grf_laplace(s, rad=None, S_part=None, K_part=None, R_part=None, dim=2, lat_ext=1.0, rate=None, K_well=None, cut_off_prec=1e-20, cond=0, cond_kw=None)[source]

The extended GRF-model for transient flow in Laplace-space.

The General Radial Flow (GRF) Model allowes fractured dimensions for transient flow under a pumping condition in a confined aquifer. The solutions assumes concentric annuli around the pumpingwell, where each annulus has its own conductivity and storativity value.

  • s (numpy.ndarray) – Array with all Laplace-space-points where the function should be evaluated

  • rad (numpy.ndarray) – Array with all radii where the function should be evaluated

  • S_part (numpy.ndarray of length N) – Given storativity values for each disk

  • K_part (numpy.ndarray of length N) – Given conductivity values for each disk

  • R_part (numpy.ndarray of length N+1) – Given radii separating the disks as well as starting- and endpoints

  • dim (float) – Flow dimension. Default: 3

  • lat_ext (float) – The lateral extend of the flow-domain, used in L^(3-dim). Default: 1

  • rate (float) – Pumpingrate at the well

  • K_well (float, optional) – Conductivity at the well. Default: K_part[0]

  • cut_off_prec (float, optional) – Define a cut-off precision for the calculation to select the disks included in the calculation. Default 1e-20

  • cond (int, optional) –

    Type of the pumping condition:

    • 0 : constant

    • 1 : periodic (needs “w” as cond_kw)

    • 2 : slug (rate will be interpreted as slug-volume)

    • 3 : interval (needs “t” as cond_kw)

    • callable: laplace-transformation of the transient pumping-rate

    Default: 0

  • cond_kw (dict optional) – Keyword args for the pumping condition. Default: None


grf_laplace – Array with all values in laplace-space

Return type



>>> grf_laplace([5,10],[1,2,3],[1e-3,1e-3],[1e-3,2e-3],[0,2,10], 2, 1, -1)
array([[-2.71359196e+00, -1.66671965e-01, -2.82986917e-02],
       [-4.58447458e-01, -1.12056319e-02, -9.85673855e-04]])