Citation: | ZHANG Weiwei, GONG Yiming, LIU Yilang. Time discretization methods in the computation of unsteady flow[J]. Advances in Mechanics, 2019, 49(1): 201907. doi: 10.6052/1000-0992-17-018 |
[1] |
陈琦, 陈坚强, 谢昱飞, 袁先旭. 2014a. 谐波平衡法在非定常流场中的应用. 航空学报, 35: 736-743
(Chen Q, Chen J Q, Xie Y F, et al.2014a. Application of harmonic balance method to unsteady flow field. Acta Aeronautica et Astronautica Sinica, 35: 736-743).
|
[2] |
陈琦, 陈坚强, 袁先旭, 谢昱飞. 2014b. 谐波平衡法在动导数快速预测中的应用研究. 力学学报, 46: 183-190
(Chen Q, Chen J Q, Yuan X X, et al.2014b. Application of a harmonic balance method in rapid predictions of dynamic stability derivatives. Chinese Journal of Theoretical and Applied Mechanics, 46: 183-190).
|
[3] |
刘南, 白俊强, 刘艳, 华俊.2016. 基于谐波平衡法和V-g法的高效颤振预测分析(英文).空气动力学学报, 34: 631-637
(Liu N, Bai J Q, Liu Y, et al.2016. Efficient flutter prediction based on harmonic balance and V-g methods. Acta Aerodynamica Sinica, 34: 631-637).
|
[4] |
刘南. 2016. 机翼跨声速非线性颤振及高校分析方法研究. [博士论文]. 西安: 西北工业大学
(Liu N.2016. Investigation of transonic nonlinear flutter and efficient analysis approach. [PhD Thesis]. Xi'an: Northwestern Polytechnical University).
|
[5] |
谢立军, 杨云军, 刘周, 周伟江. 2015. 基于时间谱方法的飞行器动导数高效计算技术. 航空学报, 36: 2016-2026
(Xie L J, Yang Y J, Liu Z, Zhou W J.2015. A high efficient method for computing dynamic derivatives of aircraft based on time spectral method. Acta Aeronautica et Astronautica Sinica, 36: 2016-2026).
|
[6] |
袁新, 苏欣荣. 2009. 谱方法用于非定常流动计算的隐式求解. 工程热物理学报, 30: 2010-2012
(Yuan X, Su X Y.2009. Implicit solution of time spectral method for periodic unsteady flows. Journal of Engineering Thermophysics, 30: 2010-2012).
|
[7] |
赵军, 刘宝杰. 2008. 非线性谐波法的进一步校验分析. 航空动力学报, 23: 680-686
(Zhao J, Liu B J.2008. Further verification of nonlinear harmonic method. Journal of Aerospace Power, 23: 680-686).
|
[8] |
Badcock K J, Richards B E, Woodgate M A.2000. Elements of computational fluid dynamics on block structured grids using implicit solvers. Progress in Aerospace Sciences, 36: 351-392.
|
[9] |
Beam R M, Warming R F.1976. An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. Journal of Computational Physics, 22: 87-110.
|
[10] |
Besem F M, Thomas J P, Kielb R E, Dowell E H.2016. An aeroelastic model for vortex-induced vibrating cylinders subject to frequency lock-in. Journal of Fluids & Structures, 61: 42-59.
|
[11] |
Bonfiglioli A, Carpentieri B, Campobasso S.2009. Parallel unstructured three-dimensional turbulent flow analyses using efficiently preconditioned Newton-Krylov Solvers//19th AIAA Computational Fluid Dynamics, San Antonio.
|
[12] |
Briley W R, Mcdonald H.1975. Solution of the three-dimensional compressible Navier Stokes equations by an implicit technique. Lecture Notes in Physics, 35: 105-110.
|
[13] |
Brunton S L, Rowley C W.2013. Empirical state-space representations for Theodorsen's lift model. Journal of Fluids & Structures, 38: 174-186.
|
[14] |
Butsuntorn N, Jameson A.2008a. Time spectral method for rotorcraft flow. [PhD Thesis]. Stanford CA: Stanford University.
|
[15] |
Butsuntorn N, Jameson A.2008b. Time spectral method for rotorcraft flow with vorticity confinement//26th AIAA Applied Aerodynamics Conference.
|
[16] |
Butsuntorn N.2008. Time spectral method for rotorcraft flow with vorticity confinement. [PhD Thesis]. California: Stanford University.
|
[17] |
Butcher J C.2016. Numerical Methods for Ordinary Differential Equations. (First Edition). John Wiley & Sons.
|
[18] |
Chen T, Vasanthakumar P, He L.2000. Analysis of unsteady blade row interaction using nonlinear harmonic approach.Journal of Propulsion & Power, 17: 651-658.
|
[19] |
Cherif M A, Emamirad H, Mnif M.2012. Derivatives for time-spectral computational fluid dynamics using an automatic differentiation adjoint. AIAA Journal, 50: 2809-2819.
|
[20] |
Choi S, Lee K H, Alonso J J, Datta A.2008. Preliminary study on time-spectral and adjoint-based design optimization of helicopter rotors//AHS specialist meeting, San Francisco, CA.
|
[21] |
Choi S, Datta A.2008. CFD prediction of rotor loads using time-spectral method and exact fluid-structure interface//26th AIAA Applied Aerodynamics Conference.
|
[22] |
Choi S, Lee K, Potsdam M M, Alonso J J.2008. Helicopter rotor design using a time-spectral and adjoint-based method//Aiaa/issmo Multidisciplinary Analysis and Optimization Conference, 412-423.
|
[23] |
Custer C H, Weiss J M, Subramanian V, Clark W S, Hall K C.2012. Unsteady simulation of a 1.5 stage turbine using an implicitly coupled nonlinear harmonic balance method//ASME Turbo Expo: Turbine Technical Conference and Exposition, 2303-2317.
|
[24] |
Dinu A D, Botez R, Cotoi I.2006. Chebyshev polynomials for unsteady aerodynamic calculations in aeroservoelasticity.Journal of Aircraft, 43: 165-171.
|
[25] |
Dong K I, Choi S, Mcclure J E, Skiles F.2015. Mapped Chebyshev pseudospectral method for unsteady flow analysis. AIAA Journal, 53: 1-16.
|
[26] |
Du P, Ning F.2012. The development and application of a time-domain harmonic balance flow solver// ASME 2012 Fluids Engineering Division Summer Meeting Collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012, International Conference on Nanochannels, Microchannels, and Minichannels.
|
[27] |
Dufour G, Gourdain N, Sicot F.2012. A time-domain harmonic balance method for rotor/stator interactions. Journal of Turbomachinery, 134: 11001-11001.
|
[28] |
Ekici K, Hall K C.2007. Nonlinear analysis of unsteady flows in multistage turbomachines using harmonic balance. AIAA Journal, 45: 1047-1057.
|
[29] |
Ekici K, Hall K C.2008. Nonlinear frequency-domain analysis of unsteady flows in turbomachinery with multiple excitation frequencies. AIAA Journal, 46: 1912.
|
[30] |
Ekici K, Beran P.2014. Adjoint sensitivity analysis of low-speed flows using an efficient harmonic balance technique. AIAA Journal, 52: 1330-1336.
|
[31] |
Farhat C, Lesoinne M.2000. Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Computer Methods in Applied Mechanics and Engineering, 182: 499-515.
|
[32] |
Frey C, Ashcroft G, Kersken H P.2015. Simulations of unsteady blade row interactions using linear and non-linear frequency domain methods//ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, V02BT39A037.
|
[33] |
Gopinath A K, Beran P S, Jameson A.2006. Comparative analysis of computational methods for limit-cycle oscillations. AIAA Paper, 2076: 1-4.
|
[34] |
Gopinath A K, Jameson A.2005. Time spectral method for periodic unsteady computations over two-and three-dimensional bodies. AIAA Paper, 1220: 10-13.
|
[35] |
Gopinath A K, Van Der Weide E, Alonso J J, Jameson A.2007. Three-dimensional unsteady multi-stage turbomachinery simulations using the harmonic balance technique//45th AIAA Aerospace Sciences Meeting and Exhibit, 892.
|
[36] |
Guédeney T, Gomar A, Gallard F, Sicot F.2013. Non-uniform time sampling for multiple-frequency harmonic balance computations. Journal of Computational Physics, 236: 317-345.
|
[37] |
Guo Y, Keller J, Parker R G.2012. Dynamic analysis of wind turbine planetary gears using an extended harmonic balance approach: Preprint. Office of Scientific & Technical Information Technical Reports, 8: 4329-4343.
|
[38] |
Hall K C, Clark W S.1991. Prediction of unsteady aerodynamic loads in cascades using the linearized Euler equations on deforming grids//27th Joint Propulsion Conference.
|
[39] |
Hall K C, Crawley E F.1989. Calculation of unsteady flows in turbomachinery using the linearized Euler equations. AIAA Journal, 27: 777-787.
|
[40] |
Hall K C, Crawley E F.1994. A linearized Euler analysis of unsteady flows in turbomachinery. Massachusetts Inst.of Tech.Report, 116: V001T03A035.
|
[41] |
Hall K C, Thomas J P, Clark W S.2002. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA Journal, 40: 879-886.
|
[42] |
Hassan D, Sicot F.2011. A time-domain harmonic balance method for dynamic derivatives predictions.//49th AIAA Aerospace Sciences Meeting including the New Horizons and Aerospace Exposition, 4-7.
|
[43] |
He L.2008. Harmonic solution of unsteady flow around blades with separation. AIAA Journal, 46: 1299-1307.
|
[44] |
He L.2010. Fourier methods for turbomachinery applications. Progress in Aerospace Sciences, 46: 329-341.
|
[45] |
He L, Ning W.1998. Efficient approach for analysis of unsteady viscous flows in turbomachines. AIAA Journal, 36: 2005-2012.
|
[46] |
Huang X, Wang D X.2016. Stabilizing and accelerating solution of harmonic balance equation system using the LU-SGS and block Jacobi methods//ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, V02DT44A026.
|
[47] |
Hull T E, Enright W H, Fellen B M, Sedgwick A E.1972. Comparing numerical methods for ordinary differential equations. SIAM Journal on Numerical Analysis, 9: 603-637.
|
[48] |
Jameson A.1991. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings//Computational Fluid Dynamics Conference.
|
[49] |
Jameson A, Shankaran S.2009. An assessment of dual-time stepping, time spectral and artificial compressibility based numerical algorithms for unsteady flow with applications to flapping wings//19th AIAA Computational Fluid Dynamics, 4273.
|
[50] |
Kurdi M H, Beran P S.2008. Spectral element method in time for rapidly actuated systems. Journal of Computational Physics, 227: 1809-1835.
|
[51] |
Lau S L, Cheung Y K.1981. Amplitude incremental variational principle for nonlinear vibration of elastic systems. Journal of Applied Mechanics, 48: 959.
|
[52] |
Lee B H K, Liu L, Chung K W.2005. Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces. Journal of Sound & Vibration, 281: 699-717.
|
[53] |
Leffell J, Sitaraman J, Lakshminarayan V, Wissink A.2016. Towards efficient parallel-in-time simulation of periodic flows//54th AIAA Aerospace Sciences Meeting (AIAA Paper 2016-0066), San Diego, CA, January 4--8.
|
[54] |
Liu L, Dowell E H.2004. The secondary bifurcation of an aeroelastic airfoil motion: Effect of high harmonics. Nonlinear Dynamics, 37: 31-49.
|
[55] |
Liu L, Dowell E H, Thomas J P.2007. A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces. Journal of Fluids & Structures, 23: 351-363.
|
[56] |
Mavriplis D J, Yang Z, Mundis N.2012. Extensions of time spectral methods for practical rotorcraft problems//50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition paper AIAA, 423: 24.
|
[57] |
McMullen M S.2003. The application of non-linear frequency domain methods to the Euler and Navier-Stokes equations.[PhD Thesis]. California: Stanford University.
|
[58] |
Mcmullen M S, Jameson A.2006. The computational efficiency of non-linear frequency domain methods. Journal of Computational Physics, 212: 637-661.
|
[59] |
Mcmullen M S, Jameson A, Alonso J J.2001. Acceleration of convergence to a periodic steady state in turbomachinery flows. AIAA Journal, 28: 100-152.
|
[60] |
Mcmullen M, Jameson A, Alonso J J.2002. Application of a non-linear frerquency domain solver to the Euler and Navier-stokes equations//40th AIAA Aerospace Sciences Meeting & Exhibit.
|
[61] |
Mcmullen M, Jameson A, Alonso J J.2006. Demonstration of nonlinear frequency domain methods. AIAA Journal, 44: 1428-1435.
|
[62] |
Mundis N L, Mavriplis D J.2013a. GMRES applied to the time-spectral and quasi-periodic time-spectral methods. AIAA Paper, 3084: 24-27.
|
[63] |
Mundis N L, Mavriplis D J.2013b. Quasi-periodic time spectral method for aeroelastic flutter analysis//AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2013-0638.
|
[64] |
Mundis N L, Mavriplis D J.2014. An efficient flexible GMRES solver for the fully-coupled time-spectral aeroelastic system. AIAA Paper, 1427: 13-17.
|
[65] |
Mundis N L, Mavriplis D J.2015a. Wave number independent preconditioning for GMRES time-spectral solvers//53rd AIAA Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, Kissimmee, Florida, 1-21.
|
[66] |
Mundis N L, Mavriplis D J.2015b. Finite-element time discretizations for the unsteady Euler equations//53rd AIAA Aerospace Sciences Meeting, 0569.
|
[67] |
Mundis N L, Mavriplis D J.2016. Toward an optimal solver for time-spectral solutions on unstructured meshes//54th AIAA Aerospace Sciences Meeting, 0069.
|
[68] |
Mundis N L, Mavriplis D J, Sitaraman J.2013. Quasi-periodic time-spectral methods for flutter and gust response//69th Forum of the American Helicopter Society, AHS International, Alexandria.
|
[69] |
Murman S M.2012. Reduced-frequency approach for calculating dynamic derivatives. AIAA Journal, 45: 2005-2840.
|
[70] |
Murman S M, Aftosmis M J, Berger M J.2004. Numerical simulation of rolling airframes using a multilevel Cartesian method. Journal of Spacecraft and Rockets, 41: 426-435.
|
[71] |
Nadarajah S, Jameson A.2007. Optimum shape design for unsteady three-dimensional viscous flows using a nonlinear frequency-domain method. Journal of Aircraft, 44: 1513-1527.
|
[72] |
Ning W, He L.1997. Computation of unsteady flows around oscillating blades using linear and nonlinear harmonic Euler methods//ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, V004T14A039-V004T14A039.
|
[73] |
Pechloff A N, Laschka B.2006. Small disturbance Navier-Stokes method: Efficient tool for predicting unsteady air loads. Journal of Aircraft, 43: 17-29.
|
[74] |
Ronch A D, Ghoreyshi M, Badcock K J, Gortz S, Widhalm M, Dwight R P, Campobasso M S.2010. Linear frequency domain and harmonic balance predictions of dynamic derivatives//AIAA Applied Aerodynamics Conference.
|
[75] |
Ronch A D, Mccracken A J, Badcock K J, Widhalm M, Campobasso M S.2013. Linear frequency domain and harmonic balance predictions of dynamic derivatives. Journal of Aircraft, 50: 694-707.
|
[76] |
Rahmati M T, He L, Wang D X, Li Y S, Wells R G, Krishnababu S K.2014. Nonlinear time and frequency domain methods for multirow aeromechanical analysis. Journal of Turbomachinery, 136: 041010.
|
[77] |
Su X, Yuan X.Implicit solution of time spectral method for periodic unsteady flows. Journal of Engineering Thermophysics, 63: 860-876.
|
[78] |
Salles L, Blanc L, Gouskov A, Jean P.2014. Dual time stepping algorithms with the high order harmonic balance method for contact interfaces with fretting-wear. Journal of Engineering for Gas Turbines & Power, 134: 913-921.
|
[79] |
Thomas J P, Dowell E H, Hall K C.2002. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations. AIAA Journal, 40: 638-646.
|
[80] |
Thomas J P, Dowell E H, Hall K C.2004. Modeling viscous transonic limit cycle oscillation behavior using a harmonic balance approach. Journal of Aircraft, 41: 1266-1274.
|
[81] |
Thomas J P, Hall K C, Dowell E H.2005. Discrete adjoint approach for modeling unsteady aerodynamic design sensitivities. AIAA Journal, 43: 1931.
|
[82] |
Van Der Weide E, Gopinath A, Jameson A.2005. Turbomachinery applications with the time spectral method. AIAA Paper, 4905: 2005.
|
[83] |
Vilmin S, Lorrain E, Hirsch C, Swoboda M.2006. Unsteady flow modeling across the rotor/stator interface using the nonlinear harmonic method//ASME Turbo Expo 2006: Power for Land, Sea, and Air.
|
[84] |
Widhalm M, Dwight R, Thormann R, Hubner A.2010. Efficient computation of dynamic stability data with a linearized frequency domain solver//Eccomas Cfd. DLR.
|
[85] |
Woodgate M A, Barakos G N.2012. Implicit computational fluid dynamics methods for fast analysis of rotor flows. AIAA Journal, 50: 1217-1244.
|
[86] |
Yang Z, Mavriplis D.2010. Time spectral method for periodic and quasi-periodic unsteady computations on unstructured meshes//40th AIAA Fluid Dynamics Conference, 28-1.
|
[87] |
Yang Z, Mavriplis D, Sitaraman J. Yang Z, Mavriplis D, Sitaraman J.2011. Prediction of helicopter maneuver loads using BDF/time spectral method on unstructured meshes//49th AIAA Aerospace Sciences Meeting, 4-7.
|
[88] |
Yi S, Im D, Choi S, Lee D.2015. An efficient fluid-structure interaction analysis based on time-spectral approaches//AIAA 53rd Aerospace Science Meeting, 5-9.
|
[89] |
Zeiler T A.2000. Results of Theodorsen and Garrick revisited. Journal of Aircraft, 37: 918-920.
|