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The Connector, the newsletter for CFD Mesh Generation from Pointwise

July / August 2011

T-Rex Hybrid Meshing in Pointwise

3D anisotropic tetrahedral extrusion (otherwise known as T-Rex) will be released soon, but the 2D surface mesh formulation of T-Rex already is available for you to use in Pointwise V16.04. You might think of T-Rex surface meshes as just symmetry boundaries for a T-Rex volume mesh, but they also can be used for 2D computational fluid dynamics (CFD) simulations and other purposes.

T-Rex is our most advanced and most automated hybrid mesh generation method. It was introduced in Gridgen in early 2007 and has been developed and enhanced continuously since. T-Rex generates hybrid meshes that resolve boundary layers, wakes, and other phenomena in viscous flows by extruding layers of high-quality, high aspect ratio tetrahedra that can be post-processed into stacks of prisms. The algorithm includes tools for optimizing cell quality and avoiding collisions of adjacent layers of cells. T-Rex has been used for many applications, including the innovative UAV from Propulsive Wing shown in Figure 1 and the sedan in Figure 2.

T-Rex volume mesh generated in Gridgen for a UAV from Propulsive Wing

Figure 1: This hybrid mesh generated by Pointwise's T-Rex technique resolves details from the external boundary layer to the region around the fan embedded in the wing of Propulsive Wing's UAV. +

T-Rex volume mesh around an automotive sedan

Figure 2: A cut through a T-Rex mesh around a generic automotive sedan geometry +

T-Rex Surface Meshing in Pointwise

As an example of what can be done with 2D T-Rex, consider the hybrid mesh shown in Figures 3, 4 and 5, a symmetry plane cut through a CAD model of an F-16 aircraft.

T-Rex mesh on the symmetry plane around an F-16 aircraft

Figure 3: T-Rex mesh on the centerline of an F-16 fighter jet. The geometry in this case is a NURBS model from an IGES file. +

Symmetry plane T-Rex mesh around the nozzle on an F-16 aircraft

Figure 4: Close-up of T-Rex mesh in the nozzle region of the F-16 centerline +

Symmetry plane T-Rex mesh around the inlet on an F-16 aircraft

Figure 5: Close-up of T-Rex mesh in inlet region along F-16 centerline +

Overview of the T-Rex Algorithm

Let's look at how T-Rex works before delving further into what you can do with it.

  1. The algorithm starts with a distribution of points around the perimeter of the surface mesh. This is the initial extrusion front.
  2. The boundary points are extruded (or advanced) one at a time into the surface mesh. The extrusion is directed normal to the boundary for a user-specified step size. This creates a candidate location for the extruded point.
  3. The candidate point then is checked to ensure that it will not collide with any other extrusion front.
  4. If the candidate point passes the collision test, it is connected to the previous front, forming a triangular cell. On the other hand, if the test fails, the candidate point is rejected and extrusion stops locally for that point.
  5. Extrusion continues, point by point, with the step size increasing at a user-specified rate, until the extruded triangle is isotropic, the collision test fails, or Max Layers is reached. This is the final front.
  6. The region enclosed by the final front is filled by a Delaunay-based, isotropic mesher.

Using T-Rex for Surface Meshing

Unstructured surface meshes are initialized automatically with a Delaunay technique that generates isotropic cells throughout the entire surface. You then use the T-Rex command in the Grid menu (Figure 6) to set the T-Rex attributes and then re-initialize.

T-Rex is found in Pointwise's Grid menu

Figure 6: The T-Rex technique is applied to unstructured meshes via the Grid menu.

As you can see in the T-Rex menu (Figure 7), there are relatively few attributes to set for T-Rex. The two most important are the maximum number of layers to extrude (Max. Layers) and the desired number of full layers (Full Layers). For Max. Layers, keep in mind that T-Rex will keep extruding triangles until they become isotropic. After that, the extrusion stops and a Delaunay-based mesher takes over. Therefore, Max. Layers is a way to stop the extrusion before isotropy is reached.

Controls for Pointwise's T-Rex

Figure 7: The main attributes for the T-Rex algorithm

Full Layers is a way for you to ensure that T-Rex succeeds across the entire front for a complete (or full) layer of extruded triangles. For example, your flow solver may require a certain number of full layers in order to accurately capture the boundary layer. The only thing preventing a full layer from being formed would be a collision with another front.

Setting boundary conditions for Pointwise's T-Rex

Figure 8: T-Rex wall spacing is set in the Boundary Conditions tab.

Boundary conditions (BCs) are the only other data you need to set for T-Rex. You define the edges from which the mesh should be extruded by setting them to the BC Type "Wall" as shown in Figure 8. Wall conditions also are where you set the size of the first extrusion step. By default, all boundaries are "Off," meaning that isotropic meshing will be applied there.

There are two other T-Rex specific BCs. "Match" indicates the extrusion should match the distribution of points along that edge. "Adjacent Grid" indicates points will be extruded off this edge and the initial step size automatically will be derived from an adjacent mesh.

With BCs and Max Layers set, you simply initialize the mesh and let T-Rex do the rest. A typical result is shown in Figure 9, a mesh on a slice through a blood vessel with an aneurysm. Figure 9 also illustrates that Pointwise's other meshing attributes - such as decay factor and Min. and Max. Edge Length - still apply when using T-Rex, except they only apply to the isotropic portion of the mesh.

T-Rex mesh on a cut through a blood vessel with an aneurysm

Figure 9: T-Rex mesh on a slice through a blood vessel with an aneurysm. The geometry for this case is a faceted model from an STL file. +

2D T-Rex Works on Curved Surfaces Too

We've been referring to Pointwise's T-Rex implementation as 2D, but that doesn't mean it's restricted to planar shapes. You can apply T-Rex to any surface mesh, including those constrained to a CAD surface, such the mixer blade in Figure 10. In this case, T-Rex gives you nice high aspect ratio cells to resolve the leading edge curvature before transitioning to an isotropic mesh.

T-Rex mesh on the leading edge of a mixer blade

Figure 10: T-Rex can be applied to 3D curved surfaces to resolve features like the leading edge of this mixer blade. +

T-Rex for Complex Geometry

The T-Rex technique is very good at resolving a complex geometry without too much intervention by the user. Earlier in this article the basic algorithm was described as including a test for colliding fronts. The goal of this test is to stop the extrusion such that a large enough gap between fronts is left for smooth filling by the Delaunay mesher. A classic 2D test of this capability is a multi-element airfoil, as shown in Figure 11. You can see how the mesh smoothly blends from the extruded regions to the isotropic mesh between the slat and main element and the main element and the flap, while the extrusion away from the collision region continues further out.

T-Rex mesh around a multi-element airfoil

Figure 11: By automatically detecting collisions, T-Rex ensures a smooth transition from the anisotropic to isotropic mesh around complex geometry. +

Summary

If you're doing 2D viscous CFD or using Pointwise to prepare surface meshes for Gridgen, T-Rex is a tool you need to try. T-Rex automatically gives you a highly clustered mesh with high-quality cells (triangles with included right angles) and the ability to smoothly handle complex geometry. And keep in mind that soon you'll have the full volume mesh formulation of T-Rex in Pointwise to use for all your hybrid meshing needs.

For more information on T-Rex, including a technical paper with all the details, go to www.pointwise.com/T-Rex.

For an evaluation license of Pointwise, go to www.pointwise.com/free.


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