ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Development of 3rd-order HWCNS and its application in hypersonic flow
Received date: 2014-05-06
Revised date: 2014-10-08
Online published: 2014-10-14
Supported by
National Natural Science Foundation of China (11372342, 11072259, 11301525)
With very high requirements on computation grids, poor stability property and low computational efficiency, the application of high-order schemes to hypersonic flow simulations is greatly constrained. Focusing on these problems, a 3rd-order hybrid cell-node and cell-center weighted compact nonlinear schemes(HWCNS3) is developed. Some improvements are made on the calculation of smoothness indicators and nonlinear weights, resulting in a new scheme named HWCNS3-OP. Spectral properties of different schemes are compared. Discontinuity capturing ability and high frequency waves' capturing ability are evaluated using Lax and Osher-Shu cases. After that HWCNS3-OP is applied to blunt cone and shuttle hypersonic flow simulations to study the prediction accuracy of heat flux and aerodynamic forces in relative practical cases. In these cases, the stability and efficiency property of HWCNS3-OP are investigated in priority. The results indicate that HWCNS3-OP has high resolution and good discontinuity capturing ability, the ability of simulating high frequency waves is improved by 3 times compared with HWCNS3 and by 4 times compared with monotonic upstream-centered scheme for conservation laws(MUSCL), HWCNS3-OP is more stable, and that HWCNS3-OP's computational efficiency is improved by 2-3 times compared with HWCNS of 5th-order. HWCNS3-OP is a high-order scheme suitable for hypersonic flow simulations with complex grids.
YAN Zhenguo , LIU Huayong , MAO Meiliang , MA Yankai , ZHU Huajun . Development of 3rd-order HWCNS and its application in hypersonic flow[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(5) : 1460 -1470 . DOI: 10.7527/S1000-6893.2014.0282
[1] Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126(1): 202-228.
[2] Deng X G, Zhang H X. Developing high-order weighted compact nonlinear schemes[J]. Journal of Computational Physics, 2000, 165(1): 22-44.
[3] Deng X G, Mao M L, Jiang Y, et al. New high-order hybrid cell-edge and cell-node weighted compact nonlinear schemes, AIAA-2011-3857[R]. Reston: AIAA, 2011.
[4] Deng X G, Jiang Y, Mao M L, et al. Developing hybrid cell-edge and cell-node dissipative compact scheme for complex geometry flows[J]. Science China Technological Sciences, 2013, 56(10): 2361-2369.
[5] Vinokur M. An analysis of finite-difference and finite-volume formulations of conservation laws[J]. Journal of Computational Physics, 1989, 81(1): 1-52.
[6] Thomas P D, Lombard C K. Geometric conservation law and its application to flow computations on moving grids[J]. AIAA Journal, 1979, 17(10): 1030-1037.
[7] Deng X G, Mao M L, Tu G H, et al. Geometric conservation law and applications to high-order finite difference schemes with stationary grids[J]. Journal of Computational Physics, 2011, 230(4): 1100-1115.
[8] Nonomura T, Iizuka N, Fujii K. Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids[J]. Computers & Fluids, 2010, 39(2): 197-214.
[9] Deng X G, Min Y B, Mao M L, et al. Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids[J]. Journal of Computational Physics, 2013, 239: 90-111.
[10] Deng X G, Mao M L, Tu G H, et al. Extending weighted compact nonlinear schemes to complex grids with characteristic-based interface conditions[J]. AIAA Journal, 2010, 48(12): 2840-2851.
[11] Wang X G, Mao M L, Deng X G, et al. P-multigrid method based on the fifth order scheme WCNS-E-5[J]. Acta Aerodynamica Sinica, 2012, 30(1): 1-6 (in Chinese). 王新光, 毛枚良, 邓小刚, 等. 基于5阶精度格式WCNS-E-5的P-multigrid方法研究[J]. 空气动力学学报, 2012, 30(1): 1-6.
[12] Yan Z G, Liu H Y, Mao M L, et al. Convergence property investigation of Gmres method based on high-order dissipative compact scheme[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(5): 1181-1192 (in Chinese). 燕振国, 刘化勇, 毛枚良, 等.基于高阶耗散紧致格式的Gmres方法收敛特性研究[J]. 航空学报, 2014, 35(5):1181-1192.
[13] Yan Z G. Investigation of implicit time integration methods with HDCS schemes[D]. Mianyang: China Aerodynamics Research and Development Center, 2013 (in Chinese). 燕振国. 高精度混合线性紧致格式的隐式时间推进方法研究[D]. 绵阳: 中国空气动力研究与发展中心, 2013.
[14] Wang G X, Zhang Y L, Li S, et al. A study on massively parallel computation[J]. Computer Engineering & Science, 2012, 34(8): 125-130 (in Chinese). 王光学, 张玉伦, 李松, 等. WCNS高精度并行软件的大规模计算研究[J]. 计算机工程与科学, 2012, 34(8): 125-130.
[15] Deng X G, Wang G X, Tu G H, et al. Applications of high-order weighted compact nonlinear scheme for complex transonic flows, AIAA-2011-0364[R]. Reston: AIAA, 2011.
[16] Wang Y T, Meng D H, Deng X G. High-order numerical study of complex flow over multi-element airfoil[J]. Acta Aerodynamica Sinica, 2012, 31(1): 88-93 (in Chinese). 王运涛, 孟德虹, 邓小刚. 多段翼型高精度数值模拟技术研究[J]. 空气动力学学报, 2012, 31(1): 88-93.
[17] Wang G X, Deng X G, Liu H Y, et al. Application of high-order scheme (WCNS) at high angles of incidence for delta wing[J]. Acta Aerodynamica Sinica, 2012, 30(1):28-33 (in Chinese). 王光学, 邓小刚, 刘化勇, 等. 高阶精度格式WCNS在三角翼大迎角模拟中的应用研究[J]. 空气动力学学报, 2012, 30(1): 28-33.
[18] Zhao Y F. Application studies of high-order accurate schemes to unsteady flows[D]. Changsha: National University of Defense Technology, 2010 (in Chinese). 赵云飞. 高精度格式在非定常流动中的应用研究[D]. 长沙: 国防科学技术大学, 2010.
[19] Zhao X H, Deng X G, Liu H Y, et al. Some applications of WCNS-e-5 on shock-wave/boundary-layer interactions and aerodynamic heating, AIAA-2011-3858[R]. Reston: AIAA, 2011.
[20] Liu X, Deng X G, Mao M L, et al. A high-order accurate scheme WCNS-e-5 applied to body heat transfer distributions[J]. Chinese Journal of Computational Physics, 2005, 22(5): 393-398 (in Chinese). 刘昕, 邓小刚, 毛枚良, 等. 高精度格式WCNS-e-5计算物面热流[J]. 计算物理, 2005, 22(5): 393-398.
[21] Hu X Y, Wang Q, Adams N A. An adaptive central-upwind weighted essentially non-oscillatory scheme[J]. Journal of Computational Physics, 2010, 229(23):8952-8965.
[22] Ghosh D, Baeder J D. Compact reconstruction schemes with weighted ENO limiting for hyperbolic conservation laws[J]. SIAM Journal of Scientific Computing, 2012, 34(3): 1678-1706.
[23] Borges R, Carmona M, Costa B, et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws[J]. Journal of Computational Physics, 2008, 227(6): 3191-3211.
[24] Castro M, Costa B, Don W S. High order weighted essentially non-oscillatory WENO-z schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 2011, 230(5): 1766-1792.
[25] Tu G H, Deng X G, Mao M L. Spectral property comparison of fifth-order nonlinear WCNS and WENO difference schemes[J]. Acta Aerodynamica Sinica, 2012, 30(6): 709-712 (in Chinese). 涂国华, 邓小刚, 毛枚良. 5阶非线性WCNS和WENO差分格式频谱特性比较[J]. 空气动力学学报, 2012, 30(6): 709-712.
[26] Li P, Zhao Q J. CFD calculations on the interaction flowfield and aerodynamic force of tiltrotor/wing in hover[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(2): 361-371 (in Chinese). 李鹏, 招启军. 悬停状态倾转旋翼/机翼干扰流场及气动力的CFD计算[J]. 航空学报, 2014, 35(2): 361-371.
[27] Liu H Y. Development of numerical method and investigation on performances of supersonic ejectors[D]. Mianyang: China Aerodynamics Research and Development Center, 2009 (in Chinese). 刘化勇. 超声速引射器的数值模拟方法及其引射特性研究[D]. 绵阳: 中国空气动力研究与发展中心, 2009.
[28] Kleb W L, Weilmuenster K J. A high angle of attack inviscid shuttle orbiter computation[J]. Journal of Spacecraft and Rockets, 1992, 29(5): 746-748.
/
| 〈 |
|
〉 |
CJA