A community benchmark for 2-D Cartesian compressible convection in the Earth's mantle

Geophysical Journal International

Volumn 180, Issue 1, 2010, Pages 73-87

  King, Scott D ^a   Lee, Changyeol ^a   van Keken, Peter E ^b   Leng, Wei ^c   Zhong, Shijie ^c   Tan, Eh ^d   Tosi, Nicola ^e,f   Kameyama, Masanori C ^g  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF COLORADO   (United States)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^e CHARLES UNIVERSITY   (Czech Republic)

^f FREIE UNIVERSITÄT BERLIN   (Germany)

^g EHIME UNIVERSITY   (Japan)

Author keywords

Dynamics of lithosphere and mantle; Equations of state; Numerical approximations and analysis; Numerical solutions

Indexed keywords

ACCURACY ASSESSMENT; BENCHMARKING; BIFURCATION; COMPRESSIBILITY; CONTINENTAL LITHOSPHERE; EARTH; EQUATION OF STATE; FINITE ELEMENT METHOD; MANTLE CONVECTION; MANTLE STRUCTURE; TWO-DIMENSIONAL FLOW; VISCOSITY;

EID: 73049085041     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2009.04413.x     Document Type: Article

References (35)

1. Birch F. Elasticity and constitution of the Earth's interior. J. geophys. Res. 1952, 57:227-286.
2. Blankenbach B. A benchmark comparison for mantle convection codes. Geophys. J. Int. 1989, 98:23-38.
3. Cahouet C, Cahbard J-P. Some fast 3D finite element solvers for the generalized Stokes' problem. Int. J. Numer. Methods Fluids 1988, 8:869-895.
4. Christensen UR, Yuen DA. Layered convection induced by phase transitions. J. geophys. Res. 1985, 90:10 291-10 300.
5. Gerya T, Yuen DA. Characteristic-based marker-in-cell method with conservative finite-differences schemes for modelling geological flows with strongly variable transport properties. Phys. Earth planet. Inter. 2003, 140:293-318.
6. Hewitt JM, McKenzie DP, Weiss NO. Dissipative heating in convective flows. J. Fluid Mech. 1975, 68:721-738.
7. Hughes TJR. The Finite Element Method 1987, Prentice-Hall, Inc., Englewood Cliffs, NJ
8. Hughes TJR, Brooks AN, Hughes TJR. A multi-dimensional upwind scheme with no crosswind diffusion. Finite Element Methods for Convection Dominated Flows 1979, Vol. 34:19-35. in, pp, ed., ASME, New York
9. Hughes TJR, Liu WK, Brooks AN. Finite element analysis of incompressible viscous flows by the penalty function formulation. J. Comput. Phys. 1979, 30:1-60.
10. Hughes TJR, Franca LP, Hulbert GM, Johan Z, Shakib F, Tezduyar TE. The Galerkin/least-squares method for advective-diffusive equations. Recent Developments in Computational Fluid Dynamics 1988, Vol. 95:75-99. in, pp, ed., ASME, New York
11. Ita J, King SD. Sensitivity of convection with an endothermic phase-change to the form of governing equations, initial conditions, boundary conditions, and equation of state. J. geophys. Res. 1994, 99(B8):15 919-15 938.
12. Ita JJ, King SD. The influence of thermodynamic formulation on simulations of subduction zone geometry and history. Geophys. Res. Lett. 1998, 125:1463-1466.
13. Jarvis GT, McKenzie DP. Convection in a compressible fluid with infinite Prandtl number. J. Fluid Mech. 1980, 96:515-583.
14. Kameyama M, Kageyama A, Sato T. Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity. J. Comp. Phys. 2005, 206:162-181.
15. King SD. On topography and geoid from 2D stagnant-lid convection calculations. Geochem. Geophys. Geosys. 2009, 10:Q3002. 10.1029/2008GC002250, doi
16. King SD, Ita JJ. The effect of slab rheology on mass transport across a phase transition boundary. J. geophys. Res. 1995, 100:20 211-20 222.
17. King SD, Raefsky A, Hager BH. Conman: Vectorizing a finite-element code for incompressible 2-dimensional convection In the Earth's mantle. Phys. Earth planet. Inter. 1990, 59:195-208.
18. Koglin DE, Ghias S, King SD, Jarvis GT, Lowman JP. Mantle convection with mobile plates: a benchmark study. Geochem. Geophys. Geosyst. 2005, 6:Q09003. 10.1029/2005GC000924, doi
19. Lee C, King SD. The effect of mantle compressibility on the thermal and flow structures of the subduction zone. Geochem. Geophys. Geosyst. 2009, 10:Q1006. 10.1029/2008GC002151, doi
20. Leng W, Zhong S. Viscous heating, adiabatic heating and energetic consistency in compressible mantle convection. Geophys. J. Int. 2008, 173:693-702.
21. Moresi L, Zhong SJ, Gurnis M. The accuracy of finite element solutions of Stokes' flow with strongly varying viscosity. Phys. Earth planet. Inter. 1996, 97:83-94.
22. Patankar SV. Numerical Heat Transfer and Fluid Flow 1980, McGraw-Hill, New York
23. Schenk O, Gartner K, Fichtner W. Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors. BIT 2000, 40(1):158-176.
24. Schubert G, Turcotte DL, Olson P. Mantle Convection in the Earth and Planets 2001, 940. pp, Cambridge Univ. Press, New York
25. Spiegelman M, Katz R. A semi-Lagrangian Crank-Nicolson algorithm for the numerical solution of advection-diffusion problems. Geochem. Geophys. Geosys. 2006, 7:Q04014. 10.1029/2005GC001073, doi
26. Tan E, Gurnis M. Metastable superplumes and mantle compressibility. Geophys. Res. Lett. 2005, 32:L20307. 10.1029/2005GL024190, doi
27. Tan E, Gurnis M. Compressible thermochemical convection and application to lower mantle structures. J. geophys. Res. 2007, 112:B06304. 10.1029/2006JB004505, doi
28. Taylor C, Hood P. A numerical solution of the Navier-Stokes equations using the finite element technique. Comput. Fluids 1973, 1:73-100.
29. Travis BJ. A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry. Geophys. Astrophys. Fluid Dyn. 1990, 55:137-160.
30. Turcotte DL, Hsui AT, Torrance KE, Schubert G. Influence of viscous dissipation on Benard convetion. J. Fluid Mech. 1974, 64:369-374.
31. van Keken PE, King SD, Schmeling H, Christensen UR, Neumeister D, Doin M-P. A comparison of methods for the modeling of thermochemical convection. J. geophys. Res. 1997, 102:22 477-22 495.
32. van Keken PE, Kiefer B, Peacock S. High resolution models of subduction zones: implications for mineral dehydration reactions and the transport of water into the deep mantle. Geochem. Geophys. Geosys. 2002, 3(10):1056. 10.1029/2001GC000256, doi
33. van Keken PE. A community benchmark for subduction zone modeling. Phys. Earth planet. Inter. 2008, 171:187-197.
34. Yuen DA, Quareni F, Hong HJ. Effects from equation of state and rheology in dissipative heating in compressible mantle convection. Nature 1987, 326:67-69.
35. Zhang S, Yuen DA. Various influences on plumes and dynamics in time-dependent, compressible mantle convection in 3-D spherical shell. Phys. Earth planet. Inter. 1996, 94:241-267.