Time spectral method for periodic and quasi-periodic unsteady computations on unstructured meshes

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 3, 2011, Pages 213-236

  Mavriplis, D J ^a   Yang, Z ^a  

^a UNIVERSITY OF WYOMING   (United States)

Author keywords

periodic; time spectral; unstructured mesh

Indexed keywords

AEROSPACE ENGINEERING PROBLEMS; COLLOCATION METHOD; CONSERVATION LAW; MULTIGRID CONVERGENCES; PERIODIC; PERIODIC BEHAVIOR; PERIODIC FLOW; PITCHING AIRFOILS; POLYNOMIAL BASIS FUNCTIONS; QUASI-PERIODIC; REDUCED COST; SPATIAL DIMENSION; SPECTRAL METHODS; TIME DOMAIN; TIME INSTANCES; TIME SPECTRAL; TIME-ACCURATE; TIME-IMPLICIT; TIME-STEPPING; TRANSIENT BEHAVIOR; UNSTRUCTURED MESH; UNSTRUCTURED MESHES;

AEROSPACE ENGINEERING; AIRFOILS; MESH GENERATION; SPECTROSCOPY;

TIME DOMAIN ANALYSIS;

EID: 79960934551     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116309     Document Type: Article

References (19)

1. C. Canuto, M. .Y. Hussaini, A. Quarteroni, T. A. Zang. Spectral methods in fluid dynamics. Springer, 1987.
2. P. Geuzaine , C. Grandmont , and C. Farhat . Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations. J. Comput. Phys., 191 (2003), No. 1, 206-227. (Pubitemid 37223476)
3. A.K. Gopinath, A. Jameson. Time spectral method for periodic unsteady computations over two- and three- dimensional bodies. AIAA Paper 2005-1220, Jan. 2005
4. D. Gottlieb, S. A. Orszag. Numerical analysis of spectral methods: theory and applications. CBMS-26, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA, 1977.
5. K. C. Hall , E. F. Crawley . Calculation of unsteady flows in turbomachinery using the linearized Euler equations. AIAA Journal, 27 (1989), No. 6, 777-787.
6. K. C. Hall , J. P. Thomas , W. S. Clark . Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. AIAA Journal, 40 (2002), No. 5, 879-886. (Pubitemid 34599874)
7. J. Hesthaven, S. Gottlieb, D. Gottlieb. Spectral methods for time-dependent problems. Cambridge Monographs on Applied and Computational Mathematics, 2007.
8. C. Lanczos. Discourse on Fourier series. Hafner, New York, 1966.
9. D. J. Mavriplis . Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. J. Comput. Phys., 145 (1998), No. 1, 141-165. (Pubitemid 128341069)
10. D. J. Mavriplis , S. Pirzadeh . Large-scale parallel unstructured mesh computations for 3D high-lift analysis. AIAA Journal of Aircraft, 36 (1999), No. 6, 987-998. (Pubitemid 30546407)
11. D. J. Mavriplis , V. Venkatakrishnan . A unified multigrid solver for the Navier-Stokes equations on mixed element meshes. International Journal of Computational Fluid Dynamics, 8 (1997), 247-263. (Pubitemid 127536560)
12. D. J. Mavriplis , Z. Yang . Construction of the discrete geometric conservation law for high-order time accurate simulations on dynamic meshes. J. Comput. Phys., 213 (2006), No. 2, 557-573. (Pubitemid 43240124)
13. M. McMullen, A. Jameson, J. J. Alonso. Acceleration of convergence to a periodic steady state in turbomachineary flows. AIAA Paper 2001-0152, 2001.
14. M. McMullen, A. Jameson, J. J. Alonso. Application of a non-linear frequency domain solver to the Euler and Navier-Stokes equations. AIAA Paper 2002-0120, 2002.
15. E. J. Nielsen , B. Diskin , N. K. Yamaleev . Discrete adjoint-based design optimization of unsteady turbulent flows on dynamic unstructured grids. AIAA Journal, 48 (2010), No. 6, 1195-1206.
16. F. Sicot , G. Puigt , M. Montagnac . Block-Jacobi implicit algorithm for the time spectral method. AIAA Journal, 46 (2008), No. 12, 3080-3089.
17. P. R. Spalart , S. R. Allmaras . A one-equation turbulence model for aerodynamic flows. La Recherche Arospatiale, 1 (1994), 5-21.
18. E. van der Weide, A. K. Gopinath, A. Jameson. Turbomachineary applications with the time spectral method. AIAA Paper 2005-4905, 2005.
19. A. H. van Zuijlen , A. de Boer , H. Bijl . High order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations. J. Comput. Phys., No. 2007 (224), No. 1, 414-430.