High-order curvilinear hybrid mesh generation for CFD simulations

Abstract

We describe a semi-structured method for the generation of high-order hybrid meshes suited for the simulation of high Reynolds number flows. This is achieved through the use of highly stretched elements in the viscous boundary layers near the wall surfaces. CADfix is used to first repair any possible defects in the CAD geometry and then generate a medial object based decomposition of the domain that wraps the wall boundaries with partitions suitable for the generation of either prismatic or hexahedral elements. The latter is a novel distinctive feature of the method that permits to obtain well-shaped hexahedral meshes at corners or junctions in the boundary layer. The medial object approach allows greater control on the "thickness" of the boundary-layer mesh than is generally achievable with advancing layer techniques. CADfix subsequently generates a hybrid straight-sided mesh of prismatic and hexahedral elements in the near-field region modelling the boundary layer, and tetrahedral elements in the far-field region covering the rest of the domain. The mesh in the near-field region provides a framework that facilitates the generation, via an isoparametric technique, of layers of highly stretched elements with a distribution of points in the direction normal to the wall tailored to efficiently and accurately capture the flow in the boundary layer. The final step is the generation of a high-order mesh using NekMesh, a high-order mesh generator within the Nektar++ framework. NekMesh uses the CADfix API as a geometry engine that handles all the geometrical queries to the CAD geometry required during the high-order mesh generation process. We will describe in some detail the methodology using a simple geometry, a NACA wing tip, for illustrative purposes. Finally, we will present two examples of application to reasonably complex geometries proposed by NASA as CFD validation cases: the Common Research Model and the Rotor 67.

Combining High-Order Metric Interpolation and Geometry Implicitization for Curved r-Adaption

“…In particular, note that these derivatives are trivial since the representation of each hyperplane entity is linear. Then, we differentiate the r-conjunction between the hyperplane representations γ CH(Γ) , see Equations ( 17) and (18). Finally, we differentiate the normalization of the convex-hull representation γCH(Γ) , see Equations (B.1) and (B.2).…”

“…To efficiently match curved solution features, many practitioners have recently started to exploit curved high-order meshes. These meshes can be stretched and aligned in a pointwise varying fashion through anisotropic procedures [12], geodesic approaches for curved edges [13,14], shock-tracking methods [15,16,17], and deformation analogies [18,19]. Alternatively, the curved r-adaption can be driven, as for straight-edged elements [4,5], by distortion measures.…”

Nektar++: enhancing the capability and application of high-fidelity spectral/$hp$ element methods

“…However, the use of a lightweight wrapper means that other commerical CAD packages can be interfaced to NekMesh if available. To this end, we have implemented a second CAD interface to the commerical CFI CAD engine, which provides a highly robust interface and is described further in references [66,67,68].…”

Naturally curved quadrilateral mesh generation using an adaptive spectral element solver

“…Such meshes are typically too coarse for spectral element analysis; it is often necessary to split them further. We take advantage of an isoparametric splitting approach described in [22] to refine strings of blocks, extended in references [23,24] for bidirectional splitting. The method leverages the mapping between physical and reference space coordinates by splitting elements in reference space to obtain valid high order elements in physical space.…”