# Diff of /trunk/doc/user/darcyflux.tex

revision 3569 by gross, Thu Sep 1 02:42:36 2011 UTC revision 3911 by jfenwick, Thu Jun 14 01:01:03 2012 UTC
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2  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3  %  %
4  % Copyright (c) 2003-2010 by University of Queensland  % Copyright (c) 2003-2012 by University of Queensland
5  % Earth Systems Science Computational Center (ESSCC)  % Earth Systems Science Computational Center (ESSCC)
6  % http://www.uq.edu.au/esscc  % http://www.uq.edu.au/esscc
7  %  %
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14  \section{Darcy Flux}  \section{Darcy Flux}
15  \label{DARCY FLUX}  \label{DARCY FLUX}
16  We want to calculate the velocity $u$ and pressure $p$ on a domain $\Omega$  We want to calculate the flux $u$ and pressure $p$ on a domain $\Omega$
17  solving the Darcy flux problem\index{Darcy flux}\index{Darcy flow}  solving the Darcy flux problem\index{Darcy flux}\index{Darcy flow}
18  \label{DARCY PROBLEM}  \label{DARCY PROBLEM}
19  \begin{array}{rcl}  \begin{array}{rcl}
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95
96  \subsection{Functions}  \subsection{Functions}
97  \begin{classdesc}{DarcyFlow}{domain, \optional{w=1., \optional{solver=\member{DarcyFlow.EVAL},  \optional{  \begin{classdesc}{DarcyFlow}{domain, \optional{w=1., \optional{solver=\member{DarcyFlow.POST},  \optional{
98  useReduced=\True, \optional{ verbose=\True} } }}}  useReduced=\True, \optional{ verbose=\True} } }}}
99  opens the Darcy flux problem\index{Darcy flux} on the \Domain domain.  opens the Darcy flux problem\index{Darcy flux} on the \Domain domain.
100  Reduced approximations for pressure and flux are used if \var{useReduced} is set.  Reduced approximations for pressure and flux are used if \var{useReduced} is set.
# Line 158  on locations where \var{location_of_fixe Line 158  on locations where \var{location_of_fixe
158  Notice that \var{g} and \var{f} are used.  Notice that \var{g} and \var{f} are used.
159  \end{methoddesc}  \end{methoddesc}
160
161    \begin{figure}
162    \centerline{\includegraphics[width=\figwidth]{darcy_result}}
163  %\subsection{Example: Gravity Flow}  \caption{Flux and pressure field of the Dary flow example.}
164  %later  \label{DIFFUSION FIG 1}
165    \end{figure}
166
167    \subsection{Example: Gravity Flow}
168    The following script \file{darcy.py}\index{scripts!\file{darcy.py.py}}\index{Darcy flow}
169    which is available in the \ExampleDirectory illustrates the usage of the
170    \class{DarcyFlow} class:
171    \begin{python}
172       from esys.escript import *
173       from esys.escript.models import DarcyFlow
174       from esys.finley import Rectangle
175       from esys.weipa import saveVTK
176       mydomain = Rectangle(l0=2.,l1=1.,n0=40, n1=20)
177       x = mydomain.getX()
178       p_BC=whereZero(x[1]-1.)*wherePositive(x[0]-1.)
179       u_BC=(whereZero(x[0])+whereZero(x[0]-2.)) * [1.,0.] + \
180         (whereZero(x[1]) + whereZero(x[1]-1.)*whereNonPositive(x[0]-1.0)) * [0., 1.]
181       mypde = DarcyFlow(domain=mydomain)
182       mypde.setValue(g=[0., 2],
183                      location_of_fixed_pressure=p_BC,
184                      location_of_fixed_flux=u_BC,
185                      permeability=100.)
186
187       u,p=mypde.solve(u0=x[1]*[0., -1.], p0=0)
188       saveVTK("u.vtu",flux=u, pressure=p)
189    \end{python}
190    In the example the pressure is fixed to the initial presure \var{p0} on the right half of the top face.
191    The normal flux is set on all other faces. The corresponding values for the flux are set by the initial value
192    \var{u0}.

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