FEM2D_STOKES_SPARSE_BIG_CAVITY
A Sample 2D Flow Problem


FEM2D_STOKES_SPARSE_BIG_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.

This is a more ambitious version of the cavity problem, with a nonuniform mesh, comprising 4,000 element, 8,185 nodes, 18,463 variables, and 539,069 nonzero entries in the jacobian matrix.

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

        ffs_sparse ( '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_STOKES_SPARSE_BIG_CAVITY is available in a MATLAB version.

Related Data and Programs:

FEM2D_STOKES_SPARSE, a MATLAB program which solves the steady (time independent) incompressible Stokes equations on an arbitrary triangulated region, using the finite element method and MATLAB's sparse facility.

FEM2D_STOKES_SPARSE_CAVITY, a MATLAB library which contains the user-supplied routines necessary to run fem2d_stokes_sparse on the "cavity" problem.

FEM2D_STOKES_SPARSE_CHANNEL, a MATLAB library which contains the user-supplied routines necessary to run fem2d_stokes_sparse on the "channel" problem.

FEM2D_STOKES_SPARSE_INOUT, a MATLAB library which contains the user-supplied routines necessary to run fem2d_stokes_sparse on the "inout" problem.

FEM2D_STOKES_SPARSE_SPIRAL, a MATLAB library which contains the user-supplied routines necessary to run fem2d_stokes_sparse on the "spiral" problem.

Source Code:

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

The printed output from a run is:

The geometry is defined by sets of nodes and triangles. The velocities use the full set of nodes, and quadratic (6 node) triangles.

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.

The pressures are a scalar quantity associated with the pressure nodes, the velocities are a vector quantity associated with the vector nodes.


Last revised on 06 July 2011.