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<html>
<head>
<title>
CHANNEL - Finite Element Model of 2D Channel Flow
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CHANNEL <br> Finite Element Model of 2D Channel Flow
</h1>
<hr>
<p>
<b>CHANNEL</b>
is a FORTRAN90 program which
computes the time-independent flow
of a viscous incompressible fluid in a 2D channel.
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>CHANNEL</b> is available in
<a href = "../../f77_src/channel/channel.html">a FORTRAN77 version</a> and
<a href = "../../f_src/channel/channel.html">a FORTRAN90 version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/bump/bump.html">
BUMP</a>,
a FORTRAN90 program which
solves a fluid flow problem
in a channel including a bump which obstructs and redirects the flow.
</p>
<p>
<a href = "../../m_src/direction_arrows_grid/direction_arrows_grid.html">
DIRECTION_ARROWS_GRID</a>,
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.
</p>
<p>
<a href = "../../f_src/fem2d_navier_stokes/fem2d_navier_stokes.html">
FEM2D_NAVIER_STOKES</a>,
a FORTRAN90 program which
solves the 2D incompressible Navier Stokes equations in an arbitrary
triangulated region.
</p>
<p>
<a href = "../../f_src/fem2d_stokes/fem2d_stokes.html">
FEM2D_STOKES</a>,
a FORTRAN90 program which
solves the steady
Stokes flow equations on a triangulated 2D region.
</p>
<p>
<a href = "../../f_src/nast2d_f90/nast2d_f90.html">
NAST2D_F90</a>,
a FORTRAN90 program which
uses the finite volume method to set up and solve
the 2D incompressible Navier Stokes equations with heat.
</p>
<p>
<a href = "../../c_src/nsasm/nsasm.html">
NSASM</a>,
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.
</p>
<p>
<a href = "../../m_src/toms866/toms866.html">
TOMS866</a>,
a MATLAB library which
is the Incompressible Flow Iterative Solution Software;<br>
this library is commonly called <b>IFISS</b>;<br>
this is ACM TOMS algorithm 866.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Max Gunzburger,<br>
Finite Element Methods for Viscous Incompressible Flows,<br>
A Guide to Theory, Practice, and Algorithms,<br>
Academic Press, 1989,<br>
ISBN: 0-12-307350-2,<br>
LC: TA357.G86.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "channel.f90">channel.f90</a>, the source code.
</li>
<li>
<a href = "channel.sh">channel.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
The program writes out "XY" (node coordinate) and "UV" (velocity
component) data files for the optimized solution.
<ul>
<li>
<a href = "channel_output.txt">channel_output.txt</a>,
printed output from a run of the program.
</li>
<li>
<a href = "xy.txt">xy.txt</a>,
grid information.
</li>
<li>
<a href = "uv.txt">uv.txt</a>,
velocity information.
</li>
<li>
<a href = "uv_dir.png">uv_dir.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity direction field.
</li>
<li>
<a href = "uv_vec.png">uv_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity field.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for CHANNEL.
</li>
<li>
<b>BSP</b> evaluates the linear basis functions associated with pressure.
</li>
<li>
<b>DAXPY</b> computes constant times a vector plus a vector.
</li>
<li>
<b>DCOPY</b> copies a vector, x, to a vector, y.
</li>
<li>
<b>DDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>DELETE</b> deletes a file.
</li>
<li>
<b>DGBFA</b> factors a double precision band matrix by elimination.
</li>
<li>
<b>DGBSL</b> solves a double precision banded system factored by DGBFA.
</li>
<li>
<b>DSCAL</b> scales a vector by a constant.
</li>
<li>
<b>GDUMP</b> writes information to a file.
</li>
<li>
<b>GETG</b> outputs field values along the profile line X = XZERO.
</li>
<li>
<b>GRAM</b> computes the Gram matrix, GR(I,J) = INTEGRAL PHI(I)*PHI(J).
</li>
<li>
<b>IDAMAX</b> finds the index of element having max. absolute value.
</li>
<li>
<b>IGETL</b> gets the local unknown number along the profile line.
</li>
<li>
<b>LINSYS</b> sets up and solves the linear system.
</li>
<li>
<b>NSTOKE</b> solves the Navier Stokes equation using Taylor-Hood elements.
</li>
<li>
<b>PVAL</b> computes a table of pressures.
</li>
<li>
<b>QBF</b> evaluates a quadratic basis function in a triangle.
</li>
<li>
<b>RESID</b> computes the residual.
</li>
<li>
<b>SETBAN</b> computes the half band width.
</li>
<li>
<b>SETBAS</b> computes the basis functions at each integration point.
</li>
<li>
<b>SETGRD</b> sets up the grid for the problem..
</li>
<li>
<b>SETLIN</b> gets the unknown indices along the profile line.
</li>
<li>
<b>SETQUD</b> sets midpoint quadrature rule information.
</li>
<li>
<b>SETXY</b> sets the X, Y coordinates of grid points.
</li>
<li>
<b>UBDRY</b> sets the parabolic inflow in terms of the value of the parameter.
</li>
<li>
<b>UVAL</b> evaluates the velocities at a given point in a particular triangle.
</li>
<li>
<b>UV_PLOT3D</b> creates a velocity file for use by PLOT3D.
</li>
<li>
<b>UV_TABLE</b> creates a velocity table file.
</li>
<li>
<b>XY_PLOT3D</b> creates a grid file for use by PLOT3D.
</li>
<li>
<b>XY_TABLE</b> creates an XY table file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 26 November 2006.
</i>
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