Replace Hard-Coded Derivatives with Automatic Differentiation

[carlosra0345]

Currently, the derivatives in this codebase are hard-coded as direct differentiations of their original functions, most of which are taken from the original MATLAB implementation nmmoc_surf_nuemann.m. This approach introduces maintainability issues, increases the risk of errors, and makes extending or modifying the code difficult.

Affected Derivatives

The derivatives that are currently hard-coded include:

• σ (the IFT equation)

• IFT with respect to surfactant concentration

• Residual saturations with respect to surfactant concentration

• Normalized saturations with respect to surfactant concentration

• Relative permeability with respect to surfactant concentration

• Relative permeability with respect to saturation

• Fractional flow with respect to saturation and concentrations

• Capillary pressure with respect to saturation and concentrations

Suggested Improvement

Consider replacing these hard-coded derivatives with automatic differentiation where possible. This would:

• Reduce maintenance overhead when modifying underlying functions.

• Minimize human error in derivative calculations.

• Facilitate extension to new functional forms or additional variables.

[bhargavakula01]

Another useful package that we could use for implementation:

https://github.com/HIPS/autograd