This document discusses generating and refining an unstructured mesh for a heat conduction simulation. It describes manually generating a simple triangular mesh with 22 points and 37 faces, specifying boundary conditions and material properties, and solving the problem with the laplacianFoam solver. It also includes a refineMeshDict file to refine the mesh along coordinate directions or faces.

1. Tutorial calculation in “An Introduction
to Computational Fluid Dynamics”
yotakagi77
August 5th, 2017

2. Ex. 11.1 Heat conduction problem in
unstructured grid.

3. Grid generation
• First trial
– blockMesh w/ wedge
– blockMesh wo/ wedge
– Square to triangle
– Shift, mirror, shift, merge, mirror, rotate, ….
– Modification of boundary patches is boring.

4. Grid generation
• Second trial
– Hand writing polyMesh data
– Investigation of a simple grid, e.g. two triangles.

5. polyMesh
• points
• faces
• owner
• neighbor
• boundary
0
1

6. Let’s try manual meshing!
• Three triangles

7. Mesh generation with section paper

8. Mesh generation with section paper

9. polyMesh of half model
• 22 points
• 37 faces
• 8 internal faces
• 6 patches
– adiabatic, low T., middle T., high T., symmetry,
empty

10. Heat conduction calculation
• Solver: laplacianFoam
• Physical property
– Thermal diffusivity, DT (=a)
• r = 7.83 x 103 kg/m3
• Cp = 461 J/kg·K
• k = 50 W/m·K
• a = k / (rCp) = 0.0147 m2/s

11. Result

12. refineMesh
$ refineMesh

13. refineMeshDict
// Cells to refine; name of cell set
set c0;
// Type of coordinate system:
// - global : coordinate system same for every cell. Usually aligned with
// x,y,z axis. Specify in globalCoeffs section below.
// - patchLocal : coordinate system different for every cell. Specify in
// patchLocalCoeffs section below.
// - fieldBased : uses the list of field names from the directions list for
// selecting the directions to cut. Meant to be used with geometricCut, but
// can also be used with useHexTopology.
//coordinateSystem global;
coordinateSystem patchLocal;
//coordinateSystem fieldBased;
// .. and its coefficients. x,y in this case. (normal direction is calculated as tan1^tan2)
globalCoeffs
{
tan1 (1 0 0);
tan2 (0 1 0);
}

14. refineMeshDict
patchLocalCoeffs
{
patch frontAndBack; // Normal direction is facenormal of zero'th face of patch
tan1 (1 0 0);
tan2 (0 1 0);
}
// List of directions to refine, if global or patchLocal
directions
(
tan1
tan2
normal
);
// List of directions to refine, if "fieldBased". Keep in mind that these
// fields must be of type "vectorField", not "volVectorField".
//directions
//(
// radialDirectionFieldName
// angularDirectionFieldName
// heightDirectionFieldName
//);

15. refineMeshDict
// Whether to use hex topology. This will
// - if patchLocal: all cells on selected patch should be hex
// - split all hexes in 2x2x2 through the middle of edges.
//useHexTopology true;
useHexTopology false;
// Cut purely geometric (will cut hexes through vertices) or take
topology
// into account. Incompatible with useHexTopology
//geometricCut false;
geometricCut true;
// Write meshes from intermediate steps
writeMesh false;