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<html>
<head>
<title>
SPIRAL_DATA - Velocity Vector Field Satisfying Continuity Equation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPIRAL_DATA <br> Velocity Vector Field Satisfying Continuity Equation
</h1>
<hr>
<p>
<b>SPIRAL_DATA</b>
is a FORTRAN90 program which
samples a velocity vector field that satisfies the
continuity equation, and writes the nodes and velocities to files.
</p>
<p>
The continuous velocity field <b>(U,V)(X,Y)</b> that is discretely
sampled here satisfies the homogeneous continuity equation, that is,
it has zero divergence. In other words:
<pre><b>
dU/dX + dV/dY = 0.
</b></pre>
This is by construction, since we have
<pre><b>
U(X,Y) = 10 * d/dY ( PHI(X) * PHI(Y) )
V(X,Y) = -10 * d/dX ( PHI(X) * PHI(Y) )
</b></pre>
which guarantees zero divergence.
</p>
<p>
The underlying function PHI is defined by
<pre><b>
PHI(Z) = ( 1 - cos ( C * pi * Z ) ) * ( 1 - Z )**2
</b></pre>
where C is a parameter.
</p>
<p>
The velocity data satisifes the (continuous) continuity equation;
this in <b>no way</b> implies that it satisfies the momentum equations
associated with Stokes or Navier-Stokes flow! Moreover, a flow solution
for those equations would normally also require specifying a value
for the scalar pressure field <b>P(X,Y)</b>.
</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/bump/bump.html">
BUMP</a>,
a FORTRAN90 program which
uses the finite element method
to study the influence of an obstacle in channel flow. The velocity
field can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../datasets/case1_flow/case1_flow.html">
CASE1_FLOW</a>,
a dataset directory which
contains a sequence of
velocity vector fields that can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../datasets/cavity_flow/cavity_flow.html">
CAVITY_FLOW</a>,
a dataset directory which
contains a sequence of
velocity vector fields that can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../f_src/channel/channel.html">
CHANNEL</a>,
a FORTRAN90 program which
uses the finite element method
to study flow in a channel. The velocity field can be plotted by
<b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../m_src/direction_arrows/direction_arrows.html">
DIRECTION_ARROWS</a>,
a MATLAB program which
can plot direction fields.
</p>
<p>
<a href = "../../datasets/inout_flow/inout_flow.html">
INOUT_FLOW</a>,
a dataset directory which
contains a sequence of
velocity vector fields that can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../datasets/inout_flow2/inout_flow2.html">
INOUT_FLOW2</a>,
a dataset directory which
contains a sequence of
velocity vector fields that can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../f_src/mhd_flow/mhd_flow.html">
MHD_FLOW</a>,
a FORTRAN90 program which
computes velocity fields
which can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../datasets/tcell_flow/tcell_flow.html">
TCELL_FLOW</a>,
a dataset directory which
contains a sequence of
velocity vector fields that can be plotted by <b>VECTOR_PLOT</b>.
</p>
<p>
<a href = "../../m_src/vector_magnitude_grid/vector_magnitude_grid.html">
VECTOR_MAGNITUDE_GRID</a>,
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 contour plot of the vector magnitude.
</p>
<p>
<a href = "../../m_src/vector_stream_grid/vector_stream_grid.html">
VECTOR_STREAM_GRID</a>,
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.
</p>
<p>
<a href = "../../m_src/velocity_arrows/velocity_arrows.html">
VELOCITY_ARROWS</a>,
a MATLAB program which
can plot velocity
fields.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "spiral_data.f90">spiral_data.f90</a>, the source code.
</li>
<li>
<a href = "spiral_data.sh">spiral_data.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
The following data was generated with N = 20 and C = 0.8.
The plots were made with VECTOR_PLOT.
<ul>
<li>
<a href = "spiral_xy.txt">spiral_xy.txt</a>,
the X, Y locations.
</li>
<li>
<a href = "spiral_uv.txt">spiral_uv.txt</a>,
the U, V velocity component values.
</li>
<li>
<a href = "spiral_dir.png">
spiral_dir.png</a>,
a <a href = "../../data/png/png.html">PNG</a>
image of the velocity direction field.
</li>
<li>
<a href = "spiral_vec.png">
spiral_vec.png</a>,
a <a href = "../../data/png/png.html">PNG</a>
image of the vector field.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for SPIRAL_DATA.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 24 March 2007.
</i>
<!-- John Burkardt -->
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