A matrix-dependent transfer multigrid method for strongly variable viscosity infinite prandtl number thermal convection

Geophysical and Astrophysical Fluid Dynamics

Volumn 92, Issue 3-4, 2000, Pages 151-195

  Yang, Woo Sun ^a   Baumgardner, John R ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Mantle convection; Matrix dependent transfer; Multigrid; Rheology; Yield stress

Indexed keywords

CONVECTION; RHEOLOGY; VISCOSITY;

MANTLE; RHEOLOGY; THERMAL CONVECTION; VISCOSITY;

ALGORITHMS; FINITE ELEMENT METHOD; GALERKIN METHODS; MATRIX ALGEBRA; PRANDTL NUMBER; PROBLEM SOLVING; RHEOLOGY; STRAIN RATE; VISCOSITY; YIELD STRESS;

CARTESIAN FINITE ELEMENT TREATMENT; MOMENTUM TREATMENT;

HEAT CONVECTION;

EID: 0034351205     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/03091920008203715     Document Type: Article

References (38)

1. Alcouffe, R. E., Brandt, A., Dendy, J. E. Jr. and Painter, J. W., "The multi-grid method for the diffusion equation with strongly discontinuous coefficients," SIAM J. Sci. Stat. Comput. 2, 430-454 (1981).
2. Atanga, J. and Silvester, D., "Iterative methods for stabilized mixed velocity-pressure finite elements," Int. J. Numer. Methods Fluids 14, 71-81 (1992).
3. Baumgardner, J. R., A Three-dimensional Finite Element Model for Mantle Convection, Ph.D. Thesis, UCLA (1983).
4. Baumgardner, J. R., "Three-dimensional treatment of convective flow in the Earth's mantle," J. Stat. Phys. 39, 501-511 (1985).
5. de Zeeuw, P. M., "Matrix-dependent prolongations and restrictions in a blackbox multigrid solver," J. Comput. Appl. Math. 33, 1-27 (1990).
6. Evans, B. and Kohlstedt, D. L., "Rheology of rocks," In: Rock Physics and Phase Relations: A Handbook of Physical Constants (Ed. Ahrens, T. J.) American Geophysical Union, Washington D. C., pp. 148-165 (1995).
7. Hackbusch, W., "Multi-grid convergence theory," In: Multigrid Methods, Proceedings of the Conference, Köln-Porz, 1981 (Eds. Hackbusch, W. and Trottenberg, U.) Lecture Notes in Mathematics 960, Springer-Verlag, pp. 177-219 (1982).
8. Karato, S. and Wu, P., "Rheology of the upper mantle: a synthesis," Science 260, 771-778 (1993).
9. Kettler, R., "Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods," In: Multigrid Methods, Proceedings of the Conference, Köln-Porz, 1981 (Eds. Hackbusch, W. and Trottenberg, U.) Lecture Notes in Mathematics 960, Springer-Verlag, pp. 502-534 (1982).
10. Kohlstedt, D. L., Evans, B. and Mackwell, S. J., "Strength of the lithosphere: constraints imposed by laboratory experiments," J. Geophys. Res. 100, 17587-17602 (1995).
11. Moresi, L.-N. and Solomatov, V. S., "Numerical investigation of 2D convection with extremely large viscosity variations," Phys. Fluids 7, 2154-2162 (1995).
12. Moresi, L. and Solomatov, V., "Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus," Geophys. J. Int. 133, 669-682 (1998).
13. Parmentier, E. M., Turcotte, D. L. and Torrance, K. E., "Studies of finite amplitude non-Newtonian thermal convection with application to convection in the Earth's mantle," J. Geophys. Res. 81, 1839-1846 (1976).
14. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Pub. Corp., Washington (1980).
15. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Brian, P., Numerical Recipes in Fortran 77: The Art of Scientific Computing, second edn., Cambridge University Press, Cambridge (1992).
16. Ramage, A. and Wathen, A. J., "Iterative solution techniques for the Stokes and Navier-Stokes equations," Int. J. Numer. Methods Fluids 19, 67-83 (1994).
17. Ranalli, G., "The microphysical approach to mantle rheology," In: Glacial Isostasy, Sea Level and Mantle Rheology. (Eds. Sabadini, R., Lambeck, K. and Boschi, E.) Kluwer Academic Publishers, Dordrecht, pp. 343-378 (1991).
18. Ratcliff, J. T., Tackley, P. J., Schubert, G. and Zebib, A., "Transitions in thermal convection with strongly variable viscosity," Phys. Earth Planet. Inter. 102, 201-212 (1997).
19. Reese, C. C., Solomatov, V. S. and Moresi, L.-N., "Heat transport efficiency for stagnant lid convection with dislocation viscosity: application to Mars and Venus," J. Geophys. Res. 103, 13643-13657 (1998).
20. Reusken, A., "Multigrid with matrix-dependent transfer operators for a singular perturbation problem," Computing 50, 199-211 (1993).
21. Reusken, A., "Multigrid with matrix-dependent transfer operators for convection-diffusion problems," In: Multigrid Methods IV, Proceedings of the Fourth European Multigrid Conference, Amsterdam, 1993 (Eds. Hemker, P. W. and Wesseling, P.) Birkhauser Verlag, Basel (1994).
22. Ricard, Y., Doglioni, C. and Sabadini, R., "Differential rotation between lithosphere and mantle: a consequence of lateral mantle viscosity variations," J. Geophys. Res. 96, 8407-8415 (1991).
23. Stocker, R. L. and Ashby, M. F., "On the rheology of the upper mantle," Rev. Geophys. Space Phys. 11, 391-426 (1973).
24. Trompert, R. A. and Hansen, U., "The application of a finite volume multigrid method to three dimensional flow problems in a highly viscous fluid with a variable viscosity," Geophys. Astrophys. Fluid Dynam. 83, 261-291 (1996).
25. Trompert, R. and Hansen, U., "Mantle convection simulations with rheologies that generate plate-like behavior," Nature 395, 686-689 (1998a).
26. Trompert, R. and Hansen, U., "On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity," Phys. Fluids 10, 351-360 (1998b).
27. Turcotte, D. L., Torrance, K. E. and Hsui, A. T., "Convection in the Earth's mantle," Meth. Comp. Physics 13, 431-451 (1973).
28. van den Berg, A., van Keken, P. E. and Yuen, D. A., "The effects of a composite non-Newtonian and Newtonian rheology on mantle convection," Geophys. J. Int. 115, 62-78 (1993).
29. van den Berg, A. and Yuen, D. A., "Convectively induced transition in mantle rheological behavior," Geophys. Res. Lett. 22, 1549-1552 (1995).
30. van den Berg, A. and Yuen, D. A., "Is the lower-mantle Newtonian today?" Geophys. Res. Lett. 23, 2033-2036 (1996).
31. van den Berg, A., Yuen, D. A. and van Keken, P. E., "Rheological transition in mantle convection with a composite temperature-dependent, non-Newtonian and Newtonian rheology," Earth Planet. Sci. Lett. 129, 249-260 (1995).
32. van Leer, B., "Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method," J. Comp. Phys. 32, 101-136 (1979).
33. Verfuerth, R., "A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem," IMA J. Numer. Anal. 4, 441-455 (1984).
34. Wagner, C., "A multigrid method with matrix-dependent transfer operators applied in groundwater science," In: Computational Methods in Water Resources (Eds. Peters, A., Wittum, G., Herrling, B., Meissner, U., Brebia, C. A., Gray, W. G. and Pinder, G. F.), Kluwer Academic Publishers, Dordrecht, X, Vol. 2, pp. 1439-1446 (1994).
35. Weertman, J., "The creep strength of the Earth's mantle," Rev. Geophys. Space Phys. 8, 145-168 (1970).
36. Weertman, J. and Weertman, J. R., "High temperature creep of rock and mantle viscosity," Ann. Rev. Earth Planet Sci. 3, 293-315 (1975).
37. Wesseling, P., An Introduction to Multigrid Methods, John Wiley and Sons, Inc., Chichester (1992).
38. Yang, W.-S., Variable Viscosity Thermal Convection at Infinite Prandtl Number in a Thick Spherical Shell, Ph.D. Thesis, University of Illinois at Urbana-Champaign (1997).