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