Progress in high-order methods for industrial large eddy simulation

WANG Zhijian

doi:10.7638/kqdlxxb-2020.0174

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Progress in high-order methods for industrial large eddy simulation

更新时间：2026-05-28

- Progress in high-order methods for industrial large eddy simulation
- Vol. 39, Issue 1, Pages: 111-124(2021)
- 作者机构：
  
  堪萨斯大学航空航天工程系,66045
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2020.0174
  CLC： V211.3;V224
- Published：2021
- 稿件说明：
移动端阅览
王志坚. 基于高阶方法的工业大涡模拟进展[J]. 空气动力学学报, 2021, 39(1): 111-124.

WANG Zhijian. Progress in high-order methods for industrial large eddy simulation[J]. 2021, 39(1): 111-124.
王志坚. 基于高阶方法的工业大涡模拟进展[J]. 空气动力学学报, 2021, 39(1): 111-124. DOI： 10.7638/kqdlxxb-2020.0174.

WANG Zhijian. Progress in high-order methods for industrial large eddy simulation[J]. 2021, 39(1): 111-124. DOI： 10.7638/kqdlxxb-2020.0174.

摘要

众所周知，在达到相同精度的情况下，用高阶方法进行大涡模拟，速度可以比二阶方法快几个数量级。由于具有这种潜力，将这些高阶方法“工业化”并在实际中应用已经取得了很大的进展。在过去的十年中，在工业界，特别是在涡轮机械中，大涡模拟的使用已显著增加，这可能是因为燃气轮机中的雷诺数不是特别高，并且此类模拟对理解关键流动机理具有很大影响。在本文中，我们回顾过去十年应用高阶方法在大涡模拟方面取得的最新进展，并展望在不久的将来将大涡模拟推入设计过程最有前景的研究领域。

Abstract

It is now well-known that high-order methods can be orders of magnitude faster than 2 order methods to achieve the same accuracy for scale resolving simulations. Because of that potential

much progress has been made in "industrializing" these high-order methods for real world applications. The use of large eddy simulation in industry especially in turbomachinery has seen a significant increase in the past decade

perhaps because of the relatively low to medium Reynolds numbers in gas-turbines and the high-impact of such simulations in understanding key flow physics. In this article

we review recent progress made in enabling LES using high-order methods in the last decade

and identify the most profitable areas of research in the near future to push LES into the design process.

关键词

Keywords

references

SLOTNICK J, KHODADOUST A, ALONSO J, et al. CFD Vision 2030 Study: A path to revolutionary computational aerosciences[R]. NASA/CR-2014-218178.

SMAGORINSKY J. General circulation experiments with the primitive equations. I. The basic experiment[J]. Mon. Weather Rev. 1963, 91(3): 99-164.

CHAPMAN D R. Computational aerodynamics development and outlook[J]. AIAA J, 1979, 17(12): 1293-1313.

CHOI H, MOIN P. Grid-point requirements for large eddy simulation: Chapman's estimates revisited[J]. Physics of Fluids, 2012, 24: 011702.

GOTTLIEB D, ORSZAG S A. Numerical analysis of spectral method: theory and applications[J]. Philadelphia: SIAM, 1977.

KIM J, MOIN P, MOSER R. Turbulence statistics in fully developed channel flow at low Reynolds number[J]. J Fluid Mechanics, 1987, 177: 133-166.

EKATERINARIS J. High-order accurate, low numerical diffusion methods for aerodynamics[J]. Progress in Aerospace Sciences, 2005, 41: 192-300.

WANG Z J. High-order methods on unstructured grids for Navier-Stokes equations[J]. Journal of Progress in Aerospace Sciences, 2007, 43(1): 1-41.

DENG X, MAO M, TU G, et al. High-order and high accurate CFD methods and their applications for complex grid problems. Commun[J]. Comput Phys, 2012, 11: 1081-1102.

WANG Z J, FIDKOWSKI K J, ABGRALL R, et al. High-order CFD methods: current status and perspective[J]. International Journal for Numerical Methods in Fluids, 2013, 72(8): 811-45.

HUYNH H T, WANG Z J, VINCENT P E. High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids[J]. Computers Fluids, 2014, 98: 209-220.

WANG Z J. High-order computational fluid dynamics tools for aircraft design[J]. Philos Trans A Math Phys Eng Sci, 2014, 13, 372(2022): 20130318.

WANG Z J. A perspective on high-order methods in computational fluid dynamics[J]. Science China Physics Mechanics Astronomy, 2016, 59(1): 1-6.

WITHERDEN F D, JAMESON A. Future directions in computational fluid dynamics[R ] . AIAA 2017-3791. https://doi.org/10.2514/6.2017-3791

BECK A D, BOLEMANN T, FLAD D, et al. High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations[J]. Int J Numer. Methods Fluids, 2014, 76(8): 522-548.

CHAPELIER J B, DE LA LLAVE PLATA M, RENAC F, et al. Evaluation of a high-order discontinuous Galerkin method for the DNS of turbulent flows[J]. Computers Fluids, 2014, 95(22): 210-226. https://doi.org/10.1016/j.compfluid.2014.02.015

LU Y, LIU K, DAWES W N. Flow simulation system based on high order space-time extension of flux reconstruction method[C]//53rd AIAA Aerospace Sciences Meeting. AIAA SciTech Forum, (AIAA 2015-0833).

CARTON DE WIART C, HILLEWAERT K, BRICTEUX L, et al. Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method[J]. International J for Numerical Methods in Fluids, 2015, (6). https://doi.org/10.1002/fld.4021

FLAD D, BECK A, MUNZ C D. Simulation of under-resolved turbulent flows by adaptive filtering using the high order discontinuous Galerkin spectral element method[J]. Journal of Computational Physics, 2016, 313(15): 1-12. https://doi.org/10.1016/j.jcp.2015.11.064

FERRER E. An interior penalty stabilized incompressible discontinuous Galerkin-Fourier solver for implicit large eddy simulations[J]. Journal of Computational Physics, 2017, 348(1): 754-775. https://doi.org/10.1016/j.jcp.2017.07.049

LV Y, MA P, IHME M. On under-resolved simulations of compressible turbulence using an entropy-bounded DG method: Solution stabilization, scheme optimization, and benchmark against a finite-volume solver[J]. Computers Fluids, 2016, 161(15): 89-106.

VERMEIRE B C, NADARAJAH S, TUCKER P G. Implicit large eddy simulation using the high-order correction procedure via reconstruction scheme[J]. J Numer Meth Fluids, 2016, 82: 231-260.

VERMEIRE B C, WITHERDEN F D, VINCENT P E. On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools[J]. Journal of Computational Physics, 2017, 334(1): 497-521. https://doi.org/10.1016/j.jcp.2016.12.049

WANG Z J, LI Y, JIA F, et al. Towards industrial large eddy simulation using the FR/CPR method[J]. Computers and Fluids, 2017, 156(12): 579-589.

JIA F, IMS J, WANG Z J, et al. Evaluation of second- and high-order solvers in wall-resolved large-eddy simulation[J]. AIAA Journal, 2019, 57(4): .

SHERWIN S J, PEIRO J. Mesh generation in curvilinear domains using high-order elements[J]. International Journal for Numerical Methods in Engineering, 2000, 53(1): 207-23.

GEUZAINE C, REMACLE J F. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities[J]. International Journal for Numerical Methods in Engineering, 2009, 47(11): 1309-1331.

IMS J, WANG Z J. Automated low-order to high-order mesh conversion[J]. Engineering with Computers, 2019, 35(1): https://doi.org/10.1007/s00366-018-0602-x.

FORTUNATO M, PERSSON P O. High-order unstructured curved mesh generation using the Winslow equations[J]. Journal of Computational Physics, 2016, 307: 1-14.

KARMAN S L, ERWIN J T, GLASBY R S, et al. High-order mesh curving using WCN mesh optimization[C]//46th AIAA Fluid Dynamics Conference, AIAA 2016-3178.

MARCON J, TURNER M, PEIRO J, et al. High-order curvilinear hybrid mesh generation for CFD simulations[R]. AIAA-2018-1403.

TURNER M, PEIRO J, MOXEY D. A variational framework for high-order mesh generation[J]. Procedia Engineering, 2016, 163: 340-352. doi: 10.1016/j.proeng.2016.11.069

YANG H Q, ZHOU X A, HARRIS R E, et al. An open source geometry kernel-based high-order element mesh generation tool[R]. AIAA-2019-1719.

ZHONG Z, MING L, LEI H, et al. High-order curvilinear mesh generation technique based on an improved RBF approach[J]. International Journal for Numerical Methods in Fluids, 2019, 91(3): 97-111. doi: 10.1002/fld.4741

BARTH T J, FREDERICKSON P O. High-order solution of the Euler equations on unstructured grids using quadratic reconstruction[R]. AIAA Paper No. 90-0013, 1990.

WANG Q, REN Y X, PAN J, et al, Compact high order finite volume method on unstructured grids Ⅲ: Variational reconstruction[J]. Journal of Computational Physics, 337: 1-26

BROOKS A N, HUGHES T J. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering, 1982, 32(1-3): 199-259. doi:10.1016/0045-7825(82)90071-8.

COCKBURN B, KARNIADAKIS GE, SHU C W. Discontinuous Galerkin methods. Theory, computation and applications[M]. Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin, 2000.

LIU Y, VINOKUR M, WANG Z J. Discontinuous spectral difference method for conservation laws on unstructured grids[J]. Journal of Computational Physics 2006; 216: 780-801.

HUYNH H T. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods[R]. AIAA Paper 4079, 2007.

WANG Z J, GAO H. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids[J]. Journal of Computational Physics, 2009, 228(21): 8161-8186.

DUMBSER M, KAISER M, TORO E F. An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes V[J]. Local time stepping and p-adaptivity. Geophysical Journal International, 2007, 171(23): 695-717.

ZHANG L, LIU W, HE L, et al. A class of hybrid DG/FV methods for conservation laws Ⅱ: Two-dimensional cases[J]. Journal of Computational Physics, 2012. 231(4): 1104-1120.

HAGA T, GAO H, WANG Z J. A high-order unifying discontinuous formulation for the Navier-Stokes equations on 3D mixed grids[J]. Math Model Nat Phenom, 2011, 6(3): 28-56.

JOURDAN E, WANG Z J. Efficient Implementation of the FR/CPR Method on GPU Clusters for Industrial Large Eddy Simulation[R]. AIAA-2020-3031.

PERSSON P O, PERAIRE J. Sub-cell shock capturing for discontinuous Galerkin methods[R]. AIAA-2006-112.

BARTER G E, DARMOFAL D L. Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation[J]. J Comput Phys, 2010, 229: 1810-1827. doi:10.1016/j.jcp.2009.11.010.

YU M L, GIRALDO F X, PENG M, et al. Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling[J]. Monthly Weather Review, 2015, 143(12): 4823-4845.

LILIA KRIVODONOVA, JIANGUO XIN, JEAN-FRANÇOIS REMACLE, et al. Shockd detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws[J]. Applied Numerical Mathematics, Elsevier, 2004, 48(3-4): 323-338. doi: 10.1016/j.apnum.2003.11.002.

PARK J S, KIM C. Higher-order multi-dimensional limiting strategy for discontinuous Galerkin methods in compressible inviscid and viscous flows[J]. Computers Fluids, 2014, 96(13): 377-396.

LI Y, WANG Z J. Recent progress in developing a convergent and accuracy preserving limiter for the FR/CPR method[C]//55th AIAA Aerospace Sciences Meeting AIAA SciTech Forum, (AIAA 2017-0756).

CORRIGAN A, KERCHER A D, KESSLER D A. A moving discontinuous Galerkin finite element method for flows with interfaces[J]. International J. for Numerical Methods in Fluids, 2019, 89(9): 362-406. https://doi.org/10.1002/fld.4697

ALTMANN C, BECK A D, HINDENLANG F, et al. An efficient high performance parallelization of a discontinuous Galerkin spectral element method. In: Keller R., Kramer D., Weiss JP. (eds) Facing the Multicore-Challenge Ⅲ. Lecture Notes in Computer Science, vol 7686[M ] . Sp ringer, Berlin, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-35893-7_4

GOTTLIEB S, SHU C W. Total variation diminishing Runge-Kutta schemes[J]. Math Comput, 1998, 67(221): 73-85.

DUMBSER M, Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier-Stokes equations[J]. Computers Fluids, 2010, 39(1): 60-76.

GASSNER G, DUMNSER M, HINDENLANG F, et al. Explicit one-step time discretization for discontinuous Galerkin and finite volume schemes based on local predictors[J]. Journal of Computational Physics, 2011, 230: 4232, 4247.

VATSA V N, CARPENTER M H, LOCKARD D P. Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) scheme for unsteady flow applications[R]. AIAA-2010-0122.

BUTCHER J C. Numerical methods for ordinary differential equations[M]. Chichester: Wiley, 2002.

JAMESON A. Evaluation of fully implicit Runge Kutta schemes for unsteady flow calculations[J]. J Sci Comput, 2017, 73: 819-852. https://doi.org/10.1007/s10915-017-0476-x

PAZNER W, PERSSON P O. Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations[J]. Journal of Computational Physics, 2017, 335: 700-717.

KENNEDY C A, CARPENTER M H. Diagonally implicit Runge-Kutta methods for ordinary differential equations. A Review[R]. NASA/TM-2016-219173, March, 2016.

PARESCHI L, RUSSO G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation[J]. Journal of Scientific Computing, 2005, 25: 129-155.

PERSSON P O. High-order LES simulations using implicit-explicit Runge-Kutta schemes, in: Proceedings of the 49th AIAA Aerospace Sciences Meet-ing and Exhibit[R]. AIAA-2011-684.

VERMEIRE B C, NADARAJAH S. Adaptive IMEX schemes for high-order unstructured methods[J]. Journal of Computational Physics, 2015, 280(1): 261-286. https://doi.org/10.1016/j.jcp.2014.09.016

BASSI F, BOTTI L, COLOMBO A, et al. Linearly implicit Rosenbrock-type Runge Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows[J]. Computers Fluids, 2015, 118: 305-320.

LIU X, XIA Y, LUO H, et al. A comparative study of rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations[J]. Communications in Computational Physics, 2016, 20(4): 1016-1044. doi:10.4208/cicp.300715.140316a.

DIOSADY L T, MURMAN S M. Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods[J]. Journal of Computational Physics, 2017, 330: 296-318.

MARTINELLI L, LOHRY M W. Implicit time integration of discontinuous Galerkin approximations to the Navier-Stokes equations[R]. AIAA-2020-0774.

WANG L, YU M L. Comparison of ROW, ESDIRK, and BDF2 for unsteady flows with the high-order flux reconstruction formulation[J]. Journal of Scientific Computing, 2020, 83(39): .

JIA F, WANG Z J, BHASKARAN R, et al. Accuracy, efficiency and scalability of explicit and implicit FR/CPR schemes in large eddy simulation[J]. Computers and Fluids, 2019, 195: 104316.

KNOLL D, KEYESD. Jacobian-free Newton-Krylov methods: a survey of approaches and applications[J]. Journal of Computational Physics, 2004, 193(2): 357-397. doi:10.1016/j.jcp.2003.08.010.

PERSSON P O. A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes[J]. Journal of Computational Physics, 2013, 233: 414-429.

YOON S, JAMESON A. Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations[J]. AIAA J, 1988, 26(9): 1025-1026.

CHEN R F, WANG Z J. Fast, block lower-upper symmetric Gauss-Seidel scheme for arbitrary grids[J]. AIAA J, 2000, 38(12): 2238-2245.

JOURDAN E, WANG Z J. A Study of p-multigrid approach for the high order FR/CPR method[R]. AIAA-2019-3711.

LOPPI N A, WITHERDEN F D, JAMESON A, et al. A high-order cross-platform incompressible Navier-Stokes solver via artificial compressibility with application to a turbulent jet[J]. Computer Physics Communications, 2018, 233: 193-205.

WANG L, YU M L. A p-multigrid flux reconstruction method for the steady Navier-Stokes equations[R]. AIAA 2019-3061.

FREY P J, ALAUZET F, Anisotropic mesh adaptation for CFD computations[J]. Comput Methods Appl Mech Engrg, 2005, 194: 5068-5082.

ROY C J. Strategies for driving mesh adaptation in CFD[R]. AIAA-2009-1302.

SHIH T, QIN Y. A method for estimating grid-induced errors in finite-difference and finite-volume methods[R]. AIAA-2003-845.

FIDKOWSKI K J. Review of output-based error estimation and mesh adaptation in computational fluid dynamics[J]. AIAA Journal, 2011, 49(4): 673-694.

YANO M, DARMOFAL D L. An optimization-based framework for anisotropic simplex mesh adaptation[J]. Journal of Computational Physics, 2012, 231(22): 7626-7649.

ZHOU C, SHI L, WANG Z J. Adaptive high-order discretization of the Reynolds-averaged Navier-Stokes equations[J]. Computers and Fluids, 2017, 159: 137-155.

FIDKOWSKI K J. Output-based space-time mesh optimization for unsteady flows using continuous-in-time adjoints[J]. Journal of Computational Physics, 2017, 341(15): 258-277.

WANG Q, HU R, BLONIGAN P. Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations[J]. Journal of Computational Physics, 2014, 267(15): 210-224.

ABBÀ A, RECANATI A, TUGNOLI M, et al. Dynamical p-adaptivity for LES of compressible flows in a high order DG framework[J]. Journal of Computational Physics, 2020, 420: 109720.

ANTEPARA O, LEHMKUHL O, BORRELL R, et al, Parallel adaptive mesh refinement for Large-Eddy Simulations of turbulent flows[J]. Comput Fluids, 2015, 110: 48-61.

BENARD P, BALARAC G, MOUREAU V, et al. Mesh adaptation for large-eddy simulations in complex geometries[J]. International Journal for Numerical Methods in Fluids, 2016, 81(12): 719-740. doi: 10.1002/fld.4204. hal-01339519

PARK M A, KLEB B, ANDERSON W K, et al. Exploring unstructured mesh adaptation for hybrid Reynolds-averaged Navier-Stokes/large eddy simulation[R]. AIAA-2020-1139.

TUGNOLI M, ABB A, BONAVENTURA L, et al. A locally p-adaptive approach for large eddy simulation of compressible flows in a DG framework[J ] . J Comput Phys, 2047, 349: 33-58. https://arxiv.org/abs/1610.03319

NADDEI F, DE LA LLAVE PLATA M, COUAILLIER V, et al. A comparison of refinement indicators for p-adaptive simulations of steady and unsteady flows using discontinuous Galerkin methods[J]. Journal of Computational Physics, 2019, 376: 508-533.

WANG L, MATTHIAS GOBBERT, YU M L. A dynamically load-balanced parallel p-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation[J]. Journal of Computational Physics, 2020, 417: 109581.

TOOSI S, LARSSON J. Anisotropic grid adaptation in large eddy simulations[J]. Comput Fluids, 2017, 156: 146-61.

ARROYO C P, DOMBARD J, DUCHAINE F, et al. Large-eddy simulation of an integrated high-pressure compressor and combustion chamber of a typical turbine engine architecture[R]. ASME Turbo Expo GT2020-16288, May 2020.

VINCENT P, WITHERDEN F, VERMEIRE B, et al. Towards green aviation with python at petascale[C]//High Performance Computing, Networking, Storage and Analysis, SC16: International Conference for, IEEE, 2016: 1-11.

FRÈRE, CARTON DE WIART C, HILLEWAERT K, et al. Application of wall-models to discontinuous Galerkin LES[J]. Physics of Fluids, 2017, 29: 085111.

LODATO G, CASTONGUAY P, JAMESON A. Structural wall-modeled LES using a high-order spectral difference scheme for unstructured meshes[J]. Flow, Turbulence and Combustion, 2014, 92(1-2): 579-606.

SHI J, YAN H, WANG Z J. Flux reconstruction implementation of an algebraic wall model for large-eddy simulation[J]. AIAA Journal, 2020, 58(7): 3051-3062.

CHAN J, DEL REY FERNÁNDEZ D C, CARPENTER M H. Efficient entropy stable Gauss collocation methods[J]. SIAM J Sci Comput, 2019, 41(5): A2938-A2966.

MANZANERO J, RUBIO G, FERRER E, et al. Insights on aliasing driven instabilities for advection equations with application to Gauss-Lobatto discontinuous Galerkin methods[J]. Journal of Scientific Computing, 2018, 75: 1262-1281.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Noise prediction and reduction methods for LAGOON landing gear based on Lattice Boltzmann method

Optimization of hot-air anti-icing structures based on neural networks and genetic algorithms

Positivity-preserving strategies and their comparision based on staggered CPR methods

Research on the characteristics of water droplets impacting moving superhydrophobic surfaces and its regulation

Impact of inter-wing spacing on aerodynamic noise in multi-flapping wing configurations

Related Author

No data

Related Institution

No data

AI问答

⁰