A Fourier spectral method for the Navier-Stokes equations with volume penalization for moving solid obstacles

Journal of Computational Physics

Volumn 228, Issue 16, 2009, Pages 5687-5709

  Kolomenskiy, Dmitry ^a   Schneider, Kai ^a,b  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b UNIVERSITÉ DE PROVENCE   (France)

Author keywords

Fluid solid interaction; Freely falling bodies; Spectral method; Volume penalization method

Indexed keywords

CYLINDERS (SHAPES); NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

EFFICIENT NUMERICAL SCHEMES; FALLING BODIES; FLUID SOLID INTERACTION; FOURIER; FREELY FALLING BODY; NAVIER-STOKES EQUATION; PENALISATION; SOLID OBSTACLES; SPECTRAL METHODS; VOLUME PENALIZATION METHOD;

VISCOUS FLOW;

EID: 67649505407     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.04.026     Document Type: Article

References (39)

1. Arquis E., and Caltagirone J.-P. Sur les conditions hydrodynamiques au voisinage d'une interface milieu fluide - milieux poreux: application à la convection naturelle. Comptes Rendus de l'Academie des Sciences Paris II 299 (1984) 1-4
2. Angot P., Bruneau C.-H., and Fabrie P. A penalization method to take into account obstacles in viscous flows. Numerische Mathematik 81 (1999) 497-520
3. A. Azzalini, Étude des écoulements barotropes en rotation en présence ou non d'obstacles: simulations pseudo-spectrales et filtrages en ondelettes, Thèse de doctorat, Université Paris VI Pierre et Marie Curie, 2004.
4. Schneider K. Numerical simulation of the transient flow behaviour in chemical reactors using a penalization method. Computers and Fluids 34 (2005) 1223-1238
5. Farge M., and Schneider K. Analyzing and computing turbulent flows using wavelets. Cours des Houches LXXIV, new trends in turbulence. In: Lesieur M., Yaglom A., and David F. (Eds) (2002), Springer 453-503
6. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1988), Springer-Verlag
7. Cole J.D. On a quasi-linear parabolic equation occurring in aerodynamics. Quarterly of Applied Mathematics 9 (1951) 225-236
8. Schneider K., and Farge M. Numerical simulation of the transient flow behaviour in tube bundles using a volume penalization method. Journal of Fluids and Structures 20 (2005) 555-566
9. Kevlahan N.K.-R., and Ghidaglia J.-M. Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization. European Journal of Mechanics B/Fluids 20 (2001) 333-350
10. Schneider K., Paget-Goy M., Pellegrino G., Verga A., and Farge M. Direct numerical simulation of impulsively started and uniformly accelerated plates using adaptive wavelet and Fourier methods with penalization. Proceedings of Turbulence and Shear Flow Phenomena III 1 (2003) 407-412
11. Unser M., Thévenaz P., and Yaroslavsky L. Convolution-based interpolation for fast, high-quality rotation of images. IEEE Transactions on Image Processing 10 4 (1995) 1371-1381
12. Belmonte A., Eisenberg H., and Moses E. From flutter to tumble: inertial drag and Froude similarity in falling paper. Physical Review Letters 81 (1998) 345
13. Pesavento U., and Wang Z.J. Falling paper: Navier-Stokes solutions model of fluid forces and center of mass elevation. Physical Review Letters 93 (2004) 144501-1
14. Andersen A., Pesavento U., and Wang Z.J. Unsteady aerodynamics of fluttering and tumbling plates. Journal of Fluid Mechanics 541 (2005) 65
15. Andersen A., Pesavento U., and Wang Z.J. Analysis of transitions between fluttering, tumbling and steady descent of falling cards. Journal of Fluid Mechanics 541 (2005) 91
16. Mittal R., and Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics 37 (2005) 239
17. Peskin C.S. The immersed boundary method. Acta Numerica 11 (2002) 479-517
18. Peskin C.S. Flow patterns around heart valves: a numerical method. Journal of Computational Physics 10 2 (1972) 252-271
19. Wang Z.J., and Russell D. Effect of forewing and hindwing interactions on aerodynamic forces and power in hovering dragonfly flight. Physical Review Letters 99 (2007) 148101
20. Sarthou A., Vincent S., Caltagirone J.-P., and Angot P. Eulerian-Lagrangian grid coupling and penalty methods for the simulation of multiphase flows interacting with complex objects. International Journal for Numerical Methods in Fluids 56 8 (2008) 1093-1099
21. Ramière I., Angot P., and Belliard M. A general fictitious domain method with immersed jumps and multilevel nested structured meshes. Journal of Computational Physics 225 2 (2007) 1347-1387
22. Keetels G.H., D'Ortona U., Kramer W., Clercx H.J.H., Schneider K., and van Heijst G.J.F. Fourier spectral and wavelet solvers for the incompressible Navier-Stokes equations with volume penalization: convergence of a dipole-wall collision. Journal of Computational Physics 227 2 (2007) 919-945
23. Edwards W.S., Tuckerman L.S., Friesner R.A., and Sorensen D.C. Krylov methods for the incompressible Navier-Stokes equations. Journal of Computational Physics 110 1 (1994) 82-102
24. Moler C., and Van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45 1 (2003) 3-49
25. Schneider K., and Farge M. Decaying two-dimensional turbulence in a circular container. Physical Review Letters 95 (2005) 244502
26. Arnoldi W.E. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quarterly of Applied Mathematics 9 (1951) 17-25
27. Monin A.S., and Yaglom A.M. Statistical Fluid Mechanics: Mechanics of Turbulence vol. 1 (1971), MIT Press, Cambridge, MA
28. Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. Journal of Computational Physics 209 2 (2005) 448-476
29. Jin C., and Xu K. Numerical study of the unsteady aerodynamics of the freely falling plates. Communications in Computational Physics 3 4 (2008) 834-851
30. Jones M.A., and Shelley M.J. Falling cards. Journal of Fluid Mechanics 540 (2005) 393-425
31. Mittal R., Dong H., Bozkurttas M., Najjar F.M., Vargas A., and von Loebbecke A. A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. Journal of Computational Physics 227 10 (2008) 4825-4852
32. Sharma N., and Patankar N.A. A fast computation technique for the direct numerical simulation of rigid particulate flows. Journal of Computational Physics 205 2 (2005) 439-457
33. Glowinski R., Pan T.W., Hesla T.I., Joseph D.D., and Periaux J. A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. Journal of Computational Physics 169 2 (2001) 363-426
34. Carbou G., and Fabrie P. Boundary layer for a penalization method for viscous incompressible flow. Advances in Differential Equations 8 (2003) 1453-1480
35. Tadmor E., and Tanner J. Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information. Foundations of Computational Mathematics 2 (2002) 155-189
36. P. Angot, J.-P. Caltagirone, New graphical and computational architecture concept for numerical simulation on supercomputers, in: Proceedings of 2nd World Congress on Computational Mechanics, vol. 1, 1990, pp. 973-976
37. Miller L.A., and Peskin C.S. A computational fluid dynamics of 'clap and fling' in the smallest insects. Journal of Experimental Biology 208 (2005) 195-212
38. Lighthill M.J. On the Weis-Fogh mechanism of lift generation. Journal of Fluid Mechanics 60 1 (1973) 1-17
39. R. Nguyen van Yen, Private communication.