NAVIER_STOKES_MESH3D
3D Meshes for Navier Stokes Problems

NAVIER_STOKES_MESH3D, MATLAB data files which define meshes for several 3D test problems involving the Navier Stokes equations for fluid flow, provided by Leo Rebholz.

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.

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.

Licensing:

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

Languages:

NAVIER_STOKES_MESH3D is available in a MATLAB version.

Related Data and Programs:

DOLFIN, Python programs which are used with the DOLFIN library to set up and solve a wide variety of problems using the finite element method.

DOLFIN-CONVERT, 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.

DOLFIN_XML is a data directory which contains examples of XML files that describe 3D finite element meshes as used by DOLFIN and FENICS.

FENICS, programs which illustrate the use of a collection of free software with an extensive list of features for automated, efficient solution of differential equations.

GMSH, examples which illustrate the use of the Gmsh program, a 3D mesh generator for the finite element method (FEM).

NAVIER_STOKES_3D_EXACT, evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.

NAVIER_STOKES_MESH2D, MATLAB data files defining meshes for several 2D test problems involving the Navier Stokes equations for flow flow, provided by Leo Rebholz.

navier_stokes_mesh3d_test

TET_MESH_ORDER20, a dataset directory which contains examples of order 20 tetrahedral meshes.

TET_MESH_TO_GMSH, 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.

Author:

Leo Rebholz

Reference:

1. Abigail Bowers, Leo Rebholz, Aziz Takhirov, Catalin Trenchea,
   Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering,
   International Journal for Numerical Methods in Fluids,
   Volume 70, Number 7, 2012, pages 805-828.

Source Code:

The following MAT files each contain a mesh, defined by a structure whose components are nodeco, elnode, and bdynde:

• cylinder_3d.mat 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.
• step_3d.mat 3D flow in a 10x50x10 channel, past a forward and backward step, using 38,992 nodes, 7,680 elements, and 2,954 boundary nodes.

The following functions operate on the mesh data:

• display_element.m reads information from the tet mesh file, and displays the coordinates of the nodes making up a particular element.
• i4mat_write.m writes an I4MAT file.
• mesh3d_extract.m loads an MAT file containing a mesh and extracts the 3 components: node coordinates, element node indices, boundary nodes.
• r8mat_write.m writes an R8MAT file.
• timestamp.m prints the YMDHMS date as a timestamp.