Abstract
The aim of this survey is to discuss some of the difficulties one can encounter both when solving Navier-Stokes equations for incompressible flows by an obstacle and analysing the approximate solutions. Far to be exhaustive, some main aspects of the numerical simulation are deliberately pointed out, in addition to the way the obstacle is taken into account and to the far field boundary conditions. Then, using one of the robust methods it is possible to simulate the transition to turbulence for increasing Reynolds numbers. That means to compute transient solutions which need to be analyze and here is the second topic of this paper. Indeed, the classical tools like Fourier analysis are very efficient as long as the solution is periodic but useless when the solution is more complex. Despite the development of wavelets and new algorithms it seems still difficult to distinguish quasi-periodic and chaotic solutions.
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References
A. Brandt, Multigrid techniques: guide with applications to fluid dynamics, GMD-Studien 85 (1984).
C.-H. Bruneau, P. Fabrie, New efficient boundary conditions for incompressible Navier-Stokes equations: A well-posedness results, M 2 AN 30 (1996).
C.-H. Bruneau, P. Fabrie, Effective downstream boundary conditions for incompressible Navier-Stokes equations, Int. J. Num. Meth. Fluids 19 (1994).
C.-H. Bruneau, C. Jouron, An efficient scheme for solving steady incompressible Navier-Stokes equations, J. Comp. Phys. 89, n 02 (1990).
J.-P. Caltagirone, Sur l'interaction fluide-milieu poreux: application au calcul des efforts exercés sur un obstacle par un fluide visqueux, CRAS 318, série 2 (1994).
C. Canuto, M.-Y. Hussaini, A. Quarteroni, T.-A. Zang, Spectral methods in fluid dynamics, Springer-Verlag (1988).
C. Chui, Wavelets: A tutorial in theory and applications, Academic Press (1992).
G. Danabasoglu, S. Biringen, C.L. Streett, Application of the spectral multidomain method to the Navier-Stokes equations, J. Comp. Phys. 113, n 02 (1994).
M. Farge, E. Goiraud, Y. Meyer, F. Pascal, M.-V. Wickerhauser, Improved predictability of two-dimensional turbulent flows using wavelet packet compression, Fluid Dyn. Res. 10 (1992).
C.-A. Fletcher, Computational techniques for fluid dynamics, Vol. 1 & 2, Springer-Verlag (1991).
V. Girault, P.-A. Raviart, Finite element methods for Navier-Stokes equations: Theory and algorithms, Springer-Verlag (1986).
D. Goldstein, R. Handler, L. Sirovich, Modeling a no-slip flow boundary with an external force field, J. Comp. Phys. 105, n 02 (1993).
P.-M. Gresho, Incompressible fluid dynamics: Some fundamental formulation issues, Ann. Rev. Fluid Mech. 23 (1991).
W. Hackbush, Multigrid methods and applications, Springer-Verlag (1985).
J.-G. Heywood, K. Masuda, R. Rautwann, S.-A. Solarnikov (ed), The Navier-Stokes equations-Theory and Numerical methods, Proceedings of the 2nd Conf., Lecture notes in math. 1530 (1992).
Ch. Hirsch, Numerical Computation of internal and external flows, Vol. 1 & 2 (1990).
P. Le Quere, T. Alziary de Roquefort, Computation of natural convection in two-dimensional cavities with Chebyshev polynomials, J. Comp. Phys. 57 (1985).
S. Mallat, Z. Zhang, Matching pursuits with time-frequency dictionaries, Report 619 Courant Institute (1992).
M. Marion, R. Temam, Navier-Stokes equations: Theory and approximation, Handbook of Numerical Analysis (to appear).
Y. Meyer, S. Roques (ed), Progress in Wavelet Analysis and Applications, Proceedings of the Int. Conf. (1992).
R. Peyret, T.-D. Taylor, Computational methods for fluid flow, Springer-Verlag (1983).
M.-B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, L. Raphael (ed), Wavelets and their applications, Jones and Barlett Publishers (1992).
E.-M. Saiki, S. Biringen, Numerical Simulation of a Cylinder in Uniform Flow: Application of a Virtual Boundary Method, J. Comp. Phys. 123 (1996).
R.-L. Sani, P.-M. Gresho, Résumé and remarks on the open boundary condition minisymposium, Int. J. Num. Meth. in Fluids, 18 (1994).
C. Taylor, J.-H. Chin, G.-M. Homsy (ed), Numerical methods in laminar and turbulent flow, Vol.7, Part 1 & 2, Proceedings of the 7t h Int. Conf (1991).
F. Thomasset, Implementation of finite elements methods for Navier-Stokes equations, Springer-Verlag (1981).
R. Temam, Navier-Stokes equations, North-Holland (1984).
C.-H. Williamson, Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers, J. Fluid Mech. 206 (1989).
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Bruneau, CH. (1997). Numerical simulation and analysis of the transition to turbulence. In: Kutler, P., Flores, J., Chattot, JJ. (eds) Fifteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107075
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DOI: https://doi.org/10.1007/BFb0107075
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