week 03 - mesh quality

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Computational Fluid Dynamics

Structured Vs. Unstructured Mesh • A single block structured mesh may comprise of square elements (2D) or hexahedral elements

(3D) which are orthogonal in i, j space (2D) or i, j, k space (3D). Although is also possible to have

wedges (3D), triangles (2D) and pyramids (3D) in a structured mesh.

• Looking at a 2D example, for simplicity:

– Every node in a 2D structured mesh has a corresponding integer i and j index value which is unique.

– The physical locations of the nodes are stored in a table or are functionally related to the mesh space (ie

(x,y)= f(i,j)).

– The neigbours of node (i,j) are (i-1,j), (i+1,j), (i,j-1), (i,j+1), (i-1,j-1), and (i+1,j+1).

– A structured mesh makes it very easy to loop through neighbours and can be efficient with memory.

• A structured mesh has many coding advantages, but it may be difficult to conform a single block

to a complicated shape. Code developers have got around this by allowing multiple blocks

(multiblock unstructured), but this can make the internal memory strucutres more inefficient.

• Another way to make the mesh generation simpler, and improve code performance is to throw

away the block structure and replace indices with node numbers and a connectivity table. This is

known as an unstructured mesh, because it lacks the i,j,k structure.

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Structured Vs. Unstructured Mesh

• A structured mesh requires the blocking as input.

• Unstructured meshes, only requires the element size on the lines and surfaces that define the geometry as input.

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• Unstructured

Hybrid Mesh

(tetras, prisms

and hexs)

• Cell count:

approx. 5 000 000

• Structured Mesh

(hexahedrals)

• Cell count:

approx. 5 000 000

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• Each mesh type has its advantages and

disadvantages.

• At the end of the day, the mesh you use must

has a good overall quality and must be

smooth.

• The mesh density should be high enough to

capture all relevant flow features.

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Mesh Quality

• Rule of thumb: ‘the elements shape and

distribution should be pleasing to the eye’.

• There is no written theory when it comes to

mesh generation and the whole process

depends on user experience.

• The user can rely on grid dependency studies,

but they are time consuming and expensive.

• No single standard benchmark or metric exists

that can effectively assess the quality of a mesh,

but you can rely on suggested best practices.

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Mesh Quality

• The most common mesh quality metrics are:

– Orthogonality.

– Skewness.

– Aspect Ratio.

– Smoothness.

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Mesh Quality

• Mesh orthogonality

– It is the angular deviation of the vector S (located

at the face center f ) from the vector d connecting

the two cell centers P and N.

– It affects the gradient of the face center f.

– It adds diffusion to the solution.

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Mesh Quality

• Mesh skewness – Skewness is the deviation of the vector d that

connects the two cells P and N, from the face center f. The deviation vector is represented with and the point where the vector d intersects the face f is fi.

– It affects the interpolation of the cell centered quantities to the face center f.

– It adds diffusion to the solution.

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Mesh Quality

• Mesh aspect ratio AR

– Mesh aspect ratio AR is the ratio between the

longest side x and the shortest side y .

– Large AR are fine if gradients in the long direction

are small.

– High AR smear gradients.

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Mesh Quality

• Smoothness – Smoothness, also known as expansion rate, growth factor

or uniformity, defines the transition in size between contiguous cells.

– Large transition ratios between cells add diffusion to the solution.

– Ideally, the maximum change in mesh spacing should be less than 20%: ∆𝑦2 ∆𝑦1 ≤ 1.2

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Steep Transition Smooth Transition


Mesh Quality

• For the same cell count, hexahedral meshes will give more accurate solutions, especially if the grid lines are aligned with the flow.

• The mesh density should be high enough to capture all relevant flow features. In areas where the solution change slowly, you can use larger elements.

• To keep cell count down, use non-uniform meshes to cluster cells only where they are needed. Use local refinements and solution adaption to further refine only on selected areas.

• In boundary layers, quad, hex, and prism/wedge cells are preferred over triangles, tetrahedras, or pyramids.

• If you are not using wall functions (turbulence modeling), the mesh adjacent to the walls should be fine enough to resolve the boundary layer flow. This will rocket the cell count.

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Mesh Quality

• In

– WM_PROJECT_DIR/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshCheck.C

you will find the quality metrics used in OpenFOAM.

• Their maximum (or minimum) values are defined as follows:

Foam::scalar Foam::primitiveMesh::closedThreshold_ = 1.0e-6;

Foam::scalar Foam::primitiveMesh::aspectThreshold_ = 1000;

Foam::scalar Foam::primitiveMesh::nonOrthThreshold_ = 70; // deg

Foam::scalar Foam::primitiveMesh::skewThreshold_ = 4;

Foam::scalar Foam::primitiveMesh::planarCosAngle_ = 1.0e-6;

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Mesh Quality

• OpenFOAM comes with the utility checkMesh which

checks the validity of the mesh.

• checkMesh will look for/check for:

– Mesh stats and overall number of cells of each type.

– Check topology (boundary conditions definitions).

– Check geometry and mesh quality (bounding box, cell

volumes, skewness, orthogonality, aspect ratio)

• If for any reason checkMesh finds errors, it will give

you a message and it will tell you what check failed.

• It will also write a set with the faulty cells, faces,

points. These sets are saved in the directory

constant/polyMesh/sets/

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Mesh Quality

• Mesh topology and patch topology errors must

be repaired.

• You will be able to run with mesh quality errors

such as skewness, aspect ratio, minimum face

area, and non-orthogonality. But remember, they

will severely tamper the solution accuracy and

eventually can make the solver blow-up.

• checkMesh does not repair these errors. You will

need to check the geometry for possible errors

and generate a new mesh.

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Mesh Conversion

• It is also possible to export a mesh generated with a third party

software and use it in OpenFOAM. Some of the utilities available

formesh conversion are listed below:

– ansysToFoam: converts an ANSYS input mesh file OpenFOAM

format.

– cfx4ToFoam: converts a CFX 4 mesh to OpenFOAM format.

– fluent3DMeshToFoam: converts a Fluent mesh to OpenFOAM format.

– gambitToFoam: converts a GAMBIT mesh to OpenFOAM format.

– gmshToFoam: reads .msh file as written by Gmsh.

– ideasUnvToFoam: I-Deas unv format mesh conversion.

– plot3dToFoam: plot3d mesh (ascii/formatted format) converter.

– star4ToFoam: converts a STAR-CD (v4) PROSTAR mesh into

OpenFOAM format.

– tetgenToFoam: Converts .ele and .node and .face files, written by

tetgen.

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Mesh Conversion

• OpenFOAM also comes with many mesh manipulation utilities.

• Some of them are listed below: – checkMesh: checks validity of a mesh.

– refineMesh: utility to refine cells in multiple directions.

– renumberMesh: renumbers the cell list in order to reduce the bandwidth, reading and renumbering all fields from all the time directories

– transformPoints: transforms the mesh points in the polyMesh directory according to the translate, rotate and scale options.

– mirrorMesh: mirrors a mesh around a given plane.

– setSet: manipulate a cell/face/point/ set or zone intera

– refineWallLayer: utility to refine cells next to patches.

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Mesh Conversion

• blockMesh

– For simple geometries, the mesh generation utility blockMesh

(supplied with OpenFOAM), can be used. The blockMesh utility

creates multiblock meshes. The mesh is generated from a dictionary

file named blockMeshDict located in the constant/polyMesh

directory.

• snappyHexMesh

– For complex geometries, the mesh generation utility snappyHexMesh

(supplied with OpenFOAM), can be used. The snappyHexMesh utility

generates 3D meshes containing hexahedra and split-hexahedra

from a triangulated surface geometry in Stereolithography (STL)

format. The mesh is generated from a dictionary file named

snappyHexMeshDict located in the system directory and a

triangulated surface geometry file located in the directory

constant/triSurface.

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week 03 - mesh quality

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