FEM2D_NAVIER_STOKES_CAVITY
"Cavity" Routines for FEM2D_NAVIER_STOKES

FEM2D_NAVIER_STOKES_CAVITY is a FORTRAN90 library which supplies information defining a Navier-Stokes flow problem in a cavity. The 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.

To run the problem directly, you only need the user-supplied routines in cavity.f90, the node data in nodes6.txt, and the element data in triangles6.txt.

You compile and link the solver with cavity.f90, using commands like:

        gfortran fem2d_navier_stokes.f90 cavity.f90
        mv a.out channel
      

        ./cavity 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_CAVITY is available in a FORTRAN90 version.

Related Data and Programs:

FEM2D_NAVIER_STOKES, a FORTRAN90 program which solves the 2D incompressible Navier-Stokes equations in an arbitrary triangulated region. In order to run, it requires user-supplied routines that define problem data.

FEM2D_NAVIER_STOKES_CHANNEL, a FORTRAN90 library which contains the user-supplied routines necessary to run fem2d_navier_stokes on the "channel" problem.

FEM2D_NAVIER_STOKES_INOUT, a FORTRAN90 library which contains the user-supplied routines necessary to run fem2d_navier_stokes on the "inout" problem.

Source Code:

• cavity.f90, the user-supplied routines to evaluate the right hand side and boundary conditions;
• cavity.sh, commands to compile the user routines, link them with the partial program, and run the program;
• cavity.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 Stokes equations are solved first, providing the solution of a linear system that can be used as a good estimate of the solution, especially for high values of the viscosity.

• stokes_pressure3.txt, a text file containing the Stokes pressure P at each linear node;
• stokes_pressure3.png, a PNG image of a contour plot of the Stokes pressure, produced by TRIANGULATION_ORDER3_CONTOUR.
• stokes_velocity6.txt, a text file containing the Stokes velocity (U,V) at each velocity node;
• stokes_velocity6_dir.png, a PNG image of the Stokes velocity direction field, created by VECTOR_PLOT.
• stokes_velocity6_vec.png, a PNG image of the Stokes velocity field, created by VECTOR_PLOT.
• stokes_velocity6_arrows.png, a PNG image of the Stokes velocity field, created by VELOCITY_ARROWS.

The nonlinear Navier Stokes equations are solved, using the Stokes solution as a starting point.

• navier_stokes_pressure3.txt, a text file containing the Navier Stokes pressure P at each pressure node;
• navier_stokes_pressure3.png, a PNG image of a contour plot of the Navier Stokes pressure, produced by TRIANGULATION_ORDER3_CONTOUR.
• navier_stokes_velocity6.txt, a text file containing the Navier Stokes velocity (U,V) at each velocity node;
• navier_stokes_velocity6_dir.png, a PNG image of the Navier Stokes velocity direction field, created by VECTOR_PLOT.
• navier_stokes_velocity6_vec.png, a PNG image of the Navier Stokes velocity field, created by VECTOR_PLOT.
• navier_stokes_velocity6_arrows.png, a PNG image of the Navier Stokes velocity field, created by VELOCITY_ARROWS.