Keywords: geometry, mesh correction, smoothing, topology-based modelling, Open Cascade, Mesquite.

In many areas, it is crucial to get the mesh to properly follow the geometry. For instance, small variations in node position in a fluid flow simulation may provide chaotic result such as that of Rayleigh-Taylor instabilities. Conceptually, the easiest way to ensure the right level of accuracy is to perform the meshing with tight integration to the CAD geometry. Unfortunately our requirements drive us to another solution where CAD geometry generation and mesh generation are performed by separated tools. So we suggest a coupled approach between our own CAD system and the ICEM-CFD Hexa mesher [1] to produce high quality meshes while maintaining geometry accuracy. Our process is as follows: the CAD model is created in our CAD tool then exported to ICEM-CFD Hexa; the mesh is generated in ICEM-CFD Hexa; finally the mesh is brought back into our CAD tool where mesh nodes are projected onto the geometry.

The numerical schemes that we use to simulate unsteady compressible flows require hexahedral mesh elements. Moreover our applications require a high level of accuracy. In some cases, the distance between mesh nodes and their geometric surfaces must be exact according to the floating point representation. The range of CAD-meshing tools we have studied does not guarantee a sufficient level of accuracy. Besides, the users of our software want a simple dedicated CAD-meshing tool that fits to their needs and not a complete and complex tool. Thus we are designing our own tools. As writing a complete hexahedral CAD-meshing tool is a huge task, we started by focusing on the accuracy problem. To achieve this goal, we suggest a loosely coupled approach where CAD generation is performed by our own CAD system and the mesh is generated by ICEM-CFD Hexa.

Oceane is our own CAD-meshing tool built on open-source components: Open Cascade [2] (geometric kernel), VTK (visualization), Qt (user interface), Python (scripting) and Mesquite [3] (smoothing). Oceane users can build 3D geometric objects from 2D ones by applying revolution or sweeping. They can also generate primitive 3D geometric objects, perform Boolean operations, exchange data with commercial software (IGES/STEP formats), view and analyse meshes and so on.

Here we describe our CAD-meshing process. First, the geometry is generated inside Oceane. This is the definition for the reference geometry. The geometry is then exported to ICEM CFD Hexa using either IGES or STEP format. We generate a hexahedral mesh with ICEM CFD Hexa. This mesh is then imported into our CAD system to check it against the reference geometry. To do that, we associate each mesh surface with one or more geometric surfaces. We select the mesh surfaces that we want to correct and Oceane performs the projection. A smoothing algorithm is then applied to spread the mesh surfaces modifications onto the complete surface mesh. Finally, the volume mesh is untangled and smoothed.

The projection of mesh nodes onto geometric surfaces is driven by two main reasons. First, to work with a commercial tool like ICEM-CFD Hexa, we have to translate a geometric model designed in Oceane into a standard exchange format (IGES or STEP) readable by another tool. The geometry is so translated twice before getting a mesh. As not all software read and write IGES/STEP formats consistently, the loss of accuracy may be huge. Besides, even in an integrated CAD-meshing tool, the projection of the mesh onto the geometry must be done carefully.

The atomic operation of mesh correction performed by Oceane is the orthogonal projection of a mesh node onto geometry. In our process, a mesh node may belong to one or more mesh surfaces, and each mesh surface may be associated to one or more geometric surfaces. So to avoid side effects, we take particular configurations into account. For instance, if a node belongs to only one mesh surface, we project the mesh node onto its corresponding geometric surfaces and we take the nearest projecting point. If a node belongs to two mesh surfaces, it must be projected onto a geometric curve or a set of geometric curves. Several particular cases are identified and treated.

The first results of this approach allow us to get a satisfying level of accuracy. The use of both Open Cascade and Mesquite libraries has permitted us to smooth the mesh surfaces and to project them onto geometric surfaces. Moreover, this projecting algorithm could be used in the hexahedral mesh algorithms that we want to integrate into Oceane.

1

"ICEM CFD Hexa", Ansys Inc., http://www.icemcfd.com/hexa.

2

Open Cascade Technology, Open Cascade S.A. Comp., http://www.open-cascade.org.

3

M. Brewer, L. Diachin, P. Knupp, T. Leurent, D. Melander, "The Mesquite Mesh Quality Improvement Toolkit", proceedings of the 12th International Meshing Roundtable, 239-250, 2003.

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