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<html>
<head>
<title>
NAVIER_STOKES_MESH3D - 3D Meshes for Navier Stokes Problems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
NAVIER_STOKES_MESH3D<br> 3D Meshes for Navier Stokes Problems
</h1>
<hr>
<p>
<b>NAVIER_STOKES_MESH3D</b>
is a set of MATLAB data files defining meshes for several
3D test problems involving the Navier Stokes equations
for fluid flow, provided by Leo Rebholz.
</p>
<p>
We are interested in these meshes as useful tests for a procedure
in which we are able to redo the related Navier Stokes calculations
using FENICS.
</p>
<p>
As part of that task, we need to take the meshes
associated with the MATLAB computation and translate them into
a format acceptable to DOLFIN / FENICS. Our proposed mechanism
for this is either to translate the files to the Gmsh msh format,
and then use DOLFIN-CONVERT to convert that to DOLFIN XML,
or else to translate the files directly into DOLFIN XML format ourselves.
</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_MESH3D</b> is available in
<a href = "../../m_src/navier_stokes_mesh3d/navier_stokes_mesh3d.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../py_src/dolfin/dolfin.html">
DOLFIN</a>,
Python programs which
are used with the DOLFIN library to set up and solve
a wide variety of problems using the finite element method.
</p>
<p>
<a href = "../../py_src/dolfin-convert/dolfin-convert.html">
DOLFIN-CONVERT</a>,
a Python program which
can convert mesh file from Gmsh, MEDIT, METIS or SCOTCH format to an
XML format suitable for use by DOLFIN or FENICS,
by Anders Logg.
</p>
<p>
<a href = "../../data/dolfin_xml/dolfin_xml.html">
DOLFIN_XML</a>
is a data directory which
contains examples of XML files that describe 3D finite element meshes
as used by DOLFIN and FENICS.
</p>
<p>
<a href = "../../examples/fenics/fenics.html">
FENICS</a>,
programs which
illustrate the use of a collection of free software
with an extensive list of features for
automated, efficient solution of differential equations.
</p>
<p>
<a href = "../../examples/gmsh/gmsh.html">
GMSH</a>,
examples which
illustrate the use of the Gmsh program,
a 3D mesh generator for the finite element method (FEM).
</p>
<p>
<a href = "../../m_src/navier_stokes_3d_exact/navier_stokes_3d_exact.html">
NAVIER_STOKES_3D_EXACT</a>,
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations over an arbitrary domain in 3D.
</p>
<p>
<a href = "../../m_src/navier_stokes_mesh2d/navier_stokes_mesh2d.html">
NAVIER_STOKES_MESH2D</a>,
MATLAB data files defining meshes for several
2D test problems involving the Navier Stokes equations
for flow flow, provided by Leo Rebholz.
</p>
<p>
<a href = "../../datasets/tet_mesh_order20/tet_mesh_order20.html">
TET_MESH_ORDER20</a>,
a dataset directory which
contains examples of order 20 tetrahedral meshes.
</p>
<p>
<a href = "../../m_src/tet_mesh_to_gmsh/tet_mesh_to_gmsh.html">
TET_MESH_TO_GMSH</a>,
a MATLAB program which
reads information defining a tet mesh, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a corresponding Gmsh mesh file.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Leo Rebholz
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Abigail Bowers, Leo Rebholz, Aziz Takhirov, Catalin Trenchea,<br>
Improved accuracy in regularization models of incompressible
flow via adaptive nonlinear filtering,<br>
International Journal for Numerical Methods in Fluids,<br>
Volume 70, Number 7, 2012, pages 805-828.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
The following MAT files each contain a mesh, defined by
a structure whose components are nodeco, elnode, and bdynde:
<ul>
<li>
<a href = "cylinder_3d.mat">cylinder_3d.mat</a>
3D flow in a 0.41x2.5x0.41 channel, past a (square) cylinder,
using 49,602 nodes, 9,792 elements, and 3,600 boundary nodes.
</li>
<li>
<a href = "step_3d.mat">step_3d.mat</a>
3D flow in a 10x50x10 channel, past a forward and backward step,
using 38,992 nodes, 7,680 elements, and 2,954 boundary nodes.
</li>
</ul>
</p>
<p>
The following functions operate on the mesh data:
<ul>
<li>
<a href = "display_element.m">display_element.m</a>
reads information from the tet mesh file, and displays the
coordinates of the nodes making up a particular element.
</li>
<li>
<a href = "i4mat_write.m">i4mat_write.m</a>
writes an I4MAT file.
</li>
<li>
<a href = "mesh3d_extract.m">mesh3d_extract.m</a>
loads an MAT file containing a mesh and extracts the
3 components: node coordinates, element node indices,
boundary nodes.
</li>
<li>
<a href = "r8mat_write.m">r8mat_write.m</a>
writes an R8MAT file.
</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 = "nsm3d_test.m">nsm3d_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "nsm3d_test_output.txt">nsm3d_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "nsm3d_test01.m">nsm3d_test01.m</a>
reports the sizes of the three mesh components, and
the range of the node coordinates; writes the information
to node and element files for a tet mesh.
</li>
</ul>
</p>
<p>
<b>CYLINDER_3D</b> is a tet mesh for 3D flow in a 0.41x2.5x0.41 channel,
past a (square) cylinder, using 49,602 nodes and 9,792 elements,
created from cylinder_3d.mat.
<ul>
<li>
<a href = "cylinder_3d_nodes.txt">cylinder_3d_nodes.txt</a>,
the node file;
</li>
<li>
<a href = "cylinder_3d_elements.txt">cylinder_3d_elements.txt</a>,
the tetra file;
</li>
</ul>
</p>
<p>
<b>STEP_3D</b> is a tet mesh associated with 3D flow in a 10x50x10 channel,
past a forward and backward step, using 38,992 nodes and 7,680 elements,
created from step_3d.mat.
<ul>
<li>
<a href = "step_3d_nodes.txt">step_3d_nodes.txt</a>,
the node file;
</li>
<li>
<a href = "step_3d_elements.txt">step_3d_elements.txt</a>,
the tetra 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 03 June 2013.
</i>
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