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navier_stokes_3d_exact.html
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<html>
<head>
<title>
NAVIER_STOKES_3D_EXACT - Exact solutions to the 3D Incompressible Time-Dependent Navier Stokes Equations
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NAVIER_STOKES_3D_EXACT<br>
Exact solutions to the <br>
3D Incompressible Time-Dependent Navier Stokes Equations
</h1>
<hr>
<p>
<b>NAVIER_STOKES_3D_EXACT</b>,
a MATLAB library which
evaluates exact solutions to the incompressible time-dependent
Navier-Stokes equations over an arbitrary domain in 3D.
</p>
<p>
The reference asserts that the given velocity and pressure fields
are exact solutions for the 3D incompressible time-dependent
Navier Stokes equations over any region.
</p>
<p>
To define a typical problem, one chooses a bounded spatial region
and a starting time, and then imposes boundary and initial conditions
by referencing the exact solution appropriately.
</p>
<p>
In the reference paper, a calculation is made for the cube centered
at (0,0,0) with a "radius" of 1 unit, and over the time interval
from t = 0 to t = 0.1, with parameters a = PI/4 and d = PI/2,
and with Dirichlet boundary conditions on all faces of the cube.
</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>NAVIER_STOKES_3D_EXACT</b> is available in
<a href = "../../c_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a C version</a> and
<a href = "../../cpp_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a C++ version</a> and
<a href = "../../f77_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a FORTRAN77 version</a> and
<a href = "../../f_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a FORTRAN90 version</a> and
<a href = "../../m_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a MATLAB version</a> and
<a href = "../../py_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/navier_stokes_2d_exact/navier_stokes_2d_exact.html">
NAVIER_STOKES_2D_EXACT</a>,
a MATLAB library which
evaluates exact solutions to the incompressible time-dependent
Navier-Stokes equations over an arbitrary domain in 2D.
</p>
<p>
<a href = "../../m_src/navier_stokes_mesh3d/navier_stokes_mesh3d.html">
NAVIER_STOKES_MESH3D</a>,
MATLAB data files defining meshes for several
3D test problems involving the Navier Stokes equations
for flow flow, provided by Leo Rebholz.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
C Ross Ethier, David Steinman,<br>
Exact fully 3D Navier-Stokes solutions for benchmarking,<br>
International Journal for Numerical Methods in Fluids,<br>
Volume 19, Number 5, March 1994, pages 369-375.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "resid_ethier.m">resid_ethier.m</a>,
evaluates the residual in the velocity and pressure equations
at any point (x,y,z) and time t.
</li>
<li>
<a href = "uvwp_ethier.m">uvwp_ethier.m</a>,
evaluates the velocity and pressure field at any point (x,y,z) and
time t.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ns3de_test.m">ns3de_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "ns3de_test01.m">ns3de_test01.m</a>,
samples the solution at the initial time, to estimate the
data range.
</li>
<li>
<a href = "ns3de_test02.m">ns3de_test02.m</a>,
samples the residual at the initial time, and many points.
</li>
<li>
<a href = "ns3de_test_output.txt">ns3de_test_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 15 January 2015.
</i>
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</html>