Examples
========

At this point, some typical commented examples are presented to illustrate how Tug works.
In general, each simulation is divided into three blocks:
    - the initialization of the grid, which is to be simulated
    - the setting of the boundary conditions
    - the setting of the simulation parameters and the start of the simulation

Two dimensional grid with constant boundaries and FTCS method
-------------------------------------------------------------
**Initialization of the grid**

For example, the initalization of a grid with 20 by 20 cells and a domain size (physical extent of the grid) of 
also 20 by 20 length units can be done as follows. The setting of the domain is optional here and is set to the 
same size as the number of cells in the standard case. As seen in the code, the cells of the grid are set to an 
initial value of 0 and only in the upper left corner (0,0) the starting concentration is set to the value 20.

.. code-block:: cpp
    
    int row = 20
    int col = 20;
    Grid grid = Grid(row,col);
    grid.setDomain(row, col);
    MatrixXd concentrations = MatrixXd::Constant(row,col,0);
    concentrations(0,0) = 20;
    grid.setConcentrations(concentrations);

**Setting of the boundary conditions**

First, a boundary class is created and then the corresponding boundary conditions are set. In this case, all four sides
of the grid are set as constant edges with a concentration of 0.

.. code-block:: cpp

    Boundary bc = Boundary(grid);
    bc.setBoundarySideConstant(BC_SIDE_LEFT, 0);
    bc.setBoundarySideConstant(BC_SIDE_RIGHT, 0);
    bc.setBoundarySideConstant(BC_SIDE_TOP, 0);
    bc.setBoundarySideConstant(BC_SIDE_BOTTOM, 0);

**Setting of the simulation parameters and simulation start**
In the last block, a simulation class is created and the objects of the grid and the boundary conditions are passed. The solution
method is also specified (either FCTS or BTCS). Furthermore, the desired time step and the number of iterations are set. The penultimate
parameter specifies the output of the simulated results in a CSV file. In the present case, the result of each iteration step is written
one below the other into the corresponding CSV file.

.. code-block:: cpp
    
    Simulation simulation = Simulation(grid, bc, FTCS_APPROACH);
    simulation.setTimestep(0.1);
    simulation.setIterations(1000);
    simulation.setOutputCSV(CSV_OUTPUT_VERBOSE);
    simulation.run();






Setting special boundary conditions on individual cells
-------------------------------------------------------