دانلود رایگان مقاله رویکرد ایزوپارامتریک برای مش بندی لایه مرزی منحنی الخط

Abstract

The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, particularly for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow. In this paper, we present a conceptually simple but very effective and modular method to address this issue. We propose an isoparametric approach, whereby a mesh containing a valid coarse discretization comprising of high-order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary-layer mesh. The validity of the prismatic mesh provides a suitable mapping that allows one to obtain very fine mesh resolutions across the thickness of the boundary layer. We describe the method in detail for a high-order approximation using modal basis functions, discuss the requirements for the splitting method to produce valid prismatic and tetrahedral meshes and provide a sufficient criterion of validity in both cases. By considering two complex aeronautical configurations, we demonstrate how highly stretched meshes with sufficient resolution within the laminar sublayer can be generated to enable the simulation of flows with Reynolds numbers of 106 and above.

4. Conclusions

We have presented a technique for generating highly stretched high-order boundary-layer meshes as required by current CFD solvers. The proposed technique is very effective, and modular in the sense that it can readily be combined with a number of existing coarse grid generation techniques in order to produce a mesh which is well-suited to boundary layer flows. Starting from a valid coarse prismatic boundary-layer mesh, our isoparametric approach permits the generation of a sequence of meshes with increased resolution with very little additional cost. This should prove valuable for mesh convergence studies at high Reynolds numbers. We have established requirements of validity for modal elemental shape functions, but the same arguments are also applicable to guarantee the validity of the mesh when using nodal shape functions. The main limitation of the technique, as presented here, is the requirement that the subdivision of the prismatic mesh should be accomplished without affecting the rest of the mesh. Although extending the method to other cases is not a difficult technical issue, it will require the use of transition elements such as pyramids. Whilst this case is beyond the scope of this article, in [28] we give a more detailed description as to how one may split different element types. This goes some way towards solving this problem, and may offer the chance to extend this technique with new functionality, such as introducing variable numbers of boundary layer elements around the profile of an aerofoil.