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<html>
<head>
<title>
FLOW5 - A Finite Element Code for Fluid Flow
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FLOW5 <br> A Finite Element Code for Fluid Flow
</h1>
<hr>
<p>
<b>FLOW5</b>
is a FORTRAN90 program which
uses the finite element method to solve for the steady state
velocity and pressure in a fluid flow region.
</p>
<p>
The fluid is presumed to be incompressible.
</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 = "../../data/fem2d/fem2d.html">
FEM2D</a>,
a data directory which
contains a description of the data files
that can be used to describe a 2D finite element model.
</p>
<p>
<a href = "../../m_src/fem_io/fem_io.html">
FEM_IO</a>,
a MATLAB library which
reads and writes the node, element and data files that define a finite element model.
</p>
<p>
<a href = "../../m_src/fem_to_tec/fem_to_tec.html">
FEM_TO_TEC</a>,
a MATLAB program which
can convert an FEM model into a TEC graphics file.
</p>
<p>
<a href = "../../f_src/fem2d_pack/fem2d_pack.html">
FEM2D_PACK</a>,
a FORTRAN90 library which
contains utilities for 2D finite element calculations.
</p>
<p>
<a href = "../../f_src/fem2d_poisson/fem2d_poisson.html">
FEM2D_POISSON</a>,
a FORTRAN90 program which
solves Poisson's equation
on a square, using the finite element method.
</p>
<p>
<a href = "../../f_src/flow3/flow3.html">
FLOW3</a>,
a FORTRAN90 program which
uses the finite element method to solve for the steady state
velocity and pressure in a fluid flow region.
</p>
<p>
<a href = "../../f77_src/inout/inout.html">
INOUT</a>,
a FORTRAN77 program which
computes the pressure
and velocity for a Navier Stokes flow in a square region with
an inlet and an outlet.
</p>
<p>
<a href = "../../f_src/mhd_control/mhd_control.html">
MHD_CONTROL</a>,
a FORTRAN90 program which
tries to control the evolution of an MHD system so that a particular
state is achieved.
</p>
<p>
<a href = "../../f_src/mhd_flow/mhd_flow.html">
MHD_FLOW</a>,
a FORTRAN90 program for the
evolution of an MHD system.
</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 = "../../f77_src/tcell/tcell.html">
TCELL</a>,
a FORTRAN77 program which
computes the pressure
and velocity for a Navier Stokes flow in a "T"-shaped region.
</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 = "flow5.f90">flow5.f90</a>, the source code;
</li>
<li>
<a href = "flow5.sh">flow5.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cavity_output.txt">cavity_output.txt</a>,
the output file;
</li>
<li>
<a href = "cavity_elements.txt">cavity_elements.txt</a>,
the element file,
suitable for input to the DISPLAY4 graphics program;
</li>
<li>
<a href = "cavity_uvp.txt">cavity_uvp.txt</a>,
the node file, suitable for
input to the DISPLAY4 graphics program;
</li>
<li>
<a href = "cavity.tec">cavity.tec</a>,
a graphics file suitable for
input to the TECPLOT graphics program;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for FLOW5.
</li>
<li>
<b>BSP</b> evaluates the linear basis functions for pressure.
</li>
<li>
<b>DGB_FA</b> factors a matrix stored in LINPACK general band storage.
</li>
<li>
<b>DGB_SL</b> solves a system factored by DGB_FA.
</li>
<li>
<b>FP</b> computes the jacobian matrix A of the Navier Stokes residual.
</li>
<li>
<b>FX</b> computes the residual RES of the Navier Stokes equations.
</li>
<li>
<b>INTPRS</b> interpolates the pressure at the midside nodes.
</li>
<li>
<b>NEWTON</b> applies Newton iteration, seeking a solution of FX(G) = 0.
</li>
<li>
<b>QBF</b> evaluates a nonisoparametric quadratic basis function.
</li>
<li>
<b>R8VEC_AMAX</b> returns the maximum absolute value in a real vector.
</li>
<li>
<b>REFBSP</b> evaluates a reference element linear basis function.
</li>
<li>
<b>REFQBF</b> evaluates a reference element quadratic basis function.
</li>
<li>
<b>SETBAN</b> computes the lower band width of the Jacobian matrix.
</li>
<li>
<b>SETBAS</b> evaluates the basis functions at each quadrature point.
</li>
<li>
<b>SETQUAD</b> sets the abscissas and weights for quadrature in a triangle.
</li>
<li>
<b>SETNOD</b> assigns numbers to the nodes and elements.
</li>
<li>
<b>SETXY</b> sets the X and Y coordinates of the nodes.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRANS</b> calculates the biquadratic reference element transformation.
</li>
<li>
<b>UVPNORM</b> returns the "norm" of the computed finite element solution.
</li>
<li>
<b>UVALQ</b> evaluates velocities and pressure at a quadrature point in an element.
</li>
<li>
<b>WRITE_DISPLAY_FILE</b> writes solution information to two files.
</li>
<li>
<b>WRITE_TECPLOT_FILE</b> writes out solution information for use with TECPLOT.
</li>
<li>
<b>XOFXSI</b> computes X and Y given XSI and ETA coordinates.
</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 12 November 2006.
</i>
</body>
</html>