CHANNEL
Finite Element Model of 2D Channel Flow

CHANNEL is a FORTRAN90 program, using double precision arithmetic, which computes the time-independent flow of a viscous incompressible fluid in a 2D channel. The strength of the flow at the inlet is determined by a parameter. The desired flow profile along a line downstream is given. The task is to determine the inflow parameter that generates a flow that minimizes the difference with the given profile data.

Related Data and Programs:

BUMP is a FORTRAN90 program which solves a fluid flow problem in a channel including a bump which obstructs and redirects the flow.

CHANNEL is also available in a FORTRAN77 version.

DIRECTION_ARROWS_GRID is a MATLAB program which reads files of node and velocity data, and, using interpolation, creates a velocity direction plot with arrows place on a uniform grid of the user's specification.

FREE_FEM_NAVIER_STOKES is a FORTRAN90 program which solves the 2D incompressible Navier Stokes equations in an arbitrary triangulated region.

FREE_FEM_STOKES is a FORTRAN90 program which solves the steady Stokes flow equations on a triangulated 2D region.

NAST2D_F90 is a FORTRAN90 program which uses the finite volume method to set up and solve the 2D incompressible Navier Stokes equations with heat.

NSASM is a C library which is intended to be used with a MATLAB calling program to set up the sparse matrix needed for a Newton iteration to solve a finite element formulation of the steady incompressible 2D Navier Stokes equations.

PLOT_POINTS is a FORTRAN90 program which can plot the nodes that define the region.

VECTOR_PLOT is a FORTRAN90 program which creates vector plots of the velocity and velocity direction fields.

VECTOR_STREAM_GRID is a MATLAB program which reads node and vector data from a file, computes an interpolatory function, evaluates on a uniform grid of points specified by the user, and displays a streamline plot of the vector field.

VELOCITY_ARROWS is a MATLAB program which plots the velocity field.

VELOCITY_ARROWS_GRID is a MATLAB program which reads files of node and velocity data, and, using interpolation, creates a vector plot with arrows place on a uniform grid of the user's specification.

Reference:

1. Max Gunzburger,
   Finite Element Methods for Viscous Incompressible Flows,
   A Guide to Theory, Practice, and Algorithms,
   Academic Press, 1989,
   ISBN: 0-12-307350-2,
   LC: TA357.G86.

Source Code:

• channel.f90, the source code.
• channel.csh, commands to compile the source code.

Examples and Tests:

The program writes out "XY" (node coordinate) and "UV" (velocity component) data files for the optimized solution.

• channel_output.txt, printed output from a run of the program.
• xy.txt, grid information.
• uv.txt, velocity information.
• uv_dir.png, a PNG image of the velocity direction field.
• uv_vec.png, a PNG image of the velocity field.

List of Routines:

• MAIN is the main program for CHANNEL.
• BSP evaluates the linear basis functions associated with pressure.
• DAXPY computes constant times a vector plus a vector.
• DCOPY copies a vector, x, to a vector, y.
• DDOT forms the dot product of two vectors.
• DELETE deletes a file.
• DGBFA factors a double precision band matrix by elimination.
• DGBSL solves a double precision banded system factored by DGBFA.
• DSCAL scales a vector by a constant.
• GDUMP writes information to a file.
• GETG outputs field values along the profile line X = XZERO.
• GRAM computes the Gram matrix, GR(I,J) = INTEGRAL PHI(I)*PHI(J).
• IDAMAX finds the index of element having max. absolute value.
• IGETL gets the local unknown number along the profile line.
• LINSYS sets up and solves the linear system.
• NSTOKE solves the Navier Stokes equation using Taylor-Hood elements.
• PVAL computes a table of pressures.
• QBF evaluates a quadratic basis function in a triangle.
• RESID computes the residual.
• SETBAN computes the half band width.
• SETBAS computes the basis functions at each integration point.
• SETGRD sets up the grid for the problem..
• SETLIN gets the unknown indices along the profile line.
• SETQUD sets midpoint quadrature rule information.
• SETXY sets the X, Y coordinates of grid points.
• UBDRY sets the parabolic inflow in terms of the value of the parameter.
• UVAL evaluates the velocities at a given point in a particular triangle.
• UV_PLOT3D creates a velocity file for use by PLOT3D.
• UV_TABLE creates a velocity table file.
• XY_PLOT3D creates a grid file for use by PLOT3D.
• XY_TABLE creates an XY table file.

You can go up one level to the FORTRAN90 source codes.