fronts.D.richards¶

fronts.D.
richards
(C, kr, Ks=None, k=None, nu=1e06, g=9.81)¶ Return a moisture diffusivity function for a Richards equation problem.
Given K_S and the functions C and \(k_r\) of S (where S is either water content or saturation), returns the function:
\[D(S) = \frac{K_S k_r(S)}{C(S)}\]This function helps transform problems of the horizontal Richards equation (for which \(K_S\), \(k_r\), and C are known parameters) into problems of the moisture diffusivity equation that can be solved with this library.
 Parameters
C (callable) – Capillary capacity function (also known as hydraulic capacity function). A twicedifferentiable 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 asC(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.kr (callable) – \(k_r\), the relative permeability function (also known as relative conductivity function). A twicedifferentiable function that maps values of S to positive values (usually between 0 and 1). It can be called as
kr(S)
to evaluate it at S. It can also be called askr(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, kr operates in a vectorized fashion with the same semantics when S is a numpy.ndarray.Ks (float, optional) – \(K_S\), the saturated hydraulic conductivity. Must be positive. If neither Ks nor k are given, the saturated hydraulic conductivity is assumed to be 1.
k (float, optional) – Intrinsic permeability of the porous medium. Can be given in place of Ks, which results in the saturated hydraulic conductivity being computed using \(K_S = kg/\nu\). Must be positive.
nu (float, optional) – \(\nu\), the kinematic viscosity of the wetting fluid. Only used if k is passed instead of Ks. Must be positive. Defaults to 1e6, approximately the kinematic viscosity of water at 20°C in SI units.
g (float, optional) – Magnitude of the gravitational acceleration. Only used if k is passed instead of Ks. Must be positive. Defaults to 9.81, the gravity of Earth in SI units.
 Returns
D – Twicedifferentiable function that maps values of S in the domains of both kr and C to positive values. It can be called as
D(S)
to evaluate it at S. It can also be called asD(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