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<html>
<head>
<title>
BUMP - Flow Over a Bump
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BUMP <br> Flow Over a Bump
</h1>
<hr>
<p>
<b>BUMP</b>
is a FORTRAN90 program which
solves a 2D steady incompressible flow problem set in a channel with a small
bump.
</p>
<p>
<b>BUMP</b> is a preliminary version of the code that eventually became
the <b>FLOW</b> programs. The code was designed to solve for the
flow field in a channel with a parameterized bump. Data for the flow
profile downstream from the bump was given, and the idea was to determine
a bump parameter value that produced the best match with the given
profile. In later programs, this task became much more elaborate.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/channel/channel.html">
CHANNEL</a>,
a FORTRAN90 program which
solves a simple channel flow problem with no bump.
</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 = "../../f_src/flow3/flow3.html">
FLOW3</a>,
a FORTRAN90 program which
solves steady incompressible
Navier Stokes equations in 2D using the finite element method.
</p>
<p>
<a href = "../../f_src/flow5/flow5.html">
FLOW5</a>,
a FORTRAN90 program which
solves steady incompressible
Navier Stokes equations in 2D using the finite element method.
</p>
<p>
<a href = "../../f77_src/hcell/hcell.html">
HCELL</a>,
a FORTRAN77 program which
computes the pressure
and velocity for a Navier Stokes flow in an "H"-shaped 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 which
computes 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 = "../../c_src/nsasm/nsasm.html">
NSASM</a>,
a C library which
sets 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 = "../../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>
John Burkardt, Max Gunzburger, Janet Peterson,<br>
Discretization of Cost and Sensitivities in Shape Optimization,<br>
in Computation and Control IV,<br>
edited by Bowers and Lund,<br>
Proceedings of the Fourth Bozeman Conference on Computation
and Control,<br>
Birkhaeuser, 1995.
</li>
<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>
<li>
Hans Rudolf Schwarz,<br>
Methode der Finiten Elemente,<br>
Teubner Studienbuecher, 1980,<br>
ISBN: 3-519-02349-0.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bump.f90">bump.f90</a>, the source code.
</li>
<li>
<a href = "bump.sh">bump.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 at each step.
<ul>
<li>
<a href = "bump_output.txt">bump_output.txt</a>, printed output from a
run of the program.
</li>
<li>
<a href = "xy_001.txt">xy_001.txt</a>,
grid information, step 1.
</li>
<li>
<a href = "uv_001.txt">uv_001.txt</a>,
velocity information, step 1.
</li>
<li>
<a href = "uv_001_vec.png">uv_001_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_002.txt">xy_002.txt</a>,
grid information, step 2.
</li>
<li>
<a href = "uv_002.txt">uv_002.txt</a>,
velocity information, step 2.
</li>
<li>
<a href = "uv_002_vec.png">uv_002_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_003.txt">xy_003.txt</a>,
grid information, step 3.
</li>
<li>
<a href = "uv_003.txt">uv_003.txt</a>,
velocity information, step 3.
</li>
<li>
<a href = "uv_003_vec.png">uv_003_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_004.txt">xy_004.txt</a>,
grid information, step 4.
</li>
<li>
<a href = "uv_004.txt">uv_004.txt</a>,
velocity information, step 4.
</li>
<li>
<a href = "uv_004_vec.png">uv_004_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_005.txt">xy_005.txt</a>,
grid information, step 5.
</li>
<li>
<a href = "uv_005.txt">uv_005.txt</a>,
velocity information, step 5.
</li>
<li>
<a href = "uv_005_vec.png">uv_005_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_006.txt">xy_006.txt</a>,
grid information, step 6.
</li>
<li>
<a href = "uv_006.txt">uv_006.txt</a>,
velocity information, step 6.
</li>
<li>
<a href = "uv_006_vec.png">uv_006_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_007.txt">xy_007.txt</a>,
grid information, step 7.
</li>
<li>
<a href = "uv_007.txt">uv_007.txt</a>,
velocity information, step 7.
</li>
<li>
<a href = "uv_007_vec.png">uv_007_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
<li>
<a href = "xy_008.txt">xy_008.txt</a>,
grid information, step 8.
</li>
<li>
<a href = "uv_008.txt">uv_008.txt</a>,
velocity information, step 8.
</li>
<li>
<a href = "uv_008_vec.png">uv_008_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the velocity information.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for BUMP.
</li>
<li>
<b>BSP</b> evaluates the linear basis function associated with pressure.
</li>
<li>
<b>DAXPY</b> computes constant times a vector plus a vector.
</li>
<li>
<b>DDOT</b> forms the dot product of two vectors.
</li>
<li>
<b>DGBFA</b> factors a real band matrix by elimination.
</li>
<li>
<b>DGBSL</b> solves a real banded system factored by DGBCO or DGBFA.
</li>
<li>
<b>DSCAL</b> scales a vector by a constant.
</li>
<li>
<b>FILE_NAME_INC</b> increments a partially numeric filename.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>GETG</b> extracts the values of a quantity along the profile line.
</li>
<li>
<b>GRAM</b> computes and stores the Gram matrix.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>IDAMAX</b> finds the index of the vector element of maximum absolute value.
</li>
<li>
<b>IGETL</b> gets the local unknown number along the profile line.
</li>
<li>
<b>LINSYS</b> solves the linearized Navier Stokes equation.
</li>
<li>
<b>NSTOKE</b> solves the Navier Stokes equation using Taylor-Hood elements.
</li>
<li>
<b>PVAL</b> computes a table of pressures at all the nodes.
</li>
<li>
<b>QBF</b> evaluates the quadratic basis functions.
</li>
<li>
<b>REFBSP</b> evaluates the linear basis functions in a reference triangle.
</li>
<li>
<b>REFQBF</b> evaluates the quadratic basis functions on reference triangle
</li>
<li>
<b>RESID</b> computes the residual.
</li>
<li>
<b>SETBAN</b> computes the half band width.
</li>
<li>
<b>SETBAS</b> evaluates the basis functions at each integration point.
</li>
<li>
<b>SETGRD</b> sets up the geometric grid.
</li>
<li>
<b>SETLIN</b> determines unknown numbers along the profile line.
</li>
<li>
<b>SETQUD</b> sets midpoint quadrature rule information.
</li>
<li>
<b>SETXY</b> sets the grid coordinates based on the value of the parameter.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRANS</b> calculates the element transformation mapping.
</li>
<li>
<b>UBDRY</b> sets the parabolic inflow in terms of the value of the parameter
</li>
<li>
<b>UBUMP</b> calculates the sensitivity dU/dA on the bump.
</li>
<li>
<b>UVAL</b> evaluates the velocities at a given quadrature point.
</li>
<li>
<b>UV_WRITE</b> writes a velocity file.
</li>
<li>
<b>XY_WRITE</b> creates node coordinate data.
</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>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>