An isoparametric approach to high-order curvilinear boundary-layer meshing

This is the final version of the article. Available from Elsevier via the DOI in this record.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.This work was partly supported by EU Grant No. 265780 as part of the EU FP7 project “IDIHOM: Industrialization of High-Order Methods — A Top-Down Approach”. We would like to thank Dr. Tobias Leicht of DLR for asking a very pertinent question concerning the validity of the generated high-order mesh that we believe to have answered in this article. We also thank Jean-Eloi Lombard for his assistance in generating the mesh for Fig. 15

Optimising the performance of the spectral/hp element method with collective linear algebra operations

This is the final version of the article. Available from Elsevier via the DOI in this record.As computing hardware evolves, increasing core counts mean that memory bandwidth is becoming the deciding factor in attaining peak performance of numerical methods. High-order finite element methods, such as those implemented in the spectral/hp framework Nektar++, are particularly well-suited to this environment. Unlike low-order methods that typically utilise sparse storage, matrices representing high-order operators have greater density and richer structure. In this paper, we show how these qualities can be exploited to increase runtime performance on nodes that comprise a typical high-performance computing system, by amalgamating the action of key operators on multiple elements into a single, memory-efficient block. We investigate different strategies for achieving optimal performance across a range of polynomial orders and element types. As these strategies all depend on external factors such as BLAS implementation and the geometry of interest, we present a technique for automatically selecting the most efficient strategy at runtime.We thank D. Ekelschot and M. Turner for their assistance in generating the mesh and parameters for the simulation of Section 6. We also thank F. Witherden for initial discussions motivating this study. This work was funded in part by support from the libHPC II EPSRC project under grant EP/K038788/1. DM additionally acknowledges support under the Laminar Flow Control Centre funded by Airbus/EADS and EPSRC under grant EP/I037946. SJS acknowledges Royal Academy of Engineering support under their research chair scheme. We thank the Imperial College High Performance Computing Service for computing time used to calculate the results seen in Section 6. We additionally acknowledge access to ARCHER with support from the UK Turbulence Consortium under EPSRC grant EP/L000261/1

A Thermo-elastic Analogy for High-order Curvilinear Meshing with Control of Mesh Validity and Quality

This is the final version of the article. Available from Elsevier via the DOI in this record.In recent years, techniques for the generation of high-order curvilinear mesh have frequently adopted mesh deformation procedures to project the curvature of the surface onto the mesh, thereby introducing curvature into the interior of the domain and lessening the occurrence of self-intersecting elements. In this article, we propose an extension of this approach whereby thermal stress terms are incorporated into the state equation to provide control on the validity and quality of the mesh, thereby adding an extra degree of robustness which is lacking in current approaches

Dealiasing techniques for high-order spectral element methods on regular and irregular grids

This is the final version of the article. Available from Elsevier via the DOI in this record.High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challenging geometries and a wide range of physical scales, typically due to high Reynolds numbers, need to be taken into account. One source of instability is aliasing effects which arise from the nonlinearity of the underlying problem. In this work we detail two dealiasing strategies based on the concept of consistent integration. The first uses a localised approach, which is useful when the nonlinearities only arise in parts of the problem. The second is based on the more traditional approach of using a higher quadrature. The main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods, thereby reducing aliasing-driven instabilities. We demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations, where, in the latter, both volumetric and interface approximations must be considered. We show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations.This work was supported by the Laminar Flow Control Centre funded by Airbus/EADS and EPSRC under grant EP/I037946. We thank Dr. Colin Cotter for helpful discussions and Jean-Eloi Lombard for his assistance in the generation of results and figures for the NACA 0012 simulation. PV acknowledges the Engineering and Physical Sciences Research Council for their support via an Early Career Fellowship (EP/K027379/1). SJS additionally acknowledges Royal Academy of Engineering support under their research chair scheme. Data supporting this publication can be obtained on request from [email protected]

Automatic generation of 3D unstructured high-order curvilinear meshes

This is the final version of the article. Available from the publisher via the DOI in this record.The generation of suitable, good quality high-order meshes is a significant obstacle in the academic and industrial uptake of high-order CFD methods. These methods have a number of favourable characteristics such as low dispersion and dissipation and higher levels of numerical accuracy than their low-order counterparts, however the methods are highly susceptible to inaccuracies caused by low quality meshes. These meshes require significant curvature to accuratly describe the geometric surfaces, which presents a number of difficult challenges in their generation. As yet, research into the field has produced a number of interesting technologies that go some way towards achieving this goal, but are yet to provide a complete system that can systematically produce curved high-order meshes for arbitrary geometries for CFD analysis. This paper presents our efforts in that direction and introduces an open-source high-order mesh generator, NekMesh, which has been created to bring high-order meshing technologies into one coherent pipeline which aims to produce 3D high-order curvilinear meshes from CAD geometries in a robust and systematic way

A framework for the generation of high-order curvilinear hybrid meshes for CFD simulations

We present a pipeline of state-of-the-art techniques for the generation of high-order meshes that contain highly stretched elements in viscous boundary layers, and are suitable for flow simulations at high Reynolds numbers. The pipeline uses CADfix to generate a medial object based decomposition of the domain, which wraps the wall boundaries with prismatic partitions. The use of medial object allows the prism height to be larger than is generally possible with advancing layer techniques. CADfix subsequently generates a hybrid straight-sided (or linear) mesh. A high-order mesh is then generated a posteriori using NekMesh, a high-order mesh generator within the Nektar++ framework. During the high-order mesh generation process, the CAD definition of the domain is interrogated; we describe the process for integrating the CADfix API as an alternative backend geometry engine for NekMesh, and discuss some of the implementation issues encountered. Finally, we illustrate the methodology using three geometries of increasing complexity: a wing tip, a simplified landing gear and an aircraft in cruise configuration

Implicit large-eddy simulation of a wingtip vortex

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordIn this article, recent developments in numerical methods for performing a large-eddy simulation of the formation and evolution of a wingtip vortex are presented. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, makes these types of test cases particularly challenging to investigate numerically. First, an overview is given of the spectral vanishing viscosity/implicit large-eddy simulation solver that is used to perform the simulations, and techniques are highlighted that have been adopted to solve various numerical issues that arise when studying such cases. To demonstrate the method's viability, results are presented from numerical simulations of flow over a NACA 0012 profile wingtip at R ec = 1.2 × 10 6 and they are compared against experimental data, which is to date the highest Reynolds number achieved for a large-eddy simulation that has been correlated with experiments for this test case. The model in this paper correlates favorably with experiment, both for the characteristic jetting in the primary vortex and pressure distribution on the wing surface. The proposed method is of general interest for the modeling of transitioning vortex-dominated flows over complex geometries.The authors acknowledge support from the United Kingdom Turbulence Consortium (UKTC) under grant EP/L000261/1 as well as from the Engineering and Physical Sciences Research Council (EPSRC) for access to ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). DM acknowledges supported by the Laminar Flow Control Centre funded by Airbus/EADS and EPSRC under grant EP/I037946. SJS additionally acknowledges Royal Academy of Engineering support under their research chair scheme. We also acknowledge the support from the Imperial College London High Performance Computing facilities