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/*============================================================================
* Code_Saturne documentation page
*============================================================================*/
/*
This file is part of Code_Saturne, a general-purpose CFD tool.
Copyright (C) 1998-2018 EDF S.A.
This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
details.
You should have received a copy of the GNU General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*-----------------------------------------------------------------------------*/
/*!
\page user_solver Solving a heat equation with a user solver (cs_user_solver.c)
\section cs_user_solver_h_intro Introduction
C user functions for the setting of a user solver. The \ref cs_user_solver
function allows one to replace the Code_Saturne solver by a solver of his
own.
The following example shows the setting of a user solver which solves
a heat equation with the finite volume method.
\section cs_user_solver_h_cs_user_solver_set Activating the user solver
If the function \ref cs_user_solver_set returns 1, the Code_Saturne
solver is replaced by the solver defined in \ref cs_user_solver .
\snippet cs_user_solver-heat-equation.c set_solver
\section cs_user_solver_h_cs_user_solver User solver implementation
\subsection cs_user_solver_h_variable Variable declaration
The following variables are declared locally and will be used
later in the code. Three pointers to \ref cs_real_t are declared
and will stand for the temperature at the time steps n and n-1, and
for the analytical solution of the heat equation;
\snippet cs_user_solver-heat-equation.c local_variables
\subsection cs_user_solver_h_initialization Initialization
Three arrays of size \c n are created. Several constants are initialized,
and the array t_old is initialized as follows :
\f[
t_{old}(x = i*dx) = sin\frac{pi(0.5+i)}{n};
\f]
\snippet cs_user_solver-heat-equation.c initialization
\subsection cs_user_solver_h_restart Restart creation
One can define a restart computation, as for the real Code_Saturne solver.
\snippet cs_user_solver-heat-equation.c restart
\subsection cs_user_solver_h_time_monitoring Time monitoring
Monitoring points can equally be created in order to plot the evolution
of the temperature over the time.
\snippet cs_user_solver-heat-equation.c time_monitoring
\subsection cs_user_solver_h_calculation Heat equation solving
At each iteration, the new temperature is computed using the Finite Volume
Method.
\f[
t(x = i \cdot dx) = t_{old}(x = i \cdot dx) + r\cdot(t_{old}(x = (i+1) \cdot dx) - 2 \cdot t_{old}(x = i \cdot dx) + t_{old}(x = (i-1) \cdot dx))
\f]
The boundary conditions at \f$ x = 0 \f$ and \f$ x = L \f$ are :
\f[
t(x = 0) = t_{old}(x = 0) + r \cdot (t_{old}(x = dx) - 3 \cdot t_{old}(x = 0) + 2 \cdot t_0)
\f]
\f[
t(x = (n-1) \cdot dx) = t_{old}(x = (n-1) \cdot dx) + r \cdot (2 \cdot t_L - 3 \cdot t_{old}(x = (n-1) \cdot dx) + t_{old}(x = (n-2) \cdot dx))
\f]
t_old is then updated and t_sol computed. Finally, the temperature at \f$ x = \frac{L}{2} \f$ and
at the current iteration is plotted.
\snippet cs_user_solver-heat-equation.c calculation
\subsection cs_user_solver_h_checkpoint Checkpoint creation
A checkpoint can be created in order to restart the computation later on.
\snippet cs_user_solver-heat-equation.c checkpoint
\subsection cs_user_solver_h_post_processing Post-processing
Finally, t and t_sol are postprocessed in order to be compared.
\snippet cs_user_solver-heat-equation.c post_processing
\subsection cs_user_solver_h_post_finalization Finalization
\snippet cs_user_solver-heat-equation.c finalization
*/
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