# fronts.D.richards¶

fronts.D.richards(K, C)

Return a moisture diffusivity function for a Richards equation problem.

Given the functions K and C (where S is either water content or saturation) returns the function:

$D(S) = \frac{K(S)}{C(S)}$

This effectively converts horizontal Richards equation problems (for which those two functions are parameters) into moisture diffusivity problems that can be solved using this library.

Parameters
• K (callable) – Hydraulic conductivity function. A twice-differentiable function that maps values of S to positive values. It can be called as K(S) to evaluate it at S. It can also be called as K(S, n) with n equal to 1 or 2, in which case the first n derivatives of the function evaluated at the same S are included (in order) as additional return values. While mathematically a scalar function, K operates in a vectorized fashion with the same semantics when S is a numpy.ndarray.

• C (callable) – Capillary capacity function. A twice-differentiable function that maps values of S to positive values. It can be called as C(S) to evaluate it at S. It can also be called as C(S, n) with n equal to 1 or 2, in which case the first n derivatives of the function evaluated at the same S are included (in order) as additional return values. While mathematically a scalar function, C operates in a vectorized fashion with the same semantics when S is a numpy.ndarray.

Returns

D – Twice-differentiable function that maps values of S in the domains of both K and C to positive values. It can be called as D(S) to evaluate it at S. It can also be called as D(S, n) with n equal to 1 or 2, in which case the first n derivatives of the function evaluated at the same S are included (in order) as additional return values. While mathematically a scalar function, D operates in a vectorized fashion with the same semantics when S is a numpy.ndarray.

Return type

callable