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An eigenvalue solution continuous in time to the spatially discretized solute transport equation in steady groundwater flow
Author(s) -
Hwang Jack C.,
Cho Woncheol C.,
Yeh G. T.
Publication year - 1984
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/wr020i011p01725
Subject(s) - discretization , groundwater flow , eigenvalues and eigenvectors , computation , groundwater , steady state (chemistry) , convection–diffusion equation , flow (mathematics) , boundary value problem , constant (computer programming) , mechanics , boundary (topology) , transient (computer programming) , groundwater flow equation , mathematics , mathematical analysis , physics , computer science , geology , aquifer , chemistry , geotechnical engineering , algorithm , quantum mechanics , programming language , operating system
The spatially discretized two‐dimensional solute transport equation in a steady groundwater flow was solved by an eigenvalue technique. The solution is exact in time. An explicit expression was obtained for each nodal point as a function of time. Thus the computer code can be implemented to calculate solute concentration at any nodal point at any given instant with a direct computation. The general solution can be obtained explicitly for transient boundary conditions and variable constant source loads. The solution for steady boundary conditions can readily be derived from the general solution. The method presented herein can provide convenience of data retrieval, particularly in groundwater management modeling.