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摘要: 计算网格是流体数值模拟误差的主要来源之一, 极大地影响着流动模拟结果的精度. 传统网格生成强烈依赖于用户经验, 加大了复杂飞行器网格生成的难度, 增加了气动特性预测数据的不确定度. 网格自适应技术是结合流动特性的计算网格自主优化技术, 可通过迭代优化消除网格因素造成的数值模拟误差, 能有效提高飞行器气动特性预测精度. 近年来在运输机高升力复杂构型的成功应用, 表明了网格自适应技术已发展到了较为成熟的阶段. 本文针对计算流体力学, 首先系统总结了网格自适应涉及的误差估计、网格编辑和物面几何保形三项关键技术的研究进展, 并介绍了相关的主要并行实现技术. 其次, 文中介绍了网格自适应技术在网格相关性分析、流场细节捕捉、气动特性计算和非定常流动模拟中的主要应用情况. 最后, 本文提出了网格自适应技术研究存在的问题及未来研究方向.Abstract: Computational mesh is one of the main source of errors in fluid numerical simulation, which greatly affects the accuracy of flow simulation result. Traditional mesh generation strongly depends on user experience, which increases the difficulty of mesh generation for complicated aircraft and increases the uncertainty of aerodynamic characteristics prediction data. Mesh adaptation is a mesh autonomous optimization technology combined with flow characteristics, which can eliminate numerical errors caused by mesh factors through iterative procedure, and can effectively improve the accuracy of aircraft aerodynamics prediction. In recent years, the successful application of mesh adaptation in the high-lift complicated configuration of transport aircraft shows that the adaptation technology has developed to a relatively mature stage. In this paper, for computational fluid dynamics, first of all, the research progress of three key techniques related to mesh adaptation, including error estimation, mesh editing and geometry shape preservation, is systematically summarized, and their parallel implementation techniques are briefly introduced. Secondly, the main applications of mesh adaptation in mesh correlation analysis, flow detail capture, aerodynamics prediction and unsteady flow simulation are introduced. Finally, the future research direction to tackle the existing problems of mesh adaptation are proposed at the end of the paper.
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图 2 两个度量张量相交的几何意义示意(Alauzet et al. 2007)
图 3 度量张量自适应与伴随自适应对比(Balan et al. 2019). 上: 阻力随网格规模的收敛特性, 下: 自适应后网格
图 4 r型网格优化示意图(Vivarelli et al. 2021). (a)优化前网格, (b)优化后网格
图 8 四面体各向异性网格生成(Alauzet和Loseille 2016). (a)流场等值线, (b)各向异性网格
图 10 基于单元的网格剖分模式 (Soukov 2022). (a) 六面体单元, (b) 三棱柱单元, (c) 金字塔单元, (d) 四面体单元
图 12 局部Coons曲面拟合示意图(Hindenlang et al. 2011)
图 13 后台阶流动网格相关性分析(Chila & Kaminski 2006). (a)监测点速度, (b)分离再附点位置
图 14 第三届高升力构型自适应计算(Alauzet & Clerici et al. 2022). (a)升力系数收敛过程, (b) 阻力系数收敛过程
图 17 阿波罗返回舱头激波自适应模拟流场(Bibb et al. 2006). (a)初始网格, (b)自适应两次网格, (c)自适应最终网格
图 18 声爆激波捕捉自适应模拟压力分布对比(Jones et al. 2006). (a)初始网格压力对比, (b)自适应后压力对比
图 19 C608低声爆飞机复杂波系各向异性自适应模拟后网格及流场分布(Vanharen et al. 2021)
图 20 NASA Rotor 37压气机流场模拟(Alauzet & Frazza et al. 2022). (a)自适应后网格及流场, (b)总压比收敛过程
图 21 第三届高升力构型自适应网格收敛计算(Alauzet & Clerici et al. 2022). (a)自适应网格收敛过程, (b)自适应后机翼等展向位置截面网格分布及流场
图 22 结合LES和网格自适应圆柱绕流模拟的分离涡系结构(Gou et al. 2018). (a)未使用自适应, (b)使用自适应
图 23 结合LES和压气机网格自适应模拟流动参数(Odier et al. 2021). (a)压气机构型, (b)自适应前后流动参数对比
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[1] 陈浩, 华如豪, 袁先旭, 唐志共, 毕林. 2022. 基于自适应笛卡尔网格的飞翼布局流动模拟. 航空学报, 43: 125674 (Chen H, Hua R H, Yuan X X, Tang Z G, Bi L. 2022. Simulation of flow around fly-wing configuration based on adaptive Cartesian grid. Acta Aeronautica et Astronautica Sinica, 43: 125674).Chen H, Hua R H, Yuan X X, Tang Z G, Bi L. 2022. Simulation of flow around fly-wing configuration based on adaptive Cartesian grid. Acta Aeronautica et Astronautica Sinica, 43: 125674). [2] 崔鹏程, 邓有奇, 唐静, 李彬. 2016. 基于伴随方程的网格自适应及误差修正. 航空学报, 37: 2992-3002 (Cui P C, Deng Y Q, Tang J, Li B. 2016. Adjoint equations-based grid adaptation and error correction. Acta Aeronautica et Astronautica Sinica, 37: 2992-3002).(Cui P C, Deng Y Q, Tang J, Li B. 2016. Adjoint equations-based grid adaptation and error correction. Acta Aeronautica et Astronautica Sinica, 37: 2992-3002). [3] 崔鹏程, 唐静, 李彬, 马明生, 邓有奇. 2018. 基于超网格的重叠网格守恒插值方法. 航空学报, 39: 121569 (Cui P C, Tang J, Li B, Ma M M, Deng Y Q. 2018. A conservative interpolation method for overset mesh. Acta Aeronautica et Astronautica Sinica, 39: 121569).(Cui P C, Tang J, Li B, Ma M M, Deng Y Q. 2018. A conservative interpolation method for overset mesh. Acta Aeronautica et Astronautica Sinica, 39: 121569). [4] 龚小权, 吴晓军, 唐静, 李明, 张健. 2022. r型网格自适应在间断Galerkin有限元激波捕捉中的应用. 北京航空航天大学学报, 48: 1889-1898 (Gong X Q, Wu X J, Tang J, Li M, Zhang J. 2022. Application of r-grid adaptive for shock capturing in discontinuous Galerkin finite element method. Journal of Beijing University of Aeronautics and Astronautics, 48: 1889-1898).(Gong X Q, Wu X J, Tang J, Li M, Zhang J. 2022. Application of r-grid adaptive for shock capturing in discontinuous Galerkin finite element method. Journal of Beijing University of Aeronautics and Astronautics, 48: 1889-1898). [5] 韩志熔, 陆志良, 郭同庆, 陈迎春. 2012. 一种用于分离流动的网格自适应算法. 空气动力学报, 30: 86-89 (Han Z R, Lu Z L, Guo T Q, Chen Y C. 2012. Grid adaption technique for separation flow. Acta Aerodynamica Sinica, 30: 86-89).Han Z R, Lu Z L, Guo T Q, Chen Y C. 2012. Grid adaption technique for separation flow. Acta Aerodynamica Sinica, 30: 86-89). [6] 李立, 白文, 梁益华. 2011. 基于伴随方程方法的非结构网格自适应技术及应用. 空气动力学报, 29: 316-309 (Li L, Bai W, Liang Y H. 2011. An adjoint-based method for unstructured mesh adaptation and its applications. Acta Aerodynamica Sinica, 29: 316-309).Li L, Bai W, Liang Y H. 2011. An adjoint-based method for unstructured mesh adaptation and its applications, Acta Aerodynamica Sinica, 29: 316-309). [7] 罗昔联, 顾兆林, 雷康斌, 加濑究. 2009. 一种求解N-S方程的自适应直角网格方法. 西安交通大学学报, 43: 11-17 (Luo X L, Gu Z L, Lei K B, Kase K. 2009. An adaptive Cartesian grid method for the incompressible Navier-Stokes equations. Journal of Xi’an Jiaotong University, 43: 11-17).Luo X L, Gu Z L, Lei K B, Kase K. 2009. An adaptive Cartesian grid method for the incompressible Navier-Stokes equations. Journal of Xi’an Jiaotong University, 43: 11-17). [8] 任登凤, 谭俊杰, 张军. 2005. 自适应方法在APFSDS干扰流场模拟中的应用. 弹道学报, 17: 1-6 (Ren D F, Tan J J, Zhang J. 2005. Adaptive mesh generation and simulation of APFSDS and SABOTS. Journal of Ballistics, 17: 1-6).Ren D F, Tan J J, Zhang J. 2005. Adaptive mesh generation and simulation of APFSDS and SABOTS. Journal of Ballistics, 17: 1-6). [9] 苏欣荣, 袁新. 2016. 用于叶轮机械复杂流动的网格自适应方法. 工程热物理学报, 37: 259-263 (Su X R, Yuan X. 2016. Adaptive mesh refinement for complex turbomachinery flow. Journal of Engineering Thermophysics, 37: 259-263).Su X R, Yuan X. 2016. Adaptive mesh refinement for complex turbomachinery flow. Journal of Engineering Thermophysics, 37: 259-263). [10] 唐静, 郑鸣, 邓有奇, 李彬. 2015. 网格自适应技术在复杂外形流场模拟中的应用. 计算力学学报, 32: 752-757 (Tang J, Zheng M, Deng Y Q, Li B. 2015. Grid adaptation for flow simulation of complicated configuration. Chinese Journal of Computational Mechanics, 32: 752-757). doi: 10.7511/jslx201506007(Tang J, Zheng M, Deng Y Q, Li B. 2015. Grid adaptation for flow simulation of complicated configuration. Chinese Journal of Computational Mechanics, 32: 752-757). doi: 10.7511/jslx201506007 [11] 唐静, 崔鹏程, 贾洪印, 李彬. 2019. 非结构混合网格鲁棒自适应技术. 航空学报, 40: 122894 (Tang J, Cui P C, Jia H Y, Li B. 2019. Robust adaptation techniques for unstructured hybrid mesh. Acta Aeronautica et Astronautica Sinica, 40: 122894).(Tang J, Cui P C, Jia H Y, Li B. 2019. Robust adaptation techniques for unstructured hybrid mesh. Acta Aeronautica et Astronautica Sinica, 40: 122894). [12] 唐静, 张健, 李彬, 崔鹏程, 周乃春. 2020. 非结构混合网格自适应并行技术. 航空学报, 41: 123202 (Tang J, Zhang J, Li B, Cui P C, Zhou N C. 2020. Parallel algorithms for unstructured hybrid mesh adaptation. Acta Aeronautica et Astronautica Sinica, 41: 123202).(Tang J, Zhang J, Li B, Cui P C, Zhou N C. 2020. Parallel algorithms for unstructured hybrid mesh adaptation. Acta Aeronautica et Astronautica Sinica, 41: 123202). [13] 唐静, 张健, 张耀冰, 周乃春, 刘刚. 2022. 一种用于TSTO级间分离CFD计算的网格动态优化技术. 空气动力学学报, 41 (Tang J, Zhang J, Zhang Y B, Zhou N C, Liu Gang. 2022. A mesh adaptation method for TSTO stages separation CFD simulation. Acta Aerodynamica Sinica, 41). doi: 10.7638/kqdlxxb-2022.0028Tang J, Zhang J, Zhang Y B, Zhou N C, Liu Gang. A mesh adaptation method for TSTO stages separation CFD simulation. Acta Aerodynamica Sinica, 2022, 41 doi: 10.7638/kqdlxxb-2022.0028 [14] 王利, 周伟江. 2017. 基于伴随方法的网格自适应DG方法. 中国科学:技术科学, 47: 1214-1224 (Wang L, Zhou W J. 2017. An adjoint-based grid adaptive discontinuous Galerkin method. Scientia Sinica Technologica, 47: 1214-1224). doi: 10.1360/N092016-00441Wang L, Zhou W J. 2017. An adjoint-based grid adaptive discontinuous Galerkin method. Scientia Sinica Technologica, 47: 1214-1224) doi: 10.1360/N092016-00441 [15] 王俊杰, 高正红. 2006. 基于复合叉树的自适应笛卡尔网格应用研究. 应用力学学报, 23: 623-626 (Wang J J, Gao Z H. 2006. Adaptive Cartesian grid based on an omni-tree. Chinese Journal of Applied Mechanics, 23: 623-626).Wang J J, Gao Z H. 2006. Adaptive Cartesian grid based on an omni-tree. Chinese Journal of Applied Mechanics, 23: 623-626). [16] 肖涵山, 陈作斌, 刘刚, 江雄. 2003. 基于Euler方程的三维自适应笛卡尔网格应用研究. 空气动力学学报, 21: 202-210 (Xiao H S, Chen Z B, Liu G, Jiang X. 2003. Application of 3-D adaptive Cartesian grid algorithm based on the Euler equations. Acta Aerodynamica Sinica, 21: 202-210).Xiao H S, Chen Z B, Liu G, Jiang X. 2003. Application of 3-D adaptive Cartesian grid algorithm based on the Euler equations. Acta Aerodynamica Sinica, 21: 202-210). [17] 许和勇, 叶正寅. 2011. 三维非结构自适应多重网格技术. 空气动力学学报, 29: 365-369 (Xu H Y, Ye Z Y. 2011. A technique of three dimensional unstructured adaptive multigrid. Acta Aerodynamica Sinica, 29: 365-369).Xu H Y, Ye Z Y. 2011. A technique of three dimensional unstructured adaptive multigrid. Acta Aerodynamica Sinica, 29: 365-369). [18] 阎超, 屈峰, 赵雅甜, 于剑, 武从海, 张树海. 2020. 航空航天CFD物理模型和计算方法的述评与挑战. 空气动力学学报, 38: 829-857 (Yan C, Qu F, Zhao Y T, Yu J, Wu C H, Zhang S H. 2020. Review of development and challenges for physical modeling and numerical scheme of CFD in aeronautics and astronautics. Acta Aerodynamica Sinica, 38: 829-857).(Yan C, Qu F, Zhao Y T, Yu J, Wu C H, Zhang S H. 2020. Review of development and challenges for physical modeling and numerical scheme of CFD in aeronautics and astronautics. Acta Aerodynamica Sinica, 38: 829-857 [19] 杨夏勰, 周春华. 2014. 目标函数误差估算及网格自适应处理. 空气动力学报, 32: 688-693 (Yang X X, Zhou C H. 2014. Output-based error estimation and grid adaptation. Acta Aerodynamica Sinica, 32: 688-693).Yang X X, Zhou C H. Output-based error estimation and grid adaptation. Acta Aerodynamica Sinica, 2014, 32: 688-693. [20] 张贺, 钟诚文, 宫建, 毕志献, 韩曙光. 2014. 气体动理论BGK格式的网格自适应方法. 航空学报, 35: 687-694 (Zhang H, Zhong C W, Gong J, Bi Z X, Han S G. 2014. Adaptive mesh refinement for gas-kinetic BGK scheme. Acta Aeronautica et Astronautica Sinica, 35: 687-694).Zhang H, Zhong C W, Gong J, Bi Z X, Han S G. 2014. Adaptive mesh refinement for gas-kinetic BGK scheme. Acta Aeronautica et Astronautica Sinica, 35: 687-694). [21] 张扬, 张来平, 赫新, 邓小刚. 2016. 基于自适应混合网格的脱体涡模拟. 航空学报, 37: 3605-3614 (Zhang Y, Zhang L P, He H, Deng X G. 2016. Detached eddy simulation based on adaptive hybrid grids. Acta Aeronautica et Astronautica Sinica, 37: 3605-3614). doi: 10.7527/S1000-6893.2016.0175Detached eddy simulation based on adaptive hybrid grids. 2016. Acta Aeronautica et Astronautica Sinica, 37: 3605-3614). doi: 10.7527/S1000-6893.2016.0175 [22] 邹建锋, 盛东, 方磊, 郑耀. 2015. 各向异性网格自适应计算在超燃模拟中的应用. 航空动力学报, 30: 2140-2150 (Zou J F, Sheng D, Fang L, Zheng Y. 2015. Applications of anisotropic unstructured mesh adaption in supersonic combustion simulations. Journal of Arospace Power, 30: 2140-2150).Zou J F, Sheng D, Fang L, Zheng Y. 2015. Applications of anisotropic unstructured mesh adaption in supersonic combustion simulations. Journal of Aerospace Power, 30: 2140-2150). [23] Alauzet F, Frey P J, George P L, Mohammadi B. 2007. 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. Journal of Computational Physics, 222: 592-623. doi: 10.1016/j.jcp.2006.08.012 [24] Alauzet F. 2010. Size gradation control of anisotropic meshes. Finite Elements in Analysis and Design, 46: 181-202. doi: 10.1016/j.finel.2009.06.028 [25] Alauzet F and Loseille A. 2016. A decade of progress on anisotropic mesh adaptation for computational fluid dynamics. Computer-Aided Design, 72: 13-39. doi: 10.1016/j.cad.2015.09.005 [26] Alauzet F. 2016. A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes. Computer Methods in Applied Mechanics and Engineering, 299: 116-142. doi: 10.1016/j.cma.2015.10.012 [27] Alauzet F, Clerici F, Loseille A, Morisco C T, Vanharen J. Some progress on CFD high lift prediction using metric-based anisotropic mesh adaptation. AIAA Scitech 2022 Forum, 2022, San Diego, CA & Virtual. [28] Alauzet F, Frazza L, Papadogiannis D. 2022. Periodic adjoints and anisotropic mesh adaptation in rotating frame for high-fidelity RANS turbomachinery applications. Journal of Computational Physics, 450: 110814. doi: 10.1016/j.jcp.2021.110814 [29] Alrutz T. 2005. Hybrid grid adaptation in TAU. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 89: 115. [30] Antepara O, Lehmkuhl O, Chiva J, Correll R. 2013. Parallel adaptive mesh refinement simulation of the flow around a square cylinder at Re = 22000. Procedia Engineering, 61: 246-250. doi: 10.1016/j.proeng.2013.08.011 [31] Azarenok B N, Ivanenko S A, Tang T. 2003. Adaptive mesh redistribution methods based on Godunov's scheme. Communications in Mathematical Sciences, 1: 152-179. doi: 10.4310/CMS.2003.v1.n1.a10 [32] Baker T J. 2005. Mesh generation: art or science. Progress in Aerospace Sciences, 41: 29-63. doi: 10.1016/j.paerosci.2005.02.002 [33] Balan A, Park M A, Anderson W K. 2019. Adjoint-based anisotropic mesh adaptation for a stabilized finite-element flow solver. AIAA Aviation 2019 Forum. Dallas, Texas, AIAA. [34] Balan A, Park M A, Wood S L, Anderson W K. 2020. Verification of anisotropic mesh adaptation for complex aerospace applications. AIAA Scitech 2020 Forum. Orlando, FL. [35] Balan A, Park M A, Wood S L, Anderson W K, Rangarajan A, Sanjaya D P, May G. 2022. A review and comparison of error estimators for anisotropic mesh adaptation for flow simulations. Computers and Fluids, 234: 105259. doi: 10.1016/j.compfluid.2021.105259 [36] Bartels R E, Vatsa V, Carlson J-R, Park M, Mineck R E. FUN3D grid refinement and adaptation studies for the Ares launch vehicle. AIAA Paper, 2010: 4372. [37] Bibb K L, Gnoffo P A, Park M A, Jones W T. Parallel, gradient-based anisotropic mesh adaptation for re-entry vehicle configurations. AIAA Paper, 2006: 3579. [38] Bonfiglioli A, Paciorri R, Mascio A D. 2012. The Role of mesh generation, adaptation, and refinement on the computation of flows featuring strong shocks. Modelling and Simulation in Engineering, 2012: 1-15. [39] Budd C J, Russell R D, Walsh E. 2015. The geometry of r-adaptive meshes generated using optimal transport methods. Journal of Computational Physics, 282: 113-137. doi: 10.1016/j.jcp.2014.11.007 [40] Buning P G, Pulliam T H. Cartesian off-body grid adaption for viscous time-accurate flow simulation. AIAA Paper, 2011: 3693. [41] Campbell R, Carter M. 2008. Efficient unstructured grid adaptation methods for sonic boom prediction. AIAA Paper, 2008: 7327. [42] Cavallo P A, Sinha N, Feldman G M. 2005. Parallel unstructured mesh adaptation method for moving body applications. AIAA Journal, 43: 1937-1945. doi: 10.2514/1.7818 [43] Ceze M A, Fidkowski K J. 2013. Anisotropic hp-adaptation framework for functional prediction. AIAA Journal, 51: 492-509. doi: 10.2514/1.J051845 [44] Ceze M A, Fidkowski K J. 2014. Drag prediction using adaptive discontinuous finite elements. AIAA Journal of Aircraft, 51: 1284-1294. doi: 10.2514/1.C032622 [45] Chand K K, Lee K D. Adaptation of structured grids with redistribution and embedding. AIAA Paper, 1999: 36515. [46] Chen J, Zheng J, Zheng Y, Si H, Hassan O, Morgan K. 2017. Improved boundary constrained tetrahedral mesh generation by shell transformation. Applied Mathematical Modelling, 51: 764-790. doi: 10.1016/j.apm.2017.07.011 [47] Chila R J, Kaminski D A. Automated grid independence via unstructured adaptive refinement. AIAA Paper, 2006: 3062. [48] Clerici F, Alauzet F, Spalart P R. Coupled adjoint solver and turbulent error estimate for anisotropic mesh adaptation in high-fidelity RANS simulations. AIAA Scitech 2022 Forum. San Diego, 2022, CA & Virtual. [49] Copeland S R, Lonkar A K, Palacios F, Alonso J J. Adjoint-based goal-oriented mesh adaptation for nonequilibrium hypersonic flows. AIAA Paper, 2013: 0552. [50] Coppeans A W, Fidkowski K J, Martins J R R A. Output-based mesh adaptation using overset methods for structured meshes. AIAA Scitech 2022 Forum. San Diego, 2022, CA & Virtual. [51] Cui P C, Chen J T, Li B, Li H, Ma M S, Tang J. 2021. A wide-template and high-accuracy data transfer method for unstructured adjoint-based grid adaptation. Journal of Physics: Conference Series, 012021: 1-8. [52] Digonnet H, Coupez T, Laure P, Silva L. 2019. Massively parallel anisotropic mesh adaptation. International Journal of High Performance Computing Applications, 33: 3-24. doi: 10.1177/1094342017693906 [53] Farrell P E, Piggott M D, Pain C C, Gorman G J, Wilson C R. 2009. Conservative interpolation between unstructured meshes via supermesh construction. Computer Methods in Applied Mechanics and Engineering, 198: 2632-2642. doi: 10.1016/j.cma.2009.03.004 [54] Fidkowski K J, Darmofal D L. 2011. Review of output-based error estimation and mesh adaptation in computational fluid dynamics. AIAA Journal, 49: 673-694. doi: 10.2514/1.J050073 [55] Frey P J, Alauzet F. 2005. Anisotropic mesh adaptation for CFD computations. Computer Methods in Applied Mechanics and Engineering, 194: 5068-5082. doi: 10.1016/j.cma.2004.11.025 [56] Galimov A Y, Sahni O, Jr. R T L, Shephard M S, Drew D A, Jansen K E. 2010. Parallel adaptive simulation of a plunging liquid jet. Acta Mathematica Scientia, 30B: 522-538. [57] Gou J, Su X, Yuan X. 2018. Adaptive mesh refinement method-based large eddy simulation for the flow over circular cylinder at ReD = 3900. International Journal of Computational Fluid Dynamics, 32: 1-18. doi: 10.1080/10618562.2018.1461845 [58] Gunney B T N, Anderson R W. 2016. Advances in patch-based adaptive mesh refinement scalability. Journal of Parallel and Distributed Computing, 89: 65-84. doi: 10.1016/j.jpdc.2015.11.005 [59] Habashi W G, Dompierre J, Bourgault Y, Ait-Ali-Yahia D, Fortin M, Vallet M-G. 2000. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles. International Journal for Numerical Methods in Fluids, 32: 725-744. doi: 10.1002/(SICI)1097-0363(20000330)32:6<725::AID-FLD935>3.0.CO;2-4 [60] Haimes R, Dannenhoffer J F. EGADSlite: a lightweight geometry kernel for HPC. AIAA Paper, 2018: 1401. [61] Hartmann R. 2013. Higher-order and adaptive discontinuous Galerkin methods with shock-capturing applied to transonic turbulent delta wing flow. International Journal for Numerical Methods in Fluids, 72: 883-894. doi: 10.1002/fld.3762 [62] Hindenlang F, Neudorfer J, Gassner G, Munz C-D. Unstructured three-dimensional high order grids for discontinuous Galerkin schemes. AIAA Paper, 2011: 3853. [63] Hunt J C R, Wray A A, Moin P. Eddies, streams, and convergence zones in turbulent flows. Studying Turbulence using Numerical Simulation Databases: 2. Proceedings of the 1988 Summer Program, NASA, Dec. 1988, 193–208. [64] Ibanez D, Barral N, Krakos J, Loseille A, Michal T, Park M. 2017. First benchmark of the unstructured grid adaptation working group. Procedia Engineering, 203: 154-166. doi: 10.1016/j.proeng.2017.09.800 [65] Ji H, Lien F S, Yee E. 2010. A new adaptive mesh refinement data structure with an application to detonation. Journal of Computational Physics, 229: 8981-8993. doi: 10.1016/j.jcp.2010.08.023 [66] Jones W T, Nielsen E J, Park M A. Validation of 3D adjoint based error estimation and mesh adaptation for sonic boom prediction. AIAA Paper, 2006: 1150. [67] Joubarne E, Guibault F, Braun O, Avellan F. 2009. Numerical capture of wing tip vortex improved by mesh adaptation. International Journal for Numerical Methods in Fluids, 67: 8-32. [68] Kamkar S J, Wissink A M, Sankaran V, Jameson A. 2011. Feature-driven Cartesian adaptive mesh refinement for vortex-dominated flows. Journal of Computational Physics, 230: 6271-6298. doi: 10.1016/j.jcp.2011.04.024 [69] Karman S L. Multi-block hierarchical unstructured grid generation with adaptation. AIAA Paper, 2014: 0116. [70] Karypis G, Kumar V. 1998. Multilevel k-way partitioning scheme for irregular graphs. Journal of Parallel and Distributed Computing, 48: 96-129. doi: 10.1006/jpdc.1997.1404 [71] Kavouklis C, Kallinderis Y. 2010. Parallel adaptation of general three-dimensional hybrid meshes. Journal of Computational Physics, 229: 3454-3473. doi: 10.1016/j.jcp.2010.01.011 [72] Kirk B S, Peterson J W, Stogner R H, Carey G F. 2006. libMesh: a C + + library for parallel adaptive mesh refinement/coarsening simulations. Engineering with Computers, 22: 237-254. doi: 10.1007/s00366-006-0049-3 [73] Knutson A L, Johnson H B, Candler G V. Adaptive mesh refinement in US3D. AIAA Scitech 2021 Forum, Virtual Event. [74] Laflin K R, Klausmeyer S M.A fast and simple solution-resolution assessment for improved CFD predictions. AIAA Paper, 2005: 1218. [75] Lee K D and Loellbach J M. A mapping technique for solution adaptive grid control. AIAA Paper, 1989: 2178. [76] Lepage C Y, Suerich-Gulick F, Habashi W G. Anisotropic 3-D mesh adaptation on unstructured hybrid meshes. AIAA Paper, 2002: 0859. [77] Lepage C Y, St-Cyr A, Habashi W G. Parallel unstructured mesh adaptation on distributed memory systems. AIAA Paper, 2004: 2532. [78] Linn R V, Awruch A M. 2017. Edge-Based Anisotropic Mesh adaptation of unstructured meshes with applications to compressible flows. Engineering with Computers, 33: 1007-1025. doi: 10.1007/s00366-017-0513-2 [79] Liu Z, Yang Y, Gong A, Zhou W. 2015. Unstructured adaptive grid refinement for flow feature capture. Procedia Engineering, 99: 477-483. doi: 10.1016/j.proeng.2014.12.561 [80] Loseille A. 2007. Achievement of global second order mesh convergence for discontinuous flows with adapted unstructured meshes. 18th AIAA Computational Fluid Dynamics Conference. Miami, FL. [81] Loseille A, Alauzet F. Optimal 3d highly anisotropic mesh adaptation based on the continuous mesh framework. Proceedings of the 18th International Meshing Roundtable, Springer, 2009. [82] Loseille A.Unstructured mesh generation and adaptation. Elsevier, 2016, 263-302. [83] Luo Y X, Fidkowski K J. Output-based space-time mesh adaptation for unsteady aerodynamics. AIAA Paper, 2011: 491. [84] MacNeice P, Olson K M, Mobarry C, Fainchtein R d, Packer C. 2000. PARAMESH: A parallel adaptive mesh refinement community toolkit. Computer Physics Communications, 126: 330-354. doi: 10.1016/S0010-4655(99)00501-9 [85] Marcum D, Alauzet F. 2017. 3D Metric-aligned and orthogonal solution adaptive mesh generation. Procedia Engineering, 203: 78-90. doi: 10.1016/j.proeng.2017.09.790 [86] Menier V, Loseilley A, Alauzet F. CFD validation and adaptivity for viscous flow simulations. AIAA Paper, 2014: 2925. [87] Michal T, Krakos J, Kamenetskiy D, Galbraith M, Ursachi C I, Park M A, Anderson W K, Alauzet F, Loseille A. 2021. Comparing unstructured adaptive mesh solutions for the high lift common research airfoil. AIAA Journal, 59: 3566-3584. doi: 10.2514/1.J060088 [88] Moigne Y L. Adaptive mesh refinement sensors for vortex flow simulations. European Congress on Computational Methods in Appied Sciences and Engineering, Jyvaskyla, 2004, 6: 24-28. [89] Moxey D, Green M D, Sherwin S J, Peiro J. 2015. An isoparametric approach to high-order curvilinear boundary-layer meshing. Computer Methods in Applied Mechanics and Engineering, 23: 636-650. [90] Mozaffari S, Guilmineau E, Visonneau M, Wackers J. 2022. Average-based mesh adaptation for hybrid RANS/LES simulation of complex flows. Computers and Fluids, 232: 105202. doi: 10.1016/j.compfluid.2021.105202 [91] Nagata T. 2005. Simple local interpolation of surfaces using normal vectors. Computer Aided Geometric Design, 22: 327-347. doi: 10.1016/j.cagd.2005.01.004 [92] Nemec M, Aftosmis M, Wintzer M. Adjoint-based adaptive mesh refinement for complex geometries. AIAA Paper, 2008: 725. [93] Odier N, Thacker A, Harnieh M, Staffelbach G, Gicquel L. 2021. A mesh adaptation strategy for complex wall-modeled turbomachinery LES. Computers and Fluids, 214: 104766. doi: 10.1016/j.compfluid.2020.104766 [94] Palacios F, Duraisamy K, Alonso J J, Zuazua E. 2012. Robust grid adaptation for efficient uncertainty quantification. AIAA Journal, 50: 1538-1546. doi: 10.2514/1.J051379 [95] Park M A. Adjoint-based, three-dimensional error prediction and grid adaptation. AIAA Paper, 2002: 3286. [96] Park M A, Darmofal D L. Parallel anisotropic tetrahedral adaptation. AIAA Paper, 2008: 917. [97] Park M A, Carlson J-R. Turbulent output-based anisotropic adaptation. AIAA Paper, 201: 168. [98] Park M A, Krakos J A, Michal T, Loseille A, Alonso J J. 2016. Unstructured grid adaptation: status, potential impacts, and recommended investments toward CFD vision 2030. 46th AIAA Fluid Dynamics Conference. Washington, D. C. [99] Park M A, Barral N, Ibanez D, Kamenetskiy D S, Krakos J A, Michal T, Loseille A. 2018. Unstructured grid adaptation and solver technology for turbulent flows. 2018 AIAA Aerospace Sciences Meeting. Kissimmee, Florida. [100] Park M A, Kleb B, Anderson W K, Wood S L, Balan A, Zhou B Y, Gauger N R. 2020. Exploring unstructured mesh adaptation for hybrid Reynolds-averaged Navier-Stokes/large eddy simulation. In AIAA Scitech 2020 Forum. Orlando, FL. [101] Pirzadeh S Z. An adaptive unstructured grid method by grid subdivision, local remeshing, and grid movement. AIAA Paper, 1999: 3255. [102] Qin N, Zhu Y. Grid adaptation for shock/turbulent boundary layer interaction. AIAA Paper, 1998: 0227. [103] Robichaud M, Ait Ali Yahia D, Peeters M, Baruzzi G, Kozel V, Habashi W G. 3-D anisotropic adaptation for external and turbomachinery flows on hybrid unstructured grids. AIAA Paper, 2000: 2248. [104] Roy C J. Strategies for driving mesh adaptation in CFD. AIAA Paper, 2009: 1302. [105] Sahni O, Ovcharenko A, Chitale K C, Jansen K E. 2017. Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations. Engineering with Computers, 33: 767-795. doi: 10.1007/s00366-016-0437-2 [106] Schloegel K, Karypis G, and Kumar V. 2001. Wavefront diffusion and LMSR: algorithms for dynamic repartitioning of adaptive meshes. IEEE Transactions on Parallel and Distributed Systems, 12: 451-466. doi: 10.1109/71.926167 [107] Senguttuvan V, Chalasani S, Luke E A, Thompson D S. Adaptive mesh refinement using general elements. AIAA Paper, 2005: 927. [108] Shenoy R, Smith M J, Park M A. 2014. Unstructured overset mesh adaptation with turbulence modeling for unsteady aerodynamic interactions. Journal of Aircraft, 51: 161-174. doi: 10.2514/1.C032195 [109] Shephard M S, Flaherty J E, Jansen K E, Li X, Luo X, Chevaugeon N, Remacle J F, Beall M W, O’Bara R M. 2005. Adaptive mesh generation for curved domains. Applied Numerical Mathematics, 52: 251-271. doi: 10.1016/j.apnum.2004.08.040 [110] Sheshadri A, Crabilly J, Jameson A. Mesh deformation and shock capturing techniques for high-order simulation of unsteady compressible flows on dynamic meshes. AIAA Paper, 2015: 1741 [111] Shih A, Ito Y, Koomullil R. Solution adaptive mesh generation using feature-aligned embedded surface meshes. AIAA Paper, 2007: 558. [112] Si H, Gärtner K. 3D boundary recovery by constrained Delaunay tetrahedralization. International Journal for Numerical Methods in Engineering, 2011, 85: 1341–1364. [113] Silva L, Coupez T, Digonnet H. 2016. Massively parallel mesh adaptation and linear system solution for multiphase flows. International Journal of Computational Fluid Dynamics, 30: 431-436. doi: 10.1080/10618562.2016.1223066 [114] Sirois Y, McKenty F, Gravel L, Guibault F. 2012. Hybrid mesh adaptation applied to industrial numerical combustion. International Journal for Numerical Methods in Fluids, 70: 222-245. [115] Slotnick J, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis D. CFD vision 2030 study: a path to revolutionary computational aeroscience. NASA/CR, 2014: 218178. [116] Soni B K, Koomullil R, Thompson D S, Thornburg H. 2000. Solution adaptive grid strategies based on point redistribution. Computer Methods in Applied Mechanics and Engineering, 189: 1183-1204. doi: 10.1016/S0045-7825(99)00373-4 [117] Soukov S A. 2022. Parallel CFD-algorithm on unstructured adaptive meshes. Mathematical Models and Computer Simulations, 14: 19-27. doi: 10.1134/S2070048222010197 [118] Stiller J. 2007. Point-normal interpolation schemes reproducing spheres, cylinders and cones. Computer Aided Geometry Design, 24: 286-301. doi: 10.1016/j.cagd.2007.03.007 [119] Su X R. 2015. Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi-block structured curvilinear mesh. International Journal for Numerical Methods in Fluids, 77: 747-766. doi: 10.1002/fld.4004 [120] Tang J, Ma M, Li B, Cui P. 2019. A local and fast interpolation method for mesh deformation. Progress in Computational Fluid Dynamics, 19: 282-292. doi: 10.1504/PCFD.2019.102042 [121] Tang J, Cui P C, Li B, Zhang Y B, Si H. 2020. Parallel hybrid mesh adaptation by refinement and coarsening. Graphical Models, 111: 101084. doi: 10.1016/j.gmod.2020.101084 [122] Tang J, Zhang J, Li B, Zhou N C. 2020. Unsteady flow simulation with mesh adaptation. International Journal of Modern Physics B, 34: -2040080. [123] Tang J, Zhang J, Wu X J, Zhang Y B, Zhou N. 2022. Parallel implementation for dynamic mesh optimization on distributed computer system. 2022 6th High Performance Computing and Cluster Technologies Conference, Fuzhou, China. [124] Vanharen J, Loseille A, Alauzet F. Nearfield anisotropic mesh adaptation for the third AIAA sonic boom workshop. AIAA Paper, 2021: 0347. [125] Venditti D A, Darmofal D L. 2002. Grid adaptation for functional outputs: application to two-dimensional inviscid flows. Journal of Computational Physics, 176: 40-69. doi: 10.1006/jcph.2001.6967 [126] Vivarelli G, Qin N, Shahpar S. Combined Hessian and adjoint error-based anisotropic mesh adaptation for turbomachinery flows. AIAA Paper, 2017: 1946. [127] Vivarelli G, Qin N, Shahpar S, Radford D. 2021. Anisotropic adjoint sensitivity-based mesh movement for industrial applications. Computers and Fluids, 221: 104929. doi: 10.1016/j.compfluid.2021.104929 [128] Waithe K. Application of USM3D for sonic boom prediction by utilizing a hybrid procedure. 46th AIAA Aerospace Sciences Meeting and Exhibit. Savannah, GA, 2008. [129] Waltz J. Parallel adaptive refinement for 3d unstructured grids. AIAA Paper, 2003: 1115. [130] Wang G, Mian H H, Ye Z Y. 2015. Improved point selection method for hybrid-unstructured mesh deformation using radial basis functions. AIAA Journal, 53: 1016-1025. doi: 10.2514/1.J053304 [131] Woopen M, May G, Schütz J. 2014. Adjoint-based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods. International Journal for Numerical Methods in Fluids, 76: 811-834. doi: 10.1002/fld.3959 [132] Wu T, Liu X, An W, Huang Z, Lyu H. 2022. A mesh optimization method using machine learning technique and variational mesh adaptation. Chinese Journal of Aeronautics, 35: 27-41. doi: 10.1016/j.cja.2021.05.018 [133] Xiao Z, Ollivier-Gooch C, Vazquez J D Z. 2022. Anisotropic tetrahedral mesh adaptation with improved metric alignment and orthogonality. Computer Aided Design, 143: 103136. doi: 10.1016/j.cad.2021.103136 [134] Xie Z Q, Sevilla R, Hassan O, Morgan K. 2013. The generation of arbitrary order curved meshes for 3d finite element analysis. Computational Mechanics, 51: 361-374. doi: 10.1007/s00466-012-0736-4 [135] Xu J, Chernikov A N. 2014. Automatic curvilinear quality mesh generation driven by smooth boundary and guaranteed fidelity. Procedia Engineering, 82: 200-212. doi: 10.1016/j.proeng.2014.10.384 [136] Yamahara T, Nakahashi K, Kim H-J. Adaptive mesh refinement using viscous adjoint method for multi-element airfoil computations. AIAA Paper, 200: 416. [137] Yang H Q, Chen Z J, Przekwas A. Adaptive Mesh refinement with high-order scheme for an unstructured pressure-based solver. AIAA Paper, 2014: 0077. [138] Zaki M, Ruffin S M. Conservation and grid adaptation enhancements to a normal ray refinement technique for Cartesian-grid based Navier-Stokes solvers. AIAA Paper, 2012: 0301. [139] Zhang S J, Liu J, Chen Y S. Adaptation for hybrid unstructured grid with hanging node method. AIAA Paper, 2001: 2657. [140] Zou J F, Zhou C L, Zhang Y, Zheng Y. 2021. Verification of anisotropic mesh adaptation for unsteady mixing and reacting flow. AIAA Journal, 59: 4071-4085. doi: 10.2514/1.J060098 -
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