CHANNEL
Finite Element Model of 2D Channel Flow

CHANNEL is a FORTRAN77 program 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

CHANNEL is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

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

FEM1D, a FORTRAN77 program which applies the finite element method, with piecewise linear basis functions, to a two point boundary value problem;

FLOW3, a FORTRAN90 program which solves steady incompressible Navier Stokes equations in 2D using the finite element method.

FLOW5, a FORTRAN90 program which solves steady incompressible Navier Stokes equations in 2D using the finite element method.

HCELL, a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in an "H"-shaped region.

INOUT, a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in a square region with an inlet and an outlet.

MHD_CONTROL, a FORTRAN90 program which tries to control the evolution of an MHD system so that a particular state is achieved.

MHD_FLOW, a FORTRAN90 program for the evolution of an MHD system.

NAST2D, a C++ program which computes the pressure and velocity for a Navier Stokes flow.

NAST2D_F90, a FORTRAN90 program which computes the pressure and velocity for a Navier Stokes flow.

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

TCELL, a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in a "T"-shaped region.

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.f, the source code.
• channel.sh, 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, the output file.
• 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: 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.
• DGBSL solves a linear system given a matrix factored by DGBFA.
• DSCAL scales a vector by a constant.
• GDUMP writes information to a file.
• GETG outputs field values along the line X=XZERO.
• GRAM computes the Gram matrix.
• IGETL gets the local index for nodes along the line X=XZERO.
• IDAMAX finds the index of element having max. absolute value.
• 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
• SETGRD sets up the grid.
• SETLIN determines the unknown numbers 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 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 (X,Y) table file.

You can go up one level to the FORTRAN77 source codes.