High‐order CFD methods: current status and perspective

Abstract

SUMMARYAfter several years of planning, the 1st International Workshop on High‐Order CFD Methods was successfully held in Nashville, Tennessee, on January 7–8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astronautics, the Air Force Office of Scientific Research, and the German Aerospace Center provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are described. Pacing items requiring further effort are presented. Copyright © 2013 John Wiley & Sons, Ltd.

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…Various authors have used high-order discontinuous methods on the TGV test case with excellent results, including classical DG [5,36,37], DGSEM [9,29] and a preliminary study by Bull and Jameson using the FR-SD scheme [41]. Wang gives a review of the current status of high-order methods for several problems including the TGV [1]. In this paper we use the TGV case to test the ability of various FR schemes to accurately represent the turbulent spectrum and examine the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 F o r P e e r R e v i e w nonlinear stability of these schemes at varying orders of approximation.…”

“…It can be estimated by the difference between 1 and 2 and will be nonzero for any method which is not kinetic-energy-preserving [1,37]. This is a useful error measure in that it is independent of the reference solution and could be used in more complex flows [1].…”

“…One of the optimized FR schemes (the OFR scheme) is shown to have greater spectral accuracy than any of the others tested, motivating its future usage for high-order, high-fidelity CFD. The well-established CFD techniques of second-order numerical schemes and Reynolds-Averaged Navier Stokes (RANS) turbulence models are capable of predicting steady attached flows at cruise conditions, but they are incapable of predicting conditions at the fringes of the flight envelope which are often characterized by turbulent separated flows [1]. Many other aerodynamic problems of central importance also feature complex turbulent flows, including combustion, acoustic noise prediction and the design of hypersonic vehicles.…”

Optimization of a regularized distortion measure to generate curved high‐order unstructured tetrahedral meshes

“…It is well known that for problems with smooth solutions, the approximation obtained with high-order methods converges exponentially with the order of the approximating polynomial. More generally, high-order methods have been shown to deliver higher accuracy with a lower computational cost than low-order methods in many practical applications [6,7,8,9,10,11,12,13,14,15]. In addition, the accurate approximation of the domain geometry eliminates the spurious effects in the solution that can arise from a piecewise linear representation of the curved domain boundaries [16,17,18,19,20].…”

A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

“…One of the main features that attracted this attention is the ability of unstructured high-order methods to converge exponentially with the order of the approximating polynomial when the exact solution of the PDE is smooth and without singularities [1,6]. Accordingly, it has been possible to show that high-order methods provide higher accuracy with lower computational cost than low-order methods in a wide range of applications [7,8,9,10,11,12,13,14,15,16].…”