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Created Mar 27, 2020 by Theresa Schollenberger@tscholMaintainer

Wrong dkrn_dswe analytical derivative in Brooks-Corey and Van Genuchten

The implementation of the analytical derivative dkrn_dswe in the Brooks-Corey law is not correct. This is also shown by a comparison with the numerical derivative.

Implemented derivative: \frac{d krn}{d swe} = 2 (swe -1) (1+\frac{1}{\lambda} \cdot swe^{\frac{2}{\lambda}} + \frac{1}{2} - (\frac{1}{2}+\frac{1}{\lambda}) \cdot swe)

Correct derivative: \frac{d krn}{d swe} = 2 (swe -1) (1+(\frac{1}{2} + \frac{1}{\lambda}) \cdot swe^{\frac{2}{\lambda}} - (\frac{3}{2}+\frac{1}{\lambda}) \cdot swe^{\frac{2}{\lambda}+1})

dkrndSw

Additionaly there is also an error in the analytical derivative dkrn_dswe in the Van Genuchten law.

Implemented derivative: \frac{d krn}{d swe} = -(1-swe)^{\gamma-1}\cdot(1-swe^{\frac{1}{m}})^{2m-1}\cdot (\gamma(1-swe^{\frac{1}{m}}) - 2\frac{1-swe}{swe} swe^{\frac{1}{m}})

Correct derivative: \frac{d krn}{d swe} = -(1-swe)^{\gamma-1}\cdot(1-swe^{\frac{1}{m}})^{2m-1}\cdot (\gamma(1-swe^{\frac{1}{m}}) \color{red}+ \color{black} 2\frac{1-swe}{swe} swe^{\frac{1}{m}})

dkrndSw_vanGenuchten

Edited Mar 30, 2020 by Theresa Schollenberger
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