# Background for Hex-dominant parametric¶

## Introduction¶

snappyHexMesh, which the Hex-dominant parametric mesh operation type is based on, is a mesh generation tool in the OPENFOAM® open-source software. This tool generates three-dimensional unstructured or hybrid meshes consisting of hexahedra (hex) and split-hexahedra (split-hex) elements. The algorithm iteratively performs the steps detailed below to obtain the final mesh.

Generally, a reference base mesh is used to project and snap cells onto the geometry. Mesh refinements can flexibly be specified on edges, surfaces, and inside or outside volumes to obtain optimum geometry feature resolution and final mesh quality. Parallel computing is fully supported with a load balancing at every iteration.

## Basic methodology¶

The basic snappyHexMesh methodology consists of 4 main steps.

1. In the first step, Castellated mesh step, the reference base mesh is created (with or without refinements) around the object.
2. Next, the castellated mesh is snapped onto the object’s surface in the Snapping step.
3. If preferred, the mesh layers are generated on selected surfaces and adjusted to the main mesh in the Layer addition.
4. Finally in the last step, Mesh quality assessment, the final mesh is checked for illegal/bad cells and further iterations are performed until the quality standards are attained.

These four steps are described and illustrated in brief detail below:

### Castellated mesh step¶

In the castellated mesh step the base mesh is created inside the bounds of the Base Mesh Box. The Base Mesh Box serves as the domain for the base mesh for the meshing process. This mesh purely contains hexahedral elements whose number is defined by the user. It is important to note that for any direction the number of cells must be larger than 1, resulting in a 3-D mesh.

Following [1] an example of external mesh around a vehicle body is used to explain the meshing process. The first image below shows the Base Mesh Box around the object.

The figure shows the Base Mesh Box around the object.

The Base Mesh is then generated inside the entire space bounded by the Base Mesh Box as shown in figure below.

The figure shows the Base Mesh around and inside the object.

#### Cell splitting:¶

To remove the mesh cells inside the body, this base mesh is then refined based on the specified edge and surface refinements and then split in the vicinity of the body’s surfaces.

The figure shows the splitting of refined cells intersecting the surface of the object.

#### Cell removal:¶

After the mesh in the locality of the body is refined and split, cells are removed based on the specification of the material point (see Main Settings for details). This requires atleast one region to be bounded by a surface inside the domain. The mesh space where the material point is located is kept while cells are removed in the other space(s). So, in this case the material point can be in the space between the bounds of the base Mesh Box and the surface of the body.

The figure shows the cell removal process based on the material point.

#### Region refinements:¶

Lastly, the mesh space is refined further based on the specified region refinements and the refinement level (detailed in Main Settings > Region refinements). After this, the castellated mesh looks similar to the one shown below.

The figure shows the region refinements for the volume mesh around the object.

### Snapping step¶

The next step is snapping or projecting the castellated mesh (staircase type mesh) to the object surface. This process is accomplished by the following algorithm:

• Displacing the cell vertices of the castellated mesh onto the object’s surfaces.
• Then, relaxing the internal mesh due the displaced vertices.
• Checking for any bad cells that violate the mesh quality parameters.
• Re-iterate the process until the quality standards are achieved.

The internal mesh after snapping process is then depicted by the figure below:

The figure shows the snapping of the cells onto the surface of the object

Depending upon the requirements, a layer mesh consisting of hexahedral cells that are aligned to the surface may be generated on selected or all surfaces. This process is also done iteratively and involves a number of steps to generate the required mesh. Here only the methodology is discussed, while the settings are further detailed in Main Settings > Layer Refinements.

The main steps are highlighted as follows:

• The internal snapped mesh is pushed back from the object’s surface in the normal direction by the specified distance (Thickness value).
• The internal mesh is then relaxed and checked to satisfy the quality parameters, otherwise the thickness is reduced.
• If quality criterion is satisfied then layers are inserted. If not then, previous steps are repeated.
• Else if, there is no possibility of achieving the required quality standards, the layers are not inserted.

The figure shows the addition of layers aligned to the object’s selected surface

### Mesh quality assessment¶

This is the last step for the SnappyHexMesh algorithm. The mesh is finally checked for quality criterion and the meshing process looped until all checks are passed or the overall iteration limit reached. In the case of reaching the iteration limit with failed checks, the resulting mesh might contain bad elements or cells.

## References¶

 [1] Snappy Hex Mesh official user guide, http://cfd.direct/openfoam/user-guide/snappyHexMesh

## Disclaimer¶

This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.