HomeIndustriesProductsServicesEventsAbout Us

Customer Login

judi online . bestdissertation.com reviews . superiorpaper . write my term paper . online essay writing service review
Home arrow CFD-GEOM User Tips arrow Gridding a Hemisphere in a Box with a Structured Butterfly Grid
Gridding a Hemisphere in a Box with a Structured Butterfly Grid Print E-mail

Since spheres, hemispheroids, ellipsoids, and related geometries are very common in a great variety of problems, some techniques have been developed to mesh this class of geometries with structured grid systems. Just as a butterfly grid can be used to grid a circular face, here we will demonstrate how this approach is used to create a 3D butterfly grid for meshing a hemisphere.

Please recall the difference between an H-grid, an O-grid, and a Butterfly-grid. An H-grid can be used to topologically deform a single square grid to a circular shape. An O-grid represents the circular shape by radial and circumfrential grid lines. A butterfly grid system requires multiple blocks but generally has the best grid quality in terms of orthogonality and mesh density.



1) The first step is to create hemispherical surface by revolving an arc by 180 degrees as shown below.

2. Next a point is placed at the hemisphere origin (0,0,0) which is extruded four times to get lines which protrude past the hemisphere. This is done in the vector mode using the following vectors: (1,1,1), (-1,1,1), (1,1,-1), (-1,1,-1).

3. The lines are then intersected with the hemispherical surface to produce four points.

4. These intersection points are used to make a square.

5. The construction lines are split at the corners of the square and then the lower portions are removed since they will not be needed anymore.

6. The arcs that make up the base of the hemisphere need to be split at the corners of the square. Use the "split curve at a point" tool to perform this operation.

7. Draw lines between the corners of the square and the ends of the arcs.


8. Make the hemispherical surface visible and project the lines created in step 7 and the square's lines onto the hemisphere.


9. Showing just points, lines, and curves we now have the following geometry.

10. At this point we could make an H-type grid for the hemisphere, but better grid quality can be obtained by adding elements to make a butterfly-type grid system. This starts by createing an inner box and connect its corners to the arc ends.

11. Make the inner "cube" region's edges, faces, and block by your favorite method (four sided faces and six sided block, or create faces and blocks using the extrusion methods for fewer mouse clicks).

12. Make the outer edges, faces, blocks to fill the region between the cube and the hemisphere.

13. As can be seen in the image above, the structured faces do not conform to the hemisphere surface due to the nature of the trans-finite-interpolation scheme used to construct the face grids. We can remedy that problem by projecting the structured face grids to the hemisphere surface as shown below.


14. The sphere grid is completed. If needed this grid system can be extended to include the "box" around the hemisphere. Start by adding some construction lines.


15. Finish by making remaining edges, faces, and blocks.

As you can see, it is not too difficult to make these types of grid systems and of course the hemisphere can be mirrored about the symmetry plane to obtain a full sphere model!

Click on hemisphere_box.GGD.zip to download the CFD-GEOM file for this model. You will need CFD-GEOM V2003.0.2.2 or greater to read this file. The latest version of CFD-GEOM can always be downloaded from the customer support website.

Matthew Slaby
Applications Engineer
CFDRC Customer Support



Face Projection on a NURBS Surface in CFD-GEOM

CFD-GEOM provides a face projection tool that enables you to modify grid points such that they adhere to prescribed geometric surfaces. This option is very useful for cases where the underlying surface has curvature in two directions.

Geometric Precision and Filtering in CFD-GEOM

In many cases, CAD models can be dirty and thus do not import well into CFD-GEOM.  Repairing these geometries can often take considerable time and effort.  Many times, duplicate points, lines, and surfaces are created when importing CAD geometries.

Using Interior Sources for Mesh Control in CFD-GEOM

To produce accurate simulation results, it is important to provide adequate mesh resolution in the areas of the model where steep solution gradients are expected. In CFD-GEOM, there are a number of tools available to achieve mesh refinement. One such tool for refining unstructured grids is the interior source option.

How to create Pyramid cells on structured-unstructured domain interfaces in CFD-GEOM

CFD-GEOM can be used to construct a variety of cell shapes: quadrilaterals (2D) and hexahedrals (3D) for structured meshes; triangles (2D) as well as tetrahedrals and polyhedral/honeycomb (3D) for unstructured meshes; prisms and pyramids (3D) for semi-structured meshes.  

Exporting STL Files From CFD-GEOM

A CFD simulation process starts from an accurate representation of the boundaries that usually originates directly from CAD systems. STL and IGES are two of the most common output formats used as a starting point for mesh generation. STL (StereoLithography) files represent 3D surface geometries using a triangular mesh allowing unambiguous transfer of files from one system to another.

© 2015 ESI Group CFD Portal