HeadWell#

class timflow.transient.well.HeadWell(model, xw=0, yw=0, rw=0.1, tsandh=[(0, 1)], res=0, layers=0, label=None)#

Bases: WellBase, timflow.transient.equation.HeadEquation

Create a well with a specified head inside the well.

The well may be screened in multiple layers. The resistance of the screen may be specified. The head is computed such that the discharge \(Q_i\) in layer \(i\) is computed as

\[Q_i = 2\pi r_wH_i(h_i - h_w)/c\]

where \(c\) is the resistance of the well screen and \(h_w\) is the head inside the well.

Parameters:

model (Model object) – model to which the element is added
xw (float) – x-coordinate of the well
yw (float) – y-coordinate of the well
rw (float) – radius of the well
tsandh (list of tuples) – tuples of starting time and discharge after starting time
res (float) – resistance of the well screen
layers (int, array or list) – layer (int) or layers (list or array) where well is screened
label (string (default: None)) – label of the well

initialize()#

Initialize the element.

Initialization of terms that cannot be initialized before other elements or the aquifer is defined.

As we don’t want to require a certain order of entering elements, these terms are initialized when Model.solve is called The initialization class needs to be overloaded by all derived classes

setflowcoef()#: Separate function so that this can be overloaded for other types.

potinf(x, y, aq=None)#: Can be called with only one x,y value.

potinfone(x, y, jtime, aq=None)#: Can be called with only one x,y value for time interval jtime.

disvecinf(x, y, aq=None)#: Can be called with only one x,y value.

headinside(t, derivative=0)#

Returns head inside the well for the layers that the well is screened in.

Parameters:: t (float, list or array) – time for which head is computed
Returns:: Q – nsreens is the number of layers with a well screen
Return type:: array of size nscreens, ntimes

plot(ax=None, layer=None)#: Plot the element.

potential(x, y, aq=None)#: Returns complex array of size (ngvbc, naq, npval).

unitpotential(x, y, aq=None)#

Returns complex array of size (naq, npval).

Can be more efficient for given elements.

unitpotentialone(x, y, jtime, aq=None)#

Returns complex array of size (naq, npval).

Can be more efficient for given elements.

disvec(x, y, aq=None)#: Returns 2 complex arrays of size (ngvbc, naq, npval).

unitdisvec(x, y, aq=None)#

Returns 2 complex arrays of size (naq, npval).

Can be more efficient for given elements.

potinflayers(x, y, layers=0, aq=None)#

Layers can be scalar, list, or array.

returns array of size (len(layers),nparam,npval) only used in building equations

potentiallayers(x, y, layers=0, aq=None)#

Returns complex array of size (ngvbc, len(layers),npval).

Only used in building equations.

unitpotentiallayers(x, y, layers=0, aq=None)#

Returns complex array of size (len(layers), npval).

Only used in building equations.

disvecinflayers(x, y, layers=0, aq=None)#

Layers can be scalar, list, or array.

returns 2 arrays of size (len(layers),nparam,npval) only used in building equations

disveclayers(x, y, layers=0, aq=None)#

Returns 2 complex array of size (ngvbc, len(layers), npval).

Only used in building equations.

unitdisveclayers(x, y, layers=0, aq=None)#

Returns complex array of size (len(layers), npval).

Only used in building equations.

discharge(t, derivative=0)#

The discharge in each layer.

Parameters:

t (scalar, list or array) – times at which discharge is computed. t must be ordered and tmin <= t <= tmax
derivative (when derivative=0, returns discharge (default)) – when derivative=1, returns derivative of the discharge when derivative=-1, returns integrated discharge

Returns:

Discharge in each screen with zeros for layers that are not screened

Return type:

array of discharges (nlayers,len(t))

dischargeold(t, derivative=0)#

The discharge in each layer.

Parameters:: t (scalar, list or array) – times at which discharge is computed. t must be ordered and tmin <= t <= tmax
Returns:: Discharge in each screen with zeros for layers that are not screened
Return type:: array of discharges (nlayers,len(t))

run_after_solve()#

Function to run after a solution is completed.

For most elements nothing needs to be done, but for strings of elements some arrays may need to be filled.

equation()#

Matrix rows for head-specified conditions.

Really written as constant potential element. Works for nunknowns = 1 Returns matrix part nunknowns,neq,npval, complex.

Returns rhs part nunknowns,nvbc,npval, complex Phi_out - c*T*q_s = Phi_in Well: q_s = Q / (2*pi*r_w*H) LineSink: q_s = sigma / H = Q / (L*H)