CAVITY
A Sample 2D Flow Problem

CAVITY is a square region that is 1 unit wide and 1 unit high. The tangential velocity is specified to be 1 along the top boundary, with a zero normal component. On all other parts of the boundary, the velocity is specified to be zero.

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

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

        f90 free_fem_stokes.f90 cavity.f90
        mv a.out cavity
      

        ./cavity nodes6.txt triangles6.txt
      

Some of the files needed to run the problem include:

• cavity.f90, the user-supplied routines to evaluate the right hand side and boundary conditions;
• cavity.csh, commands to compile the user routines, link them with the partial program, and run the program;
• cavity_output.txt, 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 pressures are a scalar quantity associated with the pressure nodes, the velocities are a vector quantity associated with the vector nodes.

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