
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