EI、Scopus 收录
中文核心期刊
Quick Search Issue Search Advanced Search
Volume 57 Issue 6
Jun.  2025
Turn off MathJax
Article Contents
Abstract
References
Related Articles
Deng Lu, Song Lunji, Luo Canyan, Gao He, Bi Lin. Cartesian grid fluid simulation method based on adaptive normal ray refinement. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(6): 1362-1371. DOI: 10.6052/0459-1879-25-073
Citation: Deng Lu, Song Lunji, Luo Canyan, Gao He, Bi Lin. Cartesian grid fluid simulation method based on adaptive normal ray refinement. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(6): 1362-1371. DOI: 10.6052/0459-1879-25-073
shu

CARTESIAN GRID FLUID SIMULATION METHOD BASED ON ADAPTIVE NORMAL RAY REFINEMENT

  • *.

    College of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

  • †.

    State Key Laboratory of Aerodynamics, Mianyang 621000, Sichuan, China

  • **.

    Hypersonic Technology Laboratory, National University of Defense Technology, Changsha 410073, China

  • Received Date: February 19, 2025
  • Accepted Date: April 16, 2025
  • Available Online: April 16, 2025
  • Published Date: April 17, 2025
    Graphical Abstract
    • Abstract
  • In viscous flow simulations, the velocity gradient in the normal direction of the wall is much larger than that in the tangential direction, presenting a significant anisotropic feature. Traditional isotropic Cartesian grid methods face the challenges of a sharp increase in the number of grids and a decline in computational efficiency when capturing the details of boundary layer flows. To address this issue, this paper proposes a Cartesian grid viscous fluid simulation method based on adaptive normal ray refinement (ANRR). The core of this method lies in adaptively generating normal ray seed points according to the degree of angle change in the tangential direction of the surface, and performing grid refinement near the normal rays to accurately capture the characteristics of boundary layer flows. Meanwhile, coarser grids are used for transition between rays, effectively reducing the overall number of grids while maintaining computational accuracy. Then, an efficient information transfer technology between rays is constructed through interpolation to ensure the accuracy of the flow field solution process. Finally, typical cases such as laminar flow over a flat plate, low Reynolds number flow around a circular cylinder, and flow around an NACA0012 airfoil are used for model verification. The results show that compared with the traditional geometric adaptive grid refinement method, the ANRR grid method significantly reduces the grid scale in the boundary layer flow region, improves computational efficiency while maintaining high accuracy, and provides a new solution for the efficient solution of viscous flow problems using adaptive Cartesian grids.
    • FullText(HTML)
    • References (41)
  • [1]
    Buning PG, Nichols RH. Overflow2 training class-afternoon session//10th Symposium on Overset Composite Grids & Solution Technology, Moffett Field, 2010
    [2]
    Spurlock WM, Aftosmis MJ, Nemec M. Cartesian Mesh Simulations for the third AIAA sonic boom prediction workshop. Journal of Aircraft, 2021, 59(3): 708-724
    [3]
    陈坚强, 袁先旭, 涂国华等. 计算流体力学2035愿景. 北京: 科学出版社, 2023 (Chen Jianqiang, Yuan Xianxu, Tu Guohua, et al. Computational Fluid Dynamics 2035 Vision in China. Beijing: Science Press, 2023 (in Chinese)

    Chen Jianqiang, Yuan Xianxu, Tu Guohua, et al. Computational Fluid Dynamics 2035 Vision in China. Beijing: Science Press, 2023 (in Chinese)
    [4]
    Anderson GR, Aftosmis MJ, Nemec M. Cart3D simulations for the second AIAA sonic boom prediction workshop. Journal of Aircraft, 2019, 56(3): 896-911 doi: 10.2514/1.C034842
    [5]
    Mani M, Dorgan AJ. A perspective on the state of aerospace computational fluid dynamics technology. Annual Review of Fluid Mechanics, 2023, 55(1): 431-457 doi: 10.1146/annurev-fluid-120720-124800
    [6]
    Zeeuw De. A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations. [PhD Thesis]. Ann Arbor: University of Michigan, 1993
    [7]
    Lourenço MA, Padilla EL. An octree structured finite volume based solver. Applied Mathematics and Computation, 2020, 365: 1-28
    [8]
    孟爽. 各向异性自适应笛卡尔网格方法研究及在高速列车中的应用. [博士论文]. 长沙: 中南大学, 2023 (Meng Shuang. Research on anisotropic adaptive Cartesian grid method and its application to high-speed trains. [PhD Thesis]. Changsha: Central South University, 2023 (in Chinese)

    Meng Shuang. Research on anisotropic adaptive Cartesian grid method and its application to high-speed trains. [PhD Thesis]. Changsha: Central South University, 2023 (in Chinese)
    [9]
    罗灿炎. 浸入式笛卡尔网格数值方法及高速列车气动性能应用研究. [博士论文]. 长沙: 中南大学, 2024 (Luo Canyan. Immersed boundary Cartesian grid numerical method and its application in high-speed train aerodynamics. [PhD Thesis]. Changsha: Central South University, 2024 (in Chinese)

    Luo Canyan. Immersed boundary Cartesian grid numerical method and its application in high-speed train aerodynamics. [PhD Thesis]. Changsha: Central South University, 2024 (in Chinese)
    [10]
    Meng S, Zhou D, Yuan X, et al. Enhanced strategy for adaptive Cartesian grid generation with arbitrarily complex 3D geometry. Advances in Engineering Software, 2022, 174: 103304 doi: 10.1016/j.advengsoft.2022.103304
    [11]
    Nakahashi K. Aeronautical CFD in the age of petaflops-scale computing: From unstructured to Cartesian meshes. European Journal of Mechanics B/Fluids, 2013, 40: 75-86 doi: 10.1016/j.euromechflu.2013.02.005
    [12]
    Chawner JR, Dannenhoffer J, Taylor NJ. Geometry, mesh generation, and the CFD 2030 vision//46th AIAA Fluid Dynamics Conference, Washington, 2016
    [13]
    Verzicco R. Immersed boundary methods: Historical perspective and future outlook. Annual Review of Fluid Mechanics, 2023, 55(1): 129-155 doi: 10.1146/annurev-fluid-120720-022129
    [14]
    赵宁, 刘剑明, 田琳琳等. 可压缩流动问题笛卡尔网格模拟方法研究进展与展望. 力学学报, 2025, 57(2): 285-314 (Zhao Ning, Liu Jianming, Tian Linlin, et al. Progress and prospects of cartesian mesh simulation methods for compressible flow problems. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(2): 285-314 (in Chinese) doi: 10.6052/0459-1879-24-374

    Zhao Ning, Liu Jianming, Tian Linlin, et al. Progress and prospects of cartesian mesh simulation methods for compressible flow problems. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(2): 285-314 (in Chinese) doi: 10.6052/0459-1879-24-374
    [15]
    Wang ZJ, Chen RF. Anisotropic solution-adaptive viscous Cartesian grid method for turbulent flow simulation. AIAA Journal, 2002, 40(10): 1969-1978
    [16]
    Li K, Wu ZN. Nonet-cartesian grid method for shock flow computations. Journal of Scientific Computing, 2003, 20(3): 303-329
    [17]
    Capizzano F. A compressible flow simulation system based on Cartesian grids with anisotropic refinements//45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, 2007
    [18]
    Keats WA, Lien FS. Two-dimensional anisotropic cartesian mesh adaptation for the compressible Euler equations. International Journal for Numerical Methods in Fluids, 2010, 46(11): 1099-1125
    [19]
    Steger JL, Dougherty FC, Benek JA. A chimera grid scheme//ASME Mini-Symposium on Advances in Grid Generation, Houston, 1982
    [20]
    Karman LJS. Splitflow-A 3D unstructured Cartesian/prismatic grid CFD code for complex geometries//33rd Aerospace Sciences Meeting and Exhibit, Reno, 1995
    [21]
    常兴华, 王年华, 马戎等. 并行重叠/变形混合网格生成技术及其应用. 气体物理, 2019, 4(6): 12-21 (Chang Xinghua, Wang Nianhua, Ma Rong, et al. Dynamic hybrid mesh generator coupled with overset and deformation in parallel environment. Physics of Gases, 2019, 4(6): 12-21 (in Chinese)

    Chang Xinghua, Wang Nianhua, Ma Rong, et al. Dynamic hybrid mesh generator coupled with overset and deformation in parallel environment. Physics of Gases, 2019, 4(6): 12-21 (in Chinese)
    [22]
    Ueno Y, Ochi A. Airframe noise prediction using Navier-Stokes code with Cartesian and boundary-fitted layer meshes//25th AIAA/CEAS Aeroacoustics Conference, Delft, 2019
    [23]
    Chesshire G, Henshaw WD. Composite overlapping meshes for the solution of partial differential equations. Journal of Computational Physics, 1990, 90: 1-64 doi: 10.1016/0021-9991(90)90196-8
    [24]
    Sitaraman J, Floros M, Wissink A, et al. Parallel domain connectivity algorithm for unsteady flow computations using overlapping and adaptive grids. Journal of Computational Physics, 2010, 229(12): 4703-4723 doi: 10.1016/j.jcp.2010.03.008
    [25]
    韩少强, 宋文萍, 韩忠华等. 高速共轴刚性旋翼非定常流动高精度数值模拟. 航空学报, 2024, 45(9): 177-196 (Han Shaoqiang, Song Wenping, Han Zhonghua, et al. High-accuracy numerical-simulation of unsteady flow over high-speed coaxial rigid rotors. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 177-196 (in Chinese)

    Han Shaoqiang, Song Wenping, Han Zhonghua, et al. High-accuracy numerical-simulation of unsteady flow over high-speed coaxial rigid rotors. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 177-196 (in Chinese)
    [26]
    刘周, 周伟江. 适于黏性计算的自适应笛卡儿网格生成及其应用. 航空学报, 2009, 30(12): 2280-2287 (Liu Zhou, Zhou Weijiang. Adaptive viscous Cartesian grid generation and application. Acta Aeronautica et Astronautica Sinica, 2009, 30(12): 2280-2287 (in Chinese) doi: 10.3321/j.issn:1000-6893.2009.12.007

    Liu Zhou, Zhou Weijiang. Adaptive viscous Cartesian grid generation and application. Acta Aeronautica et Astronautica Sinica, 2009, 30(12): 2280-2287 (in Chinese) doi: 10.3321/j.issn:1000-6893.2009.12.007
    [27]
    Lee JD. Development of an efficient viscous approach in a Cartesian grid framework and application to rotor-fuselage interaction. [PhD Thesis]. Atlanta: Georgia Institute of Technology, 2006
    [28]
    沈志伟, 赵宁, 胡偶. 可压缩黏性流动笛卡尔网格虚拟单元方法研究. 空气动力学学报, 2014, 32(6): 748-754 (Shen Zhiwei, Zhao Ning, Hu Ou. Numerical research of Cartesian based ghost cell method for compressible viscous flows. Acta Aerodynamica Sinica, 2014, 32(6): 748-754 (in Chinese)

    Shen Zhiwei, Zhao Ning, Hu Ou. Numerical research of Cartesian based ghost cell method for compressible viscous flows. Acta Aerodynamica Sinica, 2014, 32(6): 748-754 (in Chinese)
    [29]
    Liu X, Yang B, Ji C, et al. Research on the turbine blade vibration based on the immersed boundary method. Journal of Fluids Engineering, 2018, 140(6): 061402 177
    [30]
    Yang B, Song M, Zhu G. Research on the ghost cell immersed boundary method for compressible flow. Processes, 2024, 12: 1182 doi: 10.3390/pr12061182
    [31]
    罗灿炎, 毕林, 徐晶磊等. 笛卡尔网格下不同湍流模型的壁面函数方法研究. 工程力学, 2024, 41(8): 11-22 (Luo Canyan, Bi Lin, Xu Jinglei, et al. Study on wall function method of different turbulence models based on cartesian grid. Engineering Mechanics, 2024, 41(8): 11-22 (in Chinese)

    Luo Canyan, Bi Lin, Xu Jinglei, et al. Study on wall function method of different turbulence models based on cartesian grid. Engineering Mechanics, 2024, 41(8): 11-22 (in Chinese)
    [32]
    Ruffin SM, Sekhar S. A normal ray refinement technique for Cartesian-grid based Navier-Stokes solvers. International Journal of Computational Fluid Dynamics, 2012, 26(4): 231-246 doi: 10.1080/10618562.2012.691970
    [33]
    Zaki M, Ruffin SM. Conservation and grid adaptation enhancements to a normal ray refinement technique for cartesian-grid based navier-stokes solvers//50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Nashville, 2012
    [34]
    Arslanbekov R, Kolobov V, Ruffin SM, et al. Implementation and evaluation of normal ray refinement technique in adaptive cartesian framework//42nd AIAA Fluid Dynamics Conference and Exhibit, New Orleans, 2013
    [35]
    Bopp MS, Dement DC, Ruffin SM, et al. An improved object-oriented cartesian grid framework implementing three dimensional normal ray refinement//32nd AIAA Applied Aerodynamics Conference, Atlanta, 2014
    [36]
    Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics, 1997, 135: 250-258 doi: 10.1006/jcph.1997.5705
    [37]
    Leer BV. Towards the ultimate conservation difference scheme V. A second-order sequel to Godunov’s Method. Journal of Computational Physics, 1979, 32: 101-136
    [38]
    Tritton DJ. Experiments on the flow past a circular cylinder at low reynolds numbers. Journal of Fluid Mechanics, 1959, 6(4): 547-567 doi: 10.1017/S0022112059000829
    [39]
    Zhong M, Zou S, Pan D et al. A simplified discrete unified gas kinetic scheme for incompressible flow. Physics of Fluids, 2020, 32: 093601 doi: 10.1063/5.0021332
    [40]
    Jawahar P, Kamath H. A high-resolution procedure for euler and Navier-Stokes computations on unstructured grids. Journal of Computational Physics, 2000, 164(1): 165-203 doi: 10.1006/jcph.2000.6596
    [41]
    Dervieux A, Rizzi A, Van Leer B, et al. Numerical simulation of compressible Euler flows. Biotechnology Progress, 1989, 30(3): 523-534
    • Related Articles

  • Related Articles

    [1]Zhang Dayu, Luo Jianjun, Wang Hui, Ma Xiaofei. LOCKING PROBLEM AND LOCKING ALLEVIATION OF ANCF/CRBF PLANAR BEAM ELEMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 874-889. DOI: 10.6052/0459-1879-20-296
    [2]Wei Wei, Jiang Qinghui, Zhou Chuangbing. STUDY ON NUMERICAL MANIFOLD METHOD BASED ON FINITE DEFORMATION THEORY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 78-86. DOI: 10.6052/0459-1879-13-081
    [3]Shijun Li, Guowen Lin, Dawei Ma. The research on the axisymmetric plane strain problem of compressed hollow cylinder composed of elastomeric foam[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 579-582. DOI: 10.6052/0459-1879-2010-3-2009-509
    [4]Finite element model with equivalent beam elements of single-walled carbon nanotubes[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(4): 488-495. DOI: 10.6052/0459-1879-2006-4-2005-328
    [5]DISCRETE SLIP MODEL OF CRYSTALS AND FINITE ELEMENT ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(3): 278-286. DOI: 10.6052/0459-1879-1997-3-1995-227
    [6]AN ASYMPTOTIC ANALYSIS OF THE ELASTOSTATIC FIELD WITH FINITE DEFORMATION NEAR THE TIP OF AN INTERFACE-CRACK[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(4): 440-450. DOI: 10.6052/0459-1879-1994-4-1995-566
    [7]ANTI-PLANE WAVE MOTION IN FINITE ELEMENT MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 1992, 24(2): 207-215. DOI: 10.6052/0459-1879-1992-2-1995-729
    [8]A 3-D COMPOSITE CONSTITUTIVE MODEL FOR ANALYSIS OF FINITE ELASTO-PLASTIC DEFORMATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1992, 24(2): 162-170. DOI: 10.6052/0459-1879-1992-2-1995-724
    [9]ON THE INVARIANT REPRESENTATION OF SPIN AND ITS APPLICATION IN FINITE DEFORMATION THEORY[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(5): 566-573. DOI: 10.6052/0459-1879-1990-5-1995-985

Catalog

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (61) PDF downloads (32) Cited by()
    Related

    Download Center

    Author Center

      Copyright © Editorial Office of the Chinese Journal of Mechanics   京ICP备05039218号-1

      Address：15 Beishihuan Xi Lu, Haidian District, Beijing, China   China Pos：100190

      Tel：010-62536271

      Email：lxxb@cstam.org.cn

      Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

      /

      DownLoad:  Full-Size Img  PowerPoint
      Return
      Return