Mecanismos de defensa en las plantas

The Common Research Model (CRM) is a conventional configuration designed by NASA [92] to produce a database of experimental results for CFD validation. The wing/body only configuration has been chosen of the five available. The original definition of the CAD geometry in STEP format can be found in the repository [17]. Unlike the previous geometries, the first step of the process was to use CADfix

(a) (b)

Figure 5.9. Boeing RLG high-order surface mesh: (a) curved edges; (b) incorporating mesh nodes (P = 4).

(a) (b)

Figure 5.10. Enlargement of boundary layer mesh near the shoulder of the Boeing RLG wheel: (a) straight-sided mesh; (b) high-order mesh.

to thoroughly clean the CAD geometry and fix a number of inconsistencies and severe distortions present to ensure it was useable for both the generation of the medial object and the high-order mesh. The customary medial object interface at the wing-fuselage junction and the block partitioning near the aircraft are depicted in figures 5.11(a) and 5.11(b), respectively. Figure 5.12 aims at providing a better illustration of the blocks in the near-field region through a wireframe representing the edges of the partitions in that region.

The initial coarse, single-layer, mesh of the near-field partition consisted of 20,000 triangular prisms. Figure 5.13 shows the curved edges of the CRM high-order surface mesh. A more detailed view of the CRM high-order surface mesh, including interior points, is given in figure 5.14 which includes close-ups near leading edge at the wing-fuselage junction, and at the wing tip leading edge.

Finally, the coarse boundary-layer mesh is split into 10 layers. Figure 5.15 shows enlargements of that mesh in the regions adjacent to the wing-fuselage junction, and

(a) (b)

Figure 5.11. NASA CRM medial object: (a) interface of the medial object at the wing-fuselage junction, and (b) partitions in the near-field region.

(a) (b)

Figure 5.12. A wireframe representing the edges of the partitions in the near-field region: (a) global view of blocks around wing and fuselage, and (b) close-up near the wing.

Figure 5.13. CRM high-order surface mesh overview. Only the curved edges of the mesh are shown.

(a) (b)

Figure 5.14. CRM high-order surface mesh enlargement near: (a) leading edge at the wing-fuselage junction, and (b) the wing tip leading edge.

(a) (b)

Figure 5.15. Close-up of the CRM boundary layer mesh in the regions adjacent to: (a) the wing-fuselage junction, and (b) the wing tip.

6

High-order CFD methods in

industrial applications

The goal of transferring high-order CFD methods from academic to industrial, pro- duction impacting, applications is as yet unrealised. Using high-order CFD as a production tool for industry has a number of hurdles to overcome, chief among which are: robustness of the numerical methods, computational cost of the simula- tions and reliable generation of suitable curved meshes on complex geometries. This chapter will focus on the last point, with a focus to achieving practical results for industrial applications.

The robustness found in commercial linear mesh generators is due to a number of factors. Primarily the system will have a series of failsafe options which allow the mesh generator to recover and continue in the case of a critical error. These failsafes are developed over time by looking at a case, seeing what works and what does not and finding a solution for the problems at hand before moving onto the next test case. This philosophy has allowed a number of commercial mesh generators achieve significant levels of robustness over a range of very complex cases.

This kind of methodology has, as yet, not been applied to high-order mesh gener- ators. Each example in the literature aims to achieve complete geometric accuracy without compromise. This chapter explores the idea of relaxing strident criteria on the high-order mesh with the goal of producing meshes on complex geometries which would otherwise be truly impossible. The study focuses around the idea of obtaining high-order CFD results on complex geometries with the goal of achieving practical outcomes. That is, for most aerodynamic external flows, studying the lift, drag and vortex behaviour of the flow. The goal was to produce, by any means, meshes that obtain results without compromising the outcomes.

been implemented within NekMesh. While practical and applicable to wide range interesting applications, the linear mesh generation capabilities of NekMesh are far from sufficient to reliably mesh the types of geometries that will be encountered in complex industrial cases. The desire is to merge the robust meshing capabilities of an industry standard linear mesh generator, of which there are too many to list, with high-order meshing methods such as those available in NekMesh. However this is no simple task. This is demonstrated by a small number of commercial mesh generators which have attempted to add high-order capabilities to their products with somewhat limited success, such as Pointwise [67] and Centaur [14] to name a few.

It would, on the face of it, seem possible and even trivial, to take these already robust tools and simply extend them to achieve high-order meshes. In theory, all the positive properties of the linear mesher, such as the robustness and CAD capability, would be inherited, but this is far from the case.

This chapter focuses around the production of meshes for three geometries which represent the design progress of a high aerodynamic performance road car. During this study the result from the previous geometry actually influenced the design of the next. Three distinct meshing pipelines were created in the process of developing mesh generation strategies for these geometries, each representing a evolution of the last. By the end of the study, producing the high-order meshes for the geometries from the linear meshes took only minutes and required little to no interaction, or CAD modification, from the user.

6.1

Methodologies

One of the most significant factors contributing to the robustness of commercial linear mesh generators is that prior to making the mesh the CAD surface will be linearised. The surface is triangulated with no consideration for quality but simply CAD accuracy. The surface triangulation is usually produced by repeatedly sub- dividing the surface until the deviation from the true surface of the edges of the triangles is less than some tolerance. The final mesh is then built upon this lin- earised CAD representation. The primary advantage is that any poor quality CAD features can be paved over, removed or altered easily within the triangulation. The disadvantage is the reduced CAD accuracy of the resulting mesh. This can be offset by increasing the resolution of the linearised CAD surface. However for finite volume CFD methods, where these meshes are used the most, the loss in CAD accuracy

does not have a significant impact on the final flow result. Most critically, when considering high-order meshing, this means that the surface mesh vertices cannot be located in the parameter spaces of the surfaces without using some form of re- construction of this information, which can introduce errors and robustness issues. This makes the idea of curving the surface elements from a generically made linear mesh very challenging.

Two strategies have been developed which provide the relatively simple creation of high-order meshes for extremely complex cases. The first is based on being able to know the parametric information associated with the linear surface mesh, hence high-order curving of the surface is a relatively easy task and shall be referred to as analytic curving. The second is on being able to reconstruct the CAD information or project the linear mesh onto the CAD surfaces. The approach has significant issues with speed and robustness but offers an alternative method to curving the surface, which will be referred to as projection curving.