Multigrid solution of stably stratified flows: The quasigeostrophic equations

Journal of Scientific Computing

Volumn 11, Issue 1, 1996, Pages 47-69

  Yavneh, Irad ^a   McWilliams, James C ^b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Geophysical turbulence; Multigrid; Parallel computation; Quasigeostrophic equations

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARALLEL PROCESSING SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; THERMAL STRATIFICATION; TURBULENCE; TURBULENT FLOW; TWO PHASE FLOW; VECTORS;

MULTIGRID SOLUTION; QUASIGEOSTROPHIC EQUATIONS; STRATIFIED FLOWS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 0030105961     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02088949     Document Type: Article

References (29)

1. Amodio, P., and Mazzia, F. (1994). Backward error analysis of cyclic reduction for the solution of tridiagonal systems. Math. Comp. 62, 601-617.
2. Arakawa, A. (1966). Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, Part I. J. Comput. Phys. 1, 119-143.
3. Baillie, C. F., and Yavneh, I. (1994). Porting a 3D quasigeostrophic multigrid code from the CRAY C-90 to the CRAY T3D. Report.
4. Basdevant, C., Legras, B., and Sadourny, R. (1981). A study of barotropic model flows: Intermittency, waves and predictability. J. Atmos. Sci. 38, 2305-2326.
5. Borue, V., and Orszag, S. A. (1995). Self-similar decay of three-dimensional homogeneous turbulence with hyperviscosity. J. Scientific Comp. 51, R856-R859.
6. Browning, G. L., and Kreiss, H.-O. (1989). Comparison of numerical methods for the calculation of two-dimensional turbulence. Math. Comp. 52(186), 369-388.
7. Brandt, A. (1977). Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31, 333-390.
8. Brandt, A. (1982). Guide to multigrid development. In Hackbusch, W., and Trottenberg, U. (eds.), Multigrid Methods, Springer-Verlag, Berlin, pp. 220-312.
9. Brandt, A. (1985). 1984 Multigrid Guide with Applications to Fluid Dynamics. Monograph, GMD-Studie 85, GMD-FIT, Postfach 1240, D-5205, St. Augustin 1, West Germany.
10. Brandt, A., and Greenwald, J. (1991). Parabolic multigrid revisited. In Hackbusch, W., and Trottenberg, U. (eds.), Multigrid Methods III, International Series of Numerical Mathematics, Vol. 98, Birkhauser-Verlag, Basel, pp. 143-154.
11. Carnevale, G. F., McWilliams, J. C., Pomeau, Y., Weiss, J. B., and Young, W. R. (1991). Evolution of vortex statistics in two-dimensional turbulence. Phys. Rev. Let. 66(21), 2735-2737.
12. Charney, J. G. (1962). Integration of the primitive and balance equations. Proc. Int. Symp. Numerical Weather Prediction, Tokyo, Meteor. Soc. Japan, pp. 131-152.
13. Dendy, J. E., McCormick, S. F., Ruge, J. W., Russell, T. F., and Schaffer, S. (1989). Multigrid methods for three dimensional petroleum reservoir simulation. Paper SPE 18409 presented at the Tenth Symposium on Reservoir Simulation, Houston.
14. Gent, P. R., and McWilliams, J. C. (1983). Consistent balanced models in bounded and periodic domains. Dyn. Atmos. Oceans 7, 67-93.
15. Hyman, J. M. (1980). In Bishop, A. R., Campbell, D. K., and Nicolaenko, B. (eds.), Nonlinear Problems: Present and Future, North Holland Publishing Co., pp. 91-107.
16. Kreiss, H., and Lorenz, J. (1989). Initial-Boundary Value Problems and the Navier-Stokes Equations. Academic Press, San Diego, California.
17. Lorenz, E. N. (1960). Energy and numerical weather prediction. Tellus, 12, 364-373.
18. Lorenz, E. N. (1963). Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141.
19. McWilliams, J. C., Weiss, J. B., and Yavneh, I. (1994). Anisotropy and coherent structures in planetary turbulence. Science 264(5157), 410-413.
20. McWilliams, J. C., Weiss, J. B., and Yavneh, I. (1995). Fully three-dimensional geostrophic turbulence: effects of dissipation, boundary conditions, and inhomogeneities in density stratification and Coriolis frequency (in preparation).
21. Norton, N. J., McWilliams, J. C., and Gent, P. R. (1986). A numerical model of the balance equations in a periodic domain and an example of balanced turbulence. J. Comput. Phys. 67, 439-471.
22. Pedlosky, J. (1979). Geophysical Fluid Dynamics, Springer, New York.
23. Stüben, K., and Trottenberg, U. (1982). Multigrid methods: fundamental algorithms model problem analysis and applications. In Hackbusch, W., and Trottenberg, U. (eds.), Multigrid Methods, Springer-Verlag, Berlin, pp. 1-176.
24. Tanabe, K. (1971). Projection methods for solving a singular system of linear equations and its application. Numer. Math. 17, 203-214.
25. Yavneh, I. (1993). A method for devising efficient multigrid smoothers for complicated PDE systems. SIAM J. Sci. Comput. 14(6), 1437-1463.
26. Yavneh, I. (1995). Multigrid smoothing factors for Red-Black Gauss-Seidel applied to a class of elliptic operators. SIAM J. Num. Anal. 32, 1126-1138.
27. Yavneh, I. (1996). On red black SOR smoothing in multigrid. SIAM J. Sci Comput. 17, 180-192.
28. Yavneh, I., and McWilliams, J. C. (1995). Robust multigrid solution of the shallow-water balance equations. J. Comp. Phys. 119, 1-25.
29. Yavneh, I., and McWilliams, J. C. (1996). Multigrid Solution of stably stratified flows: the balance, equations (in preparation).