NS3D_FEM
Steady Navier Stokes Equations in 3D
Finite Element Solution

NS3D_FEM is a MATLAB program which sets up and solves a finite element formulation of the steady 3D Navier Stokes equations in an arbitrary geometry defined by the user, by Jeff Borggaard.

The user defines the geometry as a collection of tetrahedrons. These tetrahedrons may be linear (using four nodes) or quadratic (using ten nodes, which are the four vertices and the six midside nodes).

Graphics Options:

The data from the program can be written out to a graphics file suitable for use with a visualization program. This is done by "turning on" the appropriate call in steady_navierstokes_3d.m There are currently several functions that can be called, to make an output file of various types:

• threed_to_tecplot creates an output file for TECPLOT.
• threed_to_vtk creates a "legacy" (old style) VTK output file for PARAVIEW.
• threed_to_vtu creates a modern (XML-based) VTU output file for PARAVIEW.
• threed_to_vu creates an output file for VU.

Information about TECPLOT is available at http://www.tecplot.com/.

Information about PARAVIEW is available at http://www.paraview.org/ .

Information about VU is available at http://www.invisu.ca/e/index.php.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

TEC, a data directory which contains examples of TEC files, TECPLOT files used for storing 2D or 3D graphics with attributes;

TET_MESH, a MATLAB library which carries out various operations on tetrahedral meshes.

TET_MESH_TET_NEIGHBORS, a MATLAB program which reads information about a tet mesh and writes out a list of the tetrahedrons that are adjacent to a given tetrahedron;

THREED, a MATLAB library which contains functions useful for 3D finite element calculations.

THREED_TO_TECPLOT, a MATLAB program which accepts computational data from a 3D finite element fluid flow program and writes it to a PLT file for postprocessing by TECPLOT.

THREED_TO_VTK, a MATLAB program which accepts computational data from a 3D finite element fluid flow program and writes it to a VTK "legacy" file for postprocessing by PARAVIEW.

THREED_TO_VTU, a MATLAB program which accepts computational data from a 3D finite element fluid flow program and writes it to a VTK unstructured grid file for postprocessing by PARAVIEW.

THREED_TO_VU, a MATLAB program which accepts computational data from a 3D finite element fluid flow program and writes it to a file for postprocessing by VU.

TOMS866, a MATLAB library which is the Incompressible Flow Iterative Solution Software;
this library is commonly called IFISS;
this is ACM TOMS algorithm 866.

VTK, a data directory which contains examples of VTK files, an obsolete file format used by the Visual Toolkit, and which can be displayed by the PARAVIEW program;

VTU, a data directory which contains examples of VTU files, a modern XML-based file format for unstructured grid data, used by the Visual Toolkit, and which can be displayed by the PARAVIEW program;

Author:

NS3D_FEM was written by Jeff Borggaard, Mathematics Department, Virginia Tech.

Reference:

1. Max Gunzburger,
   Finite Element Methods for Viscous Incompressible Flows,
   A Guide to Theory, Practice, and Algorithms,
   Academic Press, 1989,
   ISBN: 0-12-307350-2,
   LC: TA357.G86.

Source Code:

• steady_navierstokes_3d.m, solves the steady incompressible 3D Navier Stokes equations.
• tet_mesh_boundary.m, reads a tetrahedral mesh and neighbor information, and produces a list of boundary edges and boundary nodes.
• threed_bilinear.m, integrates a bilinear quantity.
• threed_f_int.m, integrates a function f(x) times a test function.
• threed_gauss.m, calculates Gauss integration points for a tetrahedral element.
• threed_mesh.m, creates a mesh for a rectangular domain, using linear or quadratic tetrahedral elements.
• threed_shape.m, computes test functions and derivatives on a 3D element.
• threed_shapeiso.m, computes test functions and derivatives on a 3D isoparametric element.
• threed_to_tecplot.m, writes out a 3D finite element solution to a format readable by the Tecplot flow visualization package.
• threed_to_vtk.m, writes out a 3D finite element solution to the "legacy" VTK format, (which has been superseded by the VTU format), which can be read and displayed by the Paraview program.
• threed_to_vtu.m, writes out a 3D finite element solution to the modern XML-based VTU format, (the Visual Toolkit format for unstructured grid data), which can be read and displayed by the Paraview program.
• threed_to_vu.m, writes out a 3D finite element solution to a format readable by the Vu flow visualization package.
• vtk_puvw_write.m, writes pressure and 3D velocity vectors to a "legacy" VTK unstructured grid file.
• vtu_puvw_write.m, writes pressure and 3D velocity vectors to a modern XML-based VTU unstructured grid file.

Examples and Tests:

CASE1 is a built-in example, which can be run by the command

        steady_navierstokes_3d ( 1 )
      

• case1_output.txt, the printed output.
• case1_output.mat, a MATLAB structure which saves the values of X, E_CONN, U, V, W, and P.
• case1_output.plt, computed data in a format suitable for input to TECPLOT.
• case1.vtk, computed (U,V,W) and P data in a VTK "legacy" file format suitable for input to PARAVIEW.
• case1.vtu, computed (U,V,W) and P data in a VTU file suitable for input to PARAVIEW.
• case1.vu, computed (U,V,W) and P data in a VU file suitable for input to VU.

CASE2 is a built-in example, which can be run by the command

        steady_navierstokes_3d ( 2 )
      

• sphere_mesh2rcm.node, an input data file specifying the node coordinates.
• sphere_mesh2rcm.elem, an input data file specifying the nodes which make up each element.
• sphere_mesh2rcm.boundary, a data file specifying the boundary faces.
• case2_output.txt, the printed output.
• case2_output.plt, computed data in a format suitable for input to TECPLOT.

You can go up one level to the MATLAB source codes.