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Problem with documentation of FEMWATER conductivity tensor


James Ewart
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This post references the methodology for calculating the hydraulic conductivity tensor that appears on pp. 44-46 of the Femwater 3 reference document, and specificially equations 36 and 42. Has anyone noted the descrepancies between the terms in these two equations? In particular, the alpha3 term in equation 36 must (by eqn. 41) equal the gamma 31 term, but does not. Similarly, the beta 1 term of eqn. 36 does not match the gamma 12 term in eqn. 42. I've compared the equations to Morse and Feshbach (the cited reference, which was published in 1953; the cited publ. date of 1978 is actually the number of pages in the document). Based on my comparison, the errors in the FEMWATER documentation reside in definition of terms in eqn 36 and not in eqn 42. However, there appears to be a more serious problem. The documentation describes the euler angles as though they were the resultant angluar differences between the axes of principal conductivity and the x, y, and z axes. This is in general, not the case. A read of Morse and Feshbach confirms that the euler angles used in eqns. 36 and 41 are the angles of sequential angular rotations about the transformed axes. Therefore, it is essential that one knows the order of these transformations to evaluate the conductivity tensor using eqns 42 and. 43. That information is not provided (to be fair the original reference also fails to provide this information). The documentation gives the misimpression that one might instead use the resultant angular differences between the axes in lieu of the euler angles. I have concluded that this is a mistake and that is not possible using the method described to accurately calculate the conductivity tensor using eqns. 42 and 43. However, I doubt my own conclusion, because I am hard pressed to believe that such a fundimental error would survive uncorrected, and perhaps uncommented, for the 13 years since it first appeared in the July 1997 Femwater documentation (technical report CHL-97-12). Therefore, I would appreciate it if someone would confirm or correct my conclusions.

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I am a FEMWATER user so this is of interest to me. But I am a bit new to this area so not familiar with the mathematical subtleties.

Do you think this mistake is carried into the solution?

By the way, I have found other (minor) errors in the FEMWATER manual, which I might as well list here FYI...

- the order of the OMEMIN and OMEMAX variables in the OP3 card is reversed.

- IBSPL is missing in the IP1 card format.

- there is an extraneous value in the IP2 card sample.

- the MP2 card sample is labelled MP1.

- PROPT(13,I) is missing in the MP5 card sample.

- Yeh & Ward 1980 title should have FEMWATER not FEMWASTE.

I have the code and can follow some of the logic but get quickly lost.

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Do you think this mistake is carried into the solution?

I think the mistake would only affect the solution if the equations and method I referenced were used to calculate the conductivity tensor components for input into a model. I am new to FEMWATER and was attempting this with my first test model. This led to my discovery of the problem. The only other way the mistake could affect the model is if the same equations were used by the code to make additional transformations. I doubt this is the case, because the "euler angles" are not input variables.

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