Implicit time spectral method for periodic incompressible flows

AIAA Journal

Volumn 49, Issue 4, 2011, Pages 791-805

  Antheaume, S ^a,b   Corre, C ^a,b  

^a Domaine Universitaire   (France)

^b LEGI   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL COMPRESSIBILITY; COMPUTATIONAL COSTS; FINITE-VOLUME FORMULATION; INCOMPRESSIBLE VISCOUS FLOWS; NUMERICAL SIMULATION; REYNOLDS; SPECTRAL METHODS; STRUCTURED GRID; TIME-PERIODIC FLOWS; TRANSIENT FLOW BEHAVIOR; UNSTRUCTURED GRID;

AIRFOILS; FOURIER ANALYSIS; INCOMPRESSIBLE FLOW; SPECTROSCOPY;

NUMERICAL METHODS;

EID: 79953091942     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.J050785     Document Type: Article

References (33)

1. Peyret, R., and Taylor, T. D., Computational Methods in Fluid Flow, 2nd ed., Springer-Verlag, New York, 1983.
2. Jameson, A., "Time-Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings, " 10th AIAA Computational Fluid Dynamics Conference, AIAA Paper 91-1596, June 1991.
3. Hall, K. C., Thomas, J. P., and Clark, W. S., "Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique, " AIAA Journal, Vol. 40, No. 5, 2002, pp. 879-886 . (Pubitemid 34599874)
4. Gopinath, A., and Jameson, A., "Time Spectral Method for Periodic Unsteady Computations over Two- and Three-Dimensional Bodies, " 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2005-1220, Jan.2005.
5. van der Weide, E., Gopinath, A., and Jameson, A., "Turbomachinery Applications with the Time Spectral Method, " 35th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2005-4905, June 2005.
6. Sicot, F., Puigt, G., and Montagnac, M., "Block-Jacobi Implicit Algorithms for the Time Spectral Method, " AIAA Journal, Vol. 46, No.12, 2008, pp. 3080-3089. doi:10.2514/1. 36792
7. Woodgate, M. A., and Badcock, K. J., "Implicit Harmonic Balance Solver for Transonic Flow with Forced Motions, " AIAA Journal, Vol. 47, No. 4, 2009, pp. 893-901. doi:10.2514/1. 36311
8. Su, X., and Yuan, X., "Implicit Solution of Time Spectral Method for Periodic Unsteady Flows, " International Journal for Numerical Methods in Fluids, Vol. 63, Jan.2009, pp. 860-870. doi:10.1002/fld.2111
9. Ekici, K., and Hall, K. C., "Nonlinear Analysis of Unsteady Flows in Multistage Turbomachines Using Harmonic Balance, " AIAA Journal, Vol. 45, No. 5, 2007, pp.1047-1057. doi:10.2514/1.22888 (Pubitemid 46814140)
10. Butsuntorn, N., and Jameson, A., "Time Spectral Method for Rotorcraft Flow, " 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2008-403, Jan.2008.
11. Antheaume, S., Maitre, T., and Achard, J. -L., "Hydraulic Darrieus Turbines Efficiency for Free Fluid Flow Conditions Versus Power Farms Conditions, " Renewable Energy, Vol. 33, No.10, 2008, pp.2186-2198. doi:10.1016/j. renene.2007.12. 022
12. Amet, E., Maitre, T., Pellone, C., and Achard, J. -L., "2D Numerical Simulations of Blade-Vortex Interaction in a Darrieus Turbine, " Journal of Fluids Engineering, Vol.131, 2009, pp.111103.
13. Jameson, A., "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, AIAA Paper 2009-4273, June 2009.
14. Kinsey, T., and Dumas, G., "Parametric Study of an Oscillating Airfoil in a Power-Extraction Regime, " AIAA Journal, Vol. 46, No. 6, 2008, pp.1318-1330. doi:10.2514/1.26253
15. Kloczko, T., Corre, C., and Beccantini, A., "Low-Cost Implicit Schemes for All-Speed Flows on Unstructured Meshes, " International Journal for Numerical Methods in Fluids, Vol. 58, No. 5, 2008, pp. 493-526. doi:10.1002/fld.1730
16. Chorin, A. J., "A Numerical Method for Solving Incompressible Viscous Flow Problems, " Journal of Computational Physics, Vol.2, No.1, 1967, pp.12-26. doi:10.1016/0021-9991(67)90037-X
17. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, " Journal of Computational Physics, Vol. 43, No.2, 1981, pp. 357-372. doi:10.1016/0021-9991(81)90128-5
18. Barth, T. J., and Jespersen, D. C., "The Design and Application of Upwind Schemes on Unstructured Meshes, " 27th AIAA Aerospace Sciences Meeting, AIAA Paper 89-0366, Jan.1989.
19. Delanaye, M., "Polynomial Reconstruction Finite Volume Schemes for the Compressible Euler and Navier-Stokes Equations on Unstructured Adaptive Grids, " Ph. D. Thesis, Université de Liège, Belgium, The Netherlands, 1996.
20. Taylor, L. K., and Whitfield, D. L., "Unsteady Three-Dimensional Incompressible Euler and Navier-Stokes Solver for Stationary and Dynamic Grids, " 22nd AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference, June 1991.
21. Noh, W., "Cel: A Time-Dependent Two-Space Dimensional Coupled Eulerian-Lagrangian Code, " Methods in Computational Physics, Vol. 3, 1964, pp.117-119.
22. Nakahashi, K., and Deiwert, G. S., "Self Adaptive Grid Method with Application to Airfoil Flow, " AIAA Journal, Vol.25, No. 4, 1987, pp. 513-520. doi:10.2514/3.9655 (Pubitemid 17586228)
23. Batina, J. T., "Unsteady Euler Algorithm with Unstructured Dynamic Mesh for Complex-Aircraft Aerodynamic Analysis, " AIAA Journal, Vol.29, No. 3, 1991, pp. 327-333. doi:10.2514/3.10583
24. Luo, H., Baum, J. D., and Lohner, R., "An Accurate, Fast, Matrix-Free Implicit Method for Computing Unsteady Flows on Unstructured Grids, " Computers and Fluids, Vol. 30, No.2, 2001, pp.137-159. doi:10.1016/S0045-7930(00)00011-6
25. Hassan, O., Sørensen, K. A., Morgan, K., and Weatherill, N. P., "A Method for Time Accurate Turbulent Compressible Fluid Flow Simulation with Moving Boundary Components Employing Local Remeshing, " International Journal for Numerical Methods in Fluids, Vol. 53, No. 8, 2007, pp.1243-1266. doi:10.1002/fld.1255 (Pubitemid 46380582)
26. Koobus, B., and Farhat, C., "Second-Order Time-Accurate and Geometrically Conservative Implicit Schemes for Flow Computations on Unstructured Dynamic Meshes, " Computer Methods in Applied Mechanics and Engineering, Vol.170, Nos.1 -2, 1999, pp.103-129. doi:10.1016/S0045-7825(98) 00207-2
27. Benek, J. A., Steger, J. L., and Dougherty, F. C., "A Flexible Grid Embedding Technique with Application to the Euler Equations, " AIAA Paper 1983-1944, 1983.
28. Kannan, R., and Wang, Z. J., "Overset Adaptive Cartesian/Prism Grid Method for Moving Boundary Flow Problems, " AIAA Journal, Vol. 45, No. 7, 2007, pp.1774-1779. doi:10.2514/1.24200 (Pubitemid 47191254)
29. Jameson, A., and Yoon, S., "Lower-Upper Implicit Schemes with Multiple Grids for the Euler Equations, " AIAA Journal, Vol.25, No. 7, 1987, pp.929-935. doi:10.2514/3.9724 (Pubitemid 17601830)
30. Luo, H., Baum, J. D., and Lohner, R., "A Fast, Matrix-Free Implicit Method for Compressible Flows on Unstructured Grids, " Journal of Computational Physics, Vol.146, No.2, 1998, pp. 664-690. doi:10.1006/jcph.1998. 6076 (Pubitemid 128180423)
31. Shannon, C. E., "Communication in the Presence of Noise, " Proceedings of the Institute of Radio Engineers, Vol. 37, Jan.1949, pp.10-21.
32. Saad, Y., and Schultz, M., "GMRES: A Generalized Minimal Residual Algorithm for Solving Non-Symmetric Linear Systems, " SIAM Journal on Scientific and Statistical Computing, Vol. 7, No. 3, July 1986, pp. 856-869.
33. Liang, C., Kannan, R., and Wang, Z. J., "A p-Multigrid Spectral Difference Method with Explicit and Implicit Smoothers on Unstructured Triangular Grids, " Computers and Fluids, Vol. 38, No.2, 2009, pp.254-265. doi:10.1016/j. compfluid.2008. 02. 004