 # types of mesh used in computational fluid dynamics

Before you read further this article, I hope you read “meshing and discretisation in computational fluid dynamics” first to understand this article better. CFD simulation is very flexible and sometimes considered as an art instead of pure science, so the explanation in this article is only the generalization based on a common perspective and experience. In fact, the meshing process is commonly the longest and complicated process of CFD because it will affect the computational efficiency and even the quality and accuracy of the result.

To obtain higher resolution results (and sometimes more accurate), we need mesh size as small as possible, but the smaller the mesh, the total elements needed will be much more as well. Besides the local mesh settings, the type of mesh we used will determine the computational efficiency of our simulation. Moreover, these mesh types have each advantage and disadvantage compared to the other types.

Generally speaking, hexahedron mesh is the most ideal type of mesh. From the resolution quality (visualisation), square shape has obvious advantage compared to triangle or polygonal shape: imagine you have digital monitor with polygon pixel, the picture displayed may be weird.

Despite of its higher quality, this hexahedron mesh only feasible for a simple object such as a box or large radius. In an object with high curvature (small radius), hexahedron mesh sometimes hard to follow the curve and cant fit the object shape well, or even failed in the mesh generation process.

This problem makes the tetrahedron (triangle) mesh more popular than the hexahedron mesh. Using a tetrahedron mesh, small radius or high curvature object, or even very complicated object meshing problem can be overcome.

But, one problem using tetrahedron mesh is the total element used by the tetrahedron mesh is much more than hexahedron. Imagine a square 2D plane with 1m length and 1m height will need only one element of hexahedron mesh with 1m length and 1 meter height, but, if we used tetrahedron shape, we will need two triangles elements to construct this object with the same size (hence same accuracy). If we construct a 3D object, the situation is even worse.

In the numerical method (finite volume method for CFD), we often calculate the value of a parameter (velocity, pressure, temperature etc.) in a cell used the information from the neighboring cells. Generally speaking, the more cells neighbor, the faster the computational process (more data references). If we count the total neighbor (total faces) of hexahedron mesh, it has 6, on the other hand, tetrahedron only has 4. This idea also underlies the idea of polyhedral mesh.

CASE STUDY

In this case study, a 3D cylinder object is simulated using hexahedron and tetrahedron mesh with the same element size. The first pictures are the velocity distribution around the cylinder, and the second pictures are iso-surface of pressure around the cylinder.

Hexahedron Mesh:

Tetrahedron Mesh:

Hexahedron Mesh:

Tetrahedron Mesh:

Based on the case study above, the hexahedral mesh needs 36.000 total elements, and the tetrahedral model needs 322.000 total elements (keep in mind the element size, hence maybe the accuracy are the same). This simple experiment proofs that hexahedron mesh almost 10 times more efficient than tetrahedron in term of mesh construction. This is very crucial for computing time and our RAM resources limit.

On the other hand, from iso-surface visualisation, hexahedron mesh has better looking than tetrahedron mesh. 