Lagrangian averaging for compressible fluids

Multiscale Modeling and Simulation

Volumn 3, Issue 4, 2005, Pages 818-837

  Bhat, H S ^a   Fetecau, R C ^b   Marsden, J E ^a   Mohseni, K ^c   West, M ^d  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UCB 450   (United States)

^d 496 Lomita Mall   (United States)

Author keywords

Averaged Lagrangians; Inviscid compressible fluids

Indexed keywords

COMPRESSIBILITY OF LIQUIDS; COMPUTER SIMULATION; FUNCTIONS; MATHEMATICAL MODELS; VECTORS;

AVERAGED LAGRANGIANS; INVISCID COMPRESSIBLE FLUIDS; NONLINEAR FUNCTIONS;

FLOW OF FLUIDS;

EID: 23044496611     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/030601739     Document Type: Article

References (27)

1. R. Abraham, J. E. Marsden, and T. S. Ratiu (1988), Manifolds, Tensor Analysis and Applications, 2nd ed., Appl. Math. Sci. 75, Springer-Verlag, New York.
2. D. Andrews and M. E. McIntyre (1978), An exact theory of nonlinear waves on a Lagrangian-mean flow, J. Fluid Mech., 89, pp. 609-646.
3. R. Camassa and D. D. Holm (1993), An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71, pp. 1661-1664.
4. S. Y. Chen, C. Foias, D. D. Holm, E. J. Olson, E. S. Titi, and S. Wynne (1998), The Camassa-Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett., 81, pp. 5338-5341.
5. S. Y. Chen, D. D. Holm, L. G. Margolin, and R. Zhang (1999), Direct numerical simulations of the Navier-Stokes alpha model, Phys. D, 133, pp. 66-83.
6. W. J. Cocke (1969), Turbulent hydrodynamic line stretching: Consequences of isotropy, Phys. Fluids, 12, pp. 2488-2492.
7. D. G. Ebin and J. E. Marsden (1970), Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. (2), 92, pp. 102-163.
8. L. C. EVANS (1998), Partial Differential Equations, Grad. Stud. Math. 19, AMS, Providence, RI.
9. C. Foias, D. D. Holm, and E. S. Titi (2002), The three dimensional viscous Camassa-Holm equations and their relation to the Navier-Stokes equations and turbulence theory, J. Dynam. Differential Equations, 14, pp. 1-36.
10. D. D. Holm (1999), Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion, Phys. D, 133, pp. 215-269.
11. D. D. Holm (2002a), Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics, Phys. D, 170, pp. 253-286.
12. D. D. Holm and J. E. Marsden (2005), Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation, in The Breadth of Symplectic and Poisson Geometry, Progr. Math. 232, Birkhäuser, Boston, pp. 203-235.
13. D. D. Holm, J. E. Marsden, and T. S. Ratiu (1998a), Euler-Poincaré modeels of ideal fluids with nonlinear dispersion, Phys. Rev. Lett., 349, pp. 4173-4177.
14. D. D. Holm, J. E. Marsden, and T. S. Ratiu (1998b), The Euler-Poincaré equations and semi-direct products with applications to continuum theories, Adv. Math., 137, pp. 1-81.
15. T. Kawahara (1970), Weak nonlinear magneto-acoustic waves in a cold plasma in the presence of effective electron-ion collisions, J. Phys. Soc. Japan, 28, pp. 1321-1329.
16. T. Kakutani and T. Kawahara (1970), Weak ion-acoustic shock waves, J. Phys. Soc. Japan, 29, pp. 1068-1073.
17. I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C. Theodoropoulos (2002), Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis, Commun. Math. Sci., 1, pp. 715-762.
18. P. D. Lax and C. D. Levermore (1983), The small dispersion limit of the KdV equations. III, Comm. Pure Appl. Math., 36, pp. 809-830.
19. H. W. Liepmann and A. Roshko (1957), Elements of Gasdynamics, Wiley, New York.
20. J. E. Marsden, T. S. Ratiu, and A. Weinstein (1984), Semi-direct products and reduction in mechanics, Trans. Amer. Math. Soc., 281, pp. 147-177.
21. J. E. Marsden and S. Shkoller (2001), Global well-posedness for the LANS-α equations on bounded domains, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 359, pp. 1449-1468.
22. J. E. Marsden and S. Shkoller (2003), The anisotropic averaged Euler equations, Arch. Ration. Mech. Anal., 166, pp. 27-46.
23. K. Mohseni, B. Kosović, S. Shkoller, and J. E. Marsden (2003), Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence, Phys. Fluids, 15, pp. 524-544.
24. R. Rivlin and J. L. Erickson (1955), Stress-deformation relations for isotropic materials, J. Rational Mech. Anal., 4, pp. 323-425.
25. A. H. Shapiro (1953), The Dynamics and Thermodynamics of Compressible Fluid Flow, Ronald Press, New York.
26. G. I. Taylor (1938), The spectrum of turbulence, Proc. R. Soc. London Ser. A, 164, pp. 476-490.
27. G. B. Whitham (1974), Linear and Nonlinear Waves, Wiley-Interscience, New York.