FEM2D_STOKES_CHANNEL
A Sample 2D Flow Problem

FEM2D_STOKES_CHANNEL is a MATLAB library which defines the geometry and other data for the channel problem. The channel is a rectangular region that is 3 units wide and 1 unit high. It is used as a sample problem for the Stokes solver. The problem can be solved using 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:

• channel_output.txt, output from a run of the program;

The pressures are associated with a subset of the full set of nodes, and with an order 3 triangulation of those nodes. 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;
• 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.

The velocities are associated with the full set of nodes, and with an order 6 triangulation of those nodes.

• 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;
• 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.