FEM2D_STOKES_SPIRAL
A Sample 2D Flow Problem

FEM2D_STOKES_SPIRAL is a MATLAB library which defines the geometry and other data for the spiral problem. The spiral is a square region that is 1 unit wide and 1 unit high. Zero Dirichlet conditions have been applied on all sides. Normally, this would result in zero flow. However, the right hand sides of the two momentum equations have been devised to induce a sort of spiral flow (actually, the flow is more like a series of concentric loops). The problem can be solved using the fem2d_stokes program.

Usage:

To run the problem directly, you only need the user-supplied routines and the node data in nodes6.txt, and the element data in 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 flow constants, in this case just the kinematic viscosity NU.
• 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 equations.

The printed output from a run is:

• spiral_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.
• 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.
• velocity6_vec.png, a PNG image of the velocity field.
• velocity6_arrows.png, a PNG image of the velocity field.