Application of a Local Similarity Concept in Solving the Vertical Subsurface Flow Problem

A technique is described for solving various problems in continuum mechanics through the application of similarity transformations when all the requirements for the application of such transformations are not satisfied. The transformed equations usually involve a stray time variable that is interpre...

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Bibliographic Details
Published in:Water resources research 1971-10, Vol.7 (5), p.1241-1255
Main Authors: Drake, Ronald L., Peterson, Celeste P.
Format: Article
Language:English
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Summary:A technique is described for solving various problems in continuum mechanics through the application of similarity transformations when all the requirements for the application of such transformations are not satisfied. The transformed equations usually involve a stray time variable that is interpreted as a system parameter. When this parameter is properly interpreted, the solutions of the transformed systems are very good numerical approximations for the solutions of the original systems. The advantages of considering the transformed systems are usually two‐fold: numerical solutions can be obtained with less computer time, and qualitative analysis of the transformed systems is usually easier than that of the original systems. The problems discussed in this paper include certain previously published results and some new results obtained for the nonlinear Fokker‐Planck equation in which the vertical movement of soil moisture under the influence of gravity is described.
ISSN:0043-1397
1944-7973
DOI:10.1029/WR007i005p01241