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Numerical predictions of two‐dimensional transient groundwater flow by the method of characteristics
Author(s) -
Wiggert D. C.,
Wylie E. B.
Publication year - 1976
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/wr012i005p00971
Subject(s) - aquifer , groundwater flow , inertia , finite element method , mechanics , mathematics , computation , numerical analysis , geology , geotechnical engineering , mathematical analysis , groundwater , physics , classical mechanics , algorithm , thermodynamics
Unsteady flow in a confined or leaky aquifer can be analyzed by replacing the two‐dimensional space domain with a latticework of line elements which intersect at nodal points. Continuity and momentum principles are applied to each line element separately, resulting in a system of hyperbolic equations which can be solved by the method of characteristics. Upon combination of the continuity relation and compatibility conditions at each node an explicit solution for the time‐variable piezometric heads and seepage velocities is obtained. An inertia multiplier is introduced in the momentum equation, which varies inversely with the magnitude of the fluid acceleration. The time step, proportional to the multiplier, thus assumes large values, while the method continues to provide accurate, stable results. Numerical examples are compared with analytical solutions, and a nonhomogeneous regional aquifer analysis agrees favorably with a finite element model. The numerical scheme provides ease of programing, reduced computer storage requirements, and reasonable central processing times.