A characteristics-based method for solving the transport equation and its application to the process of mantle differentiation and continental root growth

Geophysical Journal International

Volumn 140, Issue 3, 2000, Pages 651-659

  De Smet, Jeroen H ^a   Van Den Berg, Arie P ^a   Vlaar, Nico J ^a   Yuen, David A ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Advection; Continental evolution; Diapir; Numerical techniques; Partial melting; Upper mantle

Indexed keywords

KINETIC MODEL; MATHEMATICAL ANALYSIS; MELTING POINT; TRANSPORT KINETICS;

ADVECTION; CONTINENTAL CRUST; CRUSTAL EVOLUTION; DIAPIRISM; PARTIAL MELTING; UPPER MANTLE;

EID: 0034024458     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2000.00993.x     Document Type: Article

References (24)

1. Calfin, J.D., 1988. A quantitative analysis of the dissipation inherent in the semi-Lagrangian advection, Mon. weather Rev., 116, 8330-8336.
2. Canuto, C., Hussaini, M.Y., Quarteroni, A. & Zang, T.A., 1988. Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics, Springer, New York.
3. Christensen, U.R, 1992. An Eulerian technique for thermomechanical modelling of lithospheric extension, J. geophys. Res., 97, 2015-2036.
4. De Smet, J.H., Van Den Berg, A.P. & Vlaar, N.J., 1998. Stability and growth of continental shields in mantle convection models including recurrent melt production, Tectonophysics, 296, 15-29.
5. De Smet, J.H., Van Den Berg, A.P. & Vlaar, N.J., 1999. The evolution of continental roots in numerical thermo-chemical mantle convection models including differentiation by partial melting, Lithos. 48, 153-170.
6. Hansen, U. & Yuen, D.A., 1989. Dynamical influences from thermal-chemical instabilities at the core-mantle boundary, Geophys. Res. Lett., 16, 629-632.
7. Honda, S. & Yuen, D.A., 1990. Mantle convection with moving heat-source anomalies: geophysical and geochemical implications, Earth planet. Sci. Lett., 96, 349-366.
8. Kameyama, M., Fujimoto, H. & Ogawa, M., 1996. A thermo-chemical regime in the upper mantle in the early Earth inferred from a numerical model of magma-migration in a converting upper mantle, Phys. Earth planet. Inter., 94, 187-215.
9. Kellogg, L.H. & King, S.D., 1993. Effect of mantle plumes on the growth of D″ by reaction between the core and mantle, Geophys. Res. Lett., 20, 379-382.
10. Lenardic, A. & Kaula, W.M., 1993. A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces, J. geophys. Res., 98, 8243-8260.
11. Malevsky, A.V. & Yuen, D.A., 1991. Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime, Phys. Fluids A, 3, 2105-2115.
12. Molenkamp, C.R, 1968. Accuracy of finite-difference methods applied to the advection equation, J. appl. Met., 7, 160-167.
13. Ogawa, M., 1993. A numerical model of a coupled magmatism-mantle convection system in Venus and the Earth's mantle beneath Archean continental crusts, Icarus, 102, 40-61.
14. Ogawa, M. & Nakamura, H., 1998. Thermochemical regime of the early mantle inferred from numerical models of the coupled magmatism-mantle convection system with the solid-solid phase transitions at depths around 660 km, J. geophys. Res., 103 (B6), 12 161-12 181.
15. Press, W.H., Flannery, B.P., Teukolsky, S.A. & Vetterling, W.T., 1992. Numerical Recipies, the Art of Scientific Programming, Cambridge University Press, New York.
16. Sethian, J. 1996. The Level Set Methods, Cambridge University Press, Cambridge.
17. Sotin, C. & Parmentier, E.M., 1989. Dynamical consequences of compositional and thermal density stratification beneath spreading centers, Geophys. Res. Lett., 16, 835-838.
18. Sparks, D.W. & Parmentier, E.M., 1993. The structure of three-dimensional convection beneath oceanic spreading centres, Geophys. J. Int., 112, 81-91.
19. Spiegelman, M., 1993. Physics of melt extraction: theory, implications and applications, Phil. Trans. R. Soc. Lond. A, 342, 23-41.
20. Ten, A., Yuen, D.A., Larsen, T.B. & Malevsky, A.V., 1996. The evolution of material surfaces in convection with variable viscosity as monitored by a characteristics-based method, Geophys. Res. Lett.. 23, 2001-2004.
21. Van Den Berg, A.P., Van Keken, P.E. & Yuen, D.A., 1993. The effects of a composite non-Newtonian and Newtonian rheology on mantle convection, Geophys. J. Int., 115, 62-78.
22. Van Keken, P.E., King, S.D., Schmeling, H., Christensen, U.R., Neumeister, D. & Doin, M.-P., 1997. A comparison of methods of the modeling of thermochemical convection, J. geophys. Res., 102, 22 477-22 495.
23. Vreugdenhil, C.B. & Koren, B., (Eds), 1993. Numerical methods for advection-diffusion problems, Notes on Numerical Fluid Mechanics. Vol. 45, Vieweg, Braunschweig, Germany.
24. Waugh, D.W. & Plumb, R.A., 1994. Contour advection with surgery: a technique for investigating fine-scale structure in tracer transport, J. atmos. Sci., 51, 530-540.