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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 C++ program which
samples a velocity vector field that satisfies the
continuity equation, and writes the nodes and velocities to a file,
suitable for display using GNUPLOT.
</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 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>SPIRAL_DATA</b> is available in
<a href = "../../c_src/spiral_data/spiral_data.html">a C version</a> and
<a href = "../../cpp_src/spiral_data/spiral_data.html">a C++ version</a> and
<a href = "../../f77_src/spiral_data/spiral_data.html">a FORTRAN77 version</a> and
<a href = "../../f_src/spiral_data/spiral_data.html">a FORTRAN90 version</a> and
<a href = "../../m_src/spiral_data/spiral_data.html">a MATLAB version</a> and
<a href = "../../py_src/spiral_data/spiral_data.html">a Python version</a>..
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate the use of the gnuplot graphics program.
</p>
<p>
<a href = "../../cpp_src/navier_stokes_2d_exact/navier_stokes_2d_exact.html">
NAVIER_STOKES_2D_EXACT</a>,
a C++ library which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations over an arbitrary domain in 2D.
</p>
<p>
<a href = "../../cpp_src/stokes_2d_exact/stokes_2d_exact.html">
STOKES_2D_EXACT</a>,
a C++ library which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "spiral_data.cpp">spiral_data.cpp</a>, the source code.
</li>
<li>
<a href = "spiral_data.hpp">spiral_data.hpp</a>, the include file.
</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>
<ul>
<li>
<a href = "spiral_data_prb.cpp">spiral_data_prb.cpp</a>, the source code.
</li>
<li>
<a href = "spiral_data_prb.sh">spiral_data_prb.sh</a>,
commands to compile and run the example.
</li>
<li>
<a href = "spiral_data_prb_output.txt">spiral_data_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
Sample data was generated with N = 20 and C = 0.45 and plotted
with GNUPLOT:
<ul>
<li>
<a href = "spiral_data.txt">spiral_data.txt</a>,
the X, Y, U, V values.
</li>
<li>
<a href = "spiral_commands.txt">spiral_commands.txt</a>,
commands to GNUPLOT.
</li>
<li>
<a href = "spiral.png">
spiral.png</a>,
the resulting plot.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>GRID_2D</b> returns a regular 2D grid.
</li>
<li>
<b>R8VEC_AMAX</b> returns the maximum absolute value in an R8VEC.
</li>
<li>
<b>R8VEC_AMIN</b> returns the minimum absolute value in an R8VEC.
</li>
<li>
<b>R8VEC_MAX</b> returns the value of the maximum element in an R8VEC.
</li>
<li>
<b>R8VEC_MIN</b> returns the value of the minimum element in an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_AB_NEW</b> returns a scaled pseudorandom R8VEC.
</li>
<li>
<b>RESID_SPIRAL</b> computes the residual for a spiral velocity vector field.
</li>
<li>
<b>SPIRAL_GNUPLOT</b> writes the spiral vector field to files for GNUPLOT.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UV_SPIRAL</b> computes a spiral velocity vector field.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 20 January 2015.
</i>
<!-- John Burkardt -->
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