INOUT
A Sample 2D Flow Problem

INOUT is a square region that is 1 unit wide and 1 unit high. A parabolic inflow is specified on the lower left, and a zero Neumann outflow is specified on the upper right.

The Neumann condition on the outflow is not working as expected, so we have temporarily backtracked to using a Dirichlet outflow condition there...

To run the problem directly, you only need the user-supplied routines in inout.f90, the node data in nodes6.txt, and the element data in triangles6.txt.

You compile and link the solver with inout.f90, using commands like:

        f90 free_fem_navier_stokes.f90 inout.f90
        mv a.out channel
      

        ./inout nodes6.txt triangles6.txt
      

Some of the files needed to run the problem include:

• inout.f90, the user-supplied routines to evaluate the right hand side and boundary conditions;
• inout.csh, commands to compile the user routines, link them with the partial program, and run the program;
• inout.out, output from a run of the program;

The geometry is defined by sets of nodes and triangles. The velocities use the full set of nodes, and quadratic (6 node) triangles.

• nodes6.txt, a text file containing the velocity nodes;
• nodes6.png, a PNG image of the velocity nodes;
• triangles6.txt, the quadratic triangulation;
• triangles6.png, a PNG image of the order 6 triangulation;

The pressures are associated with a subset of the nodes called "pressure nodes", and linear (3 node) triangles. Note that, in the order 3 triangulation, the nodes are renumbered, and do NOT inherit the labels used in the order 6 triangulation.

• nodes3.txt, a text file containing the pressure nodes;
• nodes3.png, a PNG image of the pressure nodes;
• triangles3.txt, the linear triangulation;
• triangles3.png, a PNG image of the linear triangulation;

The nonlinear Navier Stokes equations are solved, using the Stokes solution as a starting point.

• pressure3.txt, a text file containing the Navier Stokes pressure P at each pressure node;
• pressure3.png, a PNG image of a contour plot of the Navier Stokes pressure, produced by TRIANGULATION_ORDER3_CONTOUR.
• velocity6.txt, a text file containing the Navier Stokes velocity (U,V) at each velocity node;
• velocity6_dir.png, a PNG image of the Navier Stokes velocity direction field, created by VECTOR_PLOT.
• velocity6_vec.png, a PNG image of the Navier Stokes velocity field, created by VECTOR_PLOT.
• velocity6_arrows.png, a PNG image of the Navier Stokes velocity field, created by VELOCITY_ARROWS.