Statistical mechanics of Arakawa's discretizations

Journal of Computational Physics

Volumn 227, Issue 2, 2007, Pages 1286-1305

  Dubinkina, Svetlana ^a   Frank, Jason ^a  

^a CWI   (Netherlands)

Author keywords

Conservative discretizations; Geometric numerical integration; Geophysical fluid dynamics; Quasi geostrophic flow; Statistical mechanics

Indexed keywords

ASTROPHYSICS; COMPUTATION THEORY; DYNAMICAL SYSTEMS; EQUATIONS OF MOTION; GEOPHYSICS; INCOMPRESSIBLE FLOW; STATISTICAL MECHANICS; STATISTICS;

ANALYSIS OF SIMULATIONS; CONSERVATION PROPERTIES; CONSERVATIVE DISCRETIZATION; DISCRETIZATIONS; FLUID MODELING; GEOMETRIC NUMERICAL INTEGRATION; GEOPHYSICAL FLUID DYNAMICS; LONG TIME INTEGRATIONS; QUASI-GEOSTROPHIC FLOWS; SIMULATION DATA;

NUMERICAL METHODS;

EID: 36148939560     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.09.002     Document Type: Article

References (26)

1. Abramov R.V., and Majda A.J. Statistically relevant conserved quantities for truncated quasigeostrophic flow. Proc. Natl. Acad. Sci. USA 100 7 (2003) 3841-3846 (electronic)
2. Arakawa A. Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1 (1966) 119-143
3. Carnevale G.F., and Frederiksen J.S. Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175 (1987) 157-181
4. Frank J., Gottwald G., and Reich S. A Hamiltonian particle-mesh method for the rotating shallow-water equations. Meshfree Methods for Partial Differential Equations (Bonn, 2001). Lect. Notes Comput. Sci. Eng. vol. 26 (2003), Springer, Berlin 131-142
5. Frank J., and Reich S. Conservation properties of smoothed particle hydrodynamics applied to the shallow water equation. BIT 43 1 (2003) 41-55
6. Frank J., and Reich S. The Hamiltonian particle-mesh method for the spherical shallow water equations. Atmos. Sci. Lett. 5 (2004) 89-95
7. Hairer E., Lubich C., and Wanner G. Geometric numerical integration. Springer Series in Computational Mathematics. second ed. vol. 31 (2006), Springer-Verlag, Berlin structure-preserving algorithms for ordinary differential equations
8. Hairer E., Nørsett S.P., and Wanner G. Solving Ordinary Differential Equations. I. Springer Series in Computational Mathematics. second ed. vol. 8 (1993), Springer-Verlag, Berlin nonstiff problems
9. Kraichnan R.H. Statistical dynamics of two-dimensional flow. J. Fluid Mech. 67 (1975) 155-175
10. Leimkuhler B., and Reich S. Simulating Hamiltonian dynamics. Cambridge Monographs on Applied and Computational Mathematics vol. 14 (2004), Cambridge University Press, Cambridge
11. Lorenz E.N. Energy and numerical weather prediction. Tellus 12 (1960) 364-373
12. Majda A.J., and Wang X. Non-linear Dynamics and Statistical Theories for Basic Geophysical Flows (2006), Cambridge University Press, Cambridge
13. McLachlan R. Symplectic integration of Hamiltonian wave equations. Numer. Math. 66 4 (1994) 465-492
14. McLachlan R.I. Explicit Lie-Poisson integration and the Euler equations. Phys. Rev. Lett. 71 19 (1993) 3043-3046
15. Morrison P.J. Hamiltonian description of the ideal fluid. Rev. Modern Phys. 70 2 (1998) 467-521
16. Nambu Y. Generalized Hamiltonian dynamics. Phys. Rev. D 7 3 (1973) 2405-2412
17. Névir P., and Blender R. A Nambu representation of incompressible hydrodynamics using helicity and enstrophy. J. Phys. A 26 22 (1993) L1189-L1193
18. Pedlosky J. Geophysical Fluid Dynamics. second ed. (2005), Springer
19. Salmon R. Lectures on Geophysical Fluid Dynamics (1998), Oxford University Press, New York
20. Salmon R. Poisson-bracket approach to the construction of energy- and potential-enstrophy-conserving algorithms for the shallow-water equations. J. Atmos. Sci. 61 16 (2004) 2016-2036
21. Salmon R. A general method for conserving quantities related to potential vorticity in numerical models. Nonlinearity 18 5 (2005) R1-R16
22. Salmon R., Holloway G., and Hendershott M.C. The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75 (1976) 691-703
23. Salmon R., and Talley L.D. Generalizations of Arakawa's Jacobian. J. Comput. Phys. 83 2 (1989) 247-259
24. Sanz-Serna J.M., and Calvo M.P. Numerical Hamiltonian problems. Applied Mathematics and Mathematical Computation vol. 7 (1994), Chapman & Hall, London
25. Stuart A.M., and Humphries A.R. Dynamical systems and numerical analysis. Cambridge Monographs on Applied and Computational Mathematics vol. 2 (1996), Cambridge University Press, Cambridge
26. Zeitlin V. Finite-mode analogs of 2D ideal hydrodynamics: coadjoint orbits and local canonical structure. Physica. D 49 3 (1991) 353-362