FEM2D_NAVIER_STOKES_CHANNEL
2D Navier Stokes Channel Problem

FEM2D_NAVIER_STOKES_CHANNEL is a C++ library which supplies information defining a Navier-Stokes flow problem in a channel. The channel is a rectangular region that is 3 units wide and 1 unit high. This problem is used as a test case for the Navier-Stokes solver.

Usage:

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

You compile and link the Navier Stokes solver with channel.cpp, using commands like:

        g++ fem2d_navier_stokes.cpp channel.cpp
        mv a.out channel
      

        ./channel 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.

Languages:

FEM2D_NAVIER_STOKES_CHANNEL is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM2D_NAVIER_STOKES, a C++ program which applies the finite element method to a 2D Navier Stokes flow problem with user input.

Source Code:

Some of the files needed to run the problem include:

• channel.cpp, the user-supplied routines to evaluate the right hand side and boundary conditions;
• channel.sh, commands to compile the user routines, link them with the partial program, and run the program;
• 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, created by PLOT_POINTS;
• triangles3.txt, the linear triangulation;
• triangles3.png, a PNG image of the linear triangulation produced by TRIANGULATION_PLOT.
• 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 (based on EPS files output directly by FEM2D_NAVIER_STOKES);
• triangles6.txt, the quadratic triangulation;
• triangles6.png, a PNG image of the order 6 triangulation (based on EPS files output directly by FEM2D_NAVIER_STOKES);
• velocity6.txt, a text file containing the velocity (U,V) at each velocity node;
• velocity6_dir.png, a PNG image of the 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.