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[MPL/RelPermNonWettingPhaseVanGenuchtenMualem] replace the Newton-Raphson method with the Regula–Falsi Method

Merged wenqing requested to merge wenqing/ogs:improve_permeablility into master

In RelPermNonWettingPhaseVanGenuchtenMualem, the saturation corresponding to the minimum relative permeability is computed by using the Newton-Raphson method. With Newton-Raphson method, the solution of saturation during the linearization may exceed the range of [S_\text{r}, S_\text{max}]. Especially when S > S_\text{max}, i.e. S_e > 1, the permeability value calculation in RelPermNonWettingPhaseVanGenuchtenMualem leads to overflow.

In this MR. the local nonlinear solver in RelPermNonWettingPhaseVanGenuchtenMualem is changed to the Regula–Falsi method. With the Regula–Falsi method, the saturation is always in the range of [S_\text{r}, S_\text{max}]. That computation is only performed once on the ctor of RelPermNonWettingPhaseVanGenuchtenMualem. Since that permeability function is monotonic, the Regula–Falsi method for the root calculation can always give converged solution.

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  3. Any new feature or behavior change was documented?
Edited by wenqing