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# 3D Mesh

The mesh of a fluid simulation describes the points where the flow equations are solved.
The stability and the precision of the calculations depend strongly on the mesh type and quality. If the user wishes to calculate the temperature field of the solids in addition to the fluids, it is necessary to generate mesh cells for the solids also.

## Geometry-fitted structured mesh

Structured grids have a regular topology; the cells are placed regularly so that the cells can be indexed with integer numbers.
In order for the grid to be adapted to the geometry, the grid lines must follow the body geometry.
In order to generate the mesh of the fluid parts, a negative geometry, which comprises the whole volume between the solid parts, must first be generated. This volume will be split into smaller domains, the so-called cells. When a high-quality mesh is required, then a full hexahedral mesh is the best option. The calculation domain is first of all divided into blocks in a CAD or similar program; these blocks can be later split into hexahedrons in the meshing tool.

 Geometry-fitted hexa-mesh Geometry-fitted unstructured tetra-mesh

## Geometry-fitted unstructured mesh

Also commonly used since 2000 are mesh generation tools which are based on unstructured mesh, with triangles (in 2D) or tetrahedrons (in 3D). The program primarily generates automatic cells which are fitted to the surfaces. For complex geometries, it is quite difficult and time-consuming to generate a good tetrahedral mesh as the generation of strongly distorted cells can hinder the convergence of the calculation. The user must therefore manually choose the correct parameters in order to generate a good mesh.
It is common practice to mesh with hexahedrons close to the walls and with tetrahedrons elsewhere, as you can see on the picture on the left below.

 Mixed-structured hexa-mesh and unstructured tetra-mesh Cartesian mesh

Unstructured grids generally require much more memory than structured grids and up to three times more computing time. For this reason, new commercial software based on new types of grids has been marketed since around 2005. At that time, CD-adapco decided to develop a completely new tool called Star-CCM + instead of further improving its well sold STAR-CD

## Cartesian mesh

Cartesian meshes are the right alternative to geometry fitted meshes. CFD Tools using this mesh type like FloEFD® offer more precise and efficient algorithms. Here you do not need to create a model of the fluid region like in the classical approach; the tool recognizes the fluid region based on the empty spaces between the solid geometries and the location of the boundary regions.
The geometry bodies are immersed in the cartesian mesh. The mesh lines can no longer be fitted to the bodies of complex geometries. In locations where the boundaries of the bodies do not fit to the cartesian mesh, interpolations must be used in order to take into account the effects of the misalignment between mesh and geometry. The cartesian mesh allows the use of more efficient solving-algorithms in spite of this interpolation.
With this method, called Immersed Boundary Method, it is easier to simulate complex geometries as the cartesian mesh always remains and the body is simply immersed in the mesh.

## Rotation and moving mesh

The complete rotational domain can be defined with a rotating coordinate system, for example for the flow in pumps or turbo-machines. The connection between the rotating domain and the rest of the computational domain is made with a mixing-plane.

A more accurate method to simulate the rotation is with moving mesh. The flow is calculated transient with the input of accurate time steps; the rotating domain changed its position for each time step. The calculation time is much longer than with a rotating coordinate system. A moving mesh must be implemented when the flow is expected to be irregular over the circumference due to irregularities of the geometry; this is for example the case for axial fans. The method of the moving mesh is available for all standard CFD tools.

Moving cartesian mesh for a radial fan