Hexahedral grids present several advantages over their tetrahedral/mixed counterparts. As an example, in finite volume simulations they result in fewer edges and hence a reduced FLOP count for a given mesh density. Furthermore, they result in smaller numerical errors, as long as certain conditions on the quality of the grid are met. Multiblock grids are essentially unstructured hexahedral grids where each cell - the blocks - is further subdivided into a Cartesian array of cells.  
The original unstructured grid defines the layout of the multiblock grid. Multiblock grids are popular because they represent a compromise between the flexibility of fully unstructured grids and the favourable numerical and algorithmic properties of structured grids. The generation of good-quality multiblock-grids, however, is not a trivial task for general geometries and is still the subject of active research.  
In general, the successful generation of a high quality multiblock grid relies on the generation of a suitable layout. In many fields, a large number of meshes are required for domains which are geometrically similar but topologically identical.  
In such cases, the same multiblock layout will be suitable for a whole class of geometries, and can be reused for multiple meshes. There are four essential steps to such a strategy :  
-Creation of the initial block layout template

 -Mapping of the template to a particular geometry

 -Optimisation of the block boundary locations

-Generation of the mesh inside each block

Templating gives considerable control over the mesh topology, meaning that the users' knowledge of both the geometry, and the specific requirements of the simulation scheme the mesh will be used for can be leveraged, resulting in higher quality meshes than might be generated by automated strategies. 

This means that both the ease of mapping existing templates to new geometries and the consistent generation of high quality meshes from the initial mapping are crucial for the viability of any templating strategy.

Previous work has created templates for entire geometries, however for engineering applications, a number of complex geometries of common use can be idealised as a main trunk joined by suitably located branches.  
The internal and external geometry of cooled turbine blades follows this simple paradigm - the internal channel is the trunk, and smaller features such as films or slots are the branches.  
Grafting exploits this trunk-and-branch configuration to produce unstructured meshes.  
It is possible to exploit this to produce multiblock layouts if simple templates can be built to attach branches to a trunk.  
Creating a layout for a whole geometry would then consist of patching together existing trunk and branch templates.

This paper describes an efficient method for generating grids for trunk-and-branch configurations where the branch is small compared to the size of the trunk, as in turbine cooling configurations. The method is based on the use of templates for the creation of branch layouts and relies on an elliptic smoothing step with prescribed normal spacing and near-orthogonality at the boundaries.  
The method for generating multiblock grids is therefore as follows:  
1) Start from a hexahedral grid  
2) Introduce modifications following templated layouts, e.g. insert branches or perform local modifications to alter the nature of the layout  
3) Perform smoothing  
Details of the data structure and of the smoothing techniques are presented used are presented in the paper, as well as some layouts  and  the application of the method to geometries of interest in the study of turbine cooling cases.


Template-Based Hexahedral Mesh Generation for Turbine Cooling Geometries

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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