FEM2D_STOKES_CAVITY
A Sample 2D Flow Problem

FEM2D_STOKES_CAVITY is a MATLAB library which defines the geometry and other data for the cavity problem. The cavity is 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. The system can be solved with the fem2d_stokes program.

Usage:

To run the problem, you only need the user-supplied routines and the user-supplied node data (nodes6.txt) and element data (triangles6.txt).

You can run the program with the MATLAB command

        fem2d_stokes ( 'nodes6.txt', 'triangles6.txt' )
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

FEM2D_STOKES, a MATLAB program which solves the 2D incompressible Stokes equations in an arbitrary triangulated region. In order to run, it requires user-supplied routines that define problem data.

Source Code:

The user-supplied files needed to run the problem include:

• boundary_type.m, adjusts the program's default assignment of boundary condition types.
• constants.m, sets physical constants (just viscosity for now);
• dirichlet_condition.m, evaluates the right hand sides of the Dirichlet boundary conditions.
• neumann_condition.m, evaluates the right hand sides of the Neumann boundary conditions.
• rhs.m, evaluates the right hand sides (source terms) of the Stokes equations.

The printed output from a run is:

• 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.