fronts.D.richards

fronts.D.richards(C, kr, Ks=None, k=None, nu=1e-06, g=9.81)

Return a moisture diffusivity function for a Richards equation problem.

Given K_S and the functions C and \(k_r\) (whose argument is either water content or saturation), returns the function:

\[D(\theta) = \frac{K_S k_r(\theta)}{C(\theta)}\]

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

  • kr (callable) – \(k_r\), the relative permeability function (also known as relative conductivity function). A twice-differentiable function that maps values of \(\theta\) to positive values (usually between 0 and 1). It can be called as kr(theta) to evaluate it at theta. It can also be called as kr(theta, n) with n equal to 1 or 2, in which case the first n derivatives of the function evaluated at the same theta are included (in order) as additional return values. While mathematically a scalar function, kr operates in a vectorized fashion with the same semantics when theta is a numpy.ndarray.

  • Ks (None or 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 (None or 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 1e-6, 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 –

Function to evaluate \(D\) and its derivatives:

  • D(theta) evaluates and returns \(D\) at theta

  • D(theta, 1) returns both the value of \(D\) and its first derivative at theta

  • D(theta, 2) returns the value of \(D\), its first derivative, and its second derivative at theta

In all cases, the argument theta may be a single float or a NumPy array.

Return type:

callable