FANTOM: Two- and three-dimensional numerical modelling of creeping flows for the solution of geological problems

Physics of the Earth and Planetary Interiors

Volumn 188, Issue 1-2, 2011, Pages 47-68

  Thieulot, Cedric ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

3D numerical modelling; Arbitrary Lagrangian Eulerian technique; Finite Element Method; Geodynamics; Stokes flow; Strain localisation

Indexed keywords

3D NUMERICAL MODELLING; ARBITRARY LAGRANGIAN EULERIAN; FINITE ELEMENT; STOKES FLOWS; STRAIN LOCALISATION;

COUPLED CIRCUITS; DOMAIN DECOMPOSITION METHODS; EXPERIMENTS; FINITE ELEMENT METHOD; GEODYNAMICS; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; YIELD STRESS;

THREE DIMENSIONAL;

ALGORITHM; CREEP; CRUSTAL STRUCTURE; DEFORMATION; FINITE ELEMENT METHOD; GEODYNAMICS; LITHOSPHERIC STRUCTURE; NUMERICAL MODEL; OROGENY; RHEOLOGY; STOKES FORMULA; STRAIN; THREE-DIMENSIONAL MODELING; TWO-DIMENSIONAL MODELING;

EID: 80053312507     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2011.06.011     Document Type: Article

References (112)

1. Allken, V., Huismans, R., Thieulot, C., submitted for publication. On the influence of brittle-ductile coupling in crustal systems undergoing extension: a 3D numerical study. Geochemistry Geophysics Geosystems.
2. Allken, V., Huismans, R., Thieulot, C., 2011. Three dimensional numerical modelling of extensional systems. Journal of Geophysical Research. submitted for publication.
3. Anderson J. Computational Fluid Dynamics 1995, McGraw-Hill.
4. Babeyko A., Sobolev S. High-resolution numerical modeling of stress distribution in visco-elasto-plastic subducting slabs. Lithos 2008, 103:205-216.
5. Babeyko A., Sobolev S., Trumbull R., Oncken O., Lavier L. Numerical models of crustal scale convection and partial melting beneath the Altiplano-Puna plateau. Earth and Planetary Science Letters 2002, 199:373-388.
6. Bachelor G. An Introduction to Fluid Dynamics 1967, Cambridge University Press.
7. Bathe K.J. Finite Element Procedures in Engineering Analysis 1982, Prentice-Hall.
8. Beaumont C., Fullsack P., Hamilton J. Erosional control of active compressional orogens. Thrust Tectonics 1992, 99:1-18.
9. Braun J. Three-dimensional numerical modelling of compressional orogens: thrust geometry and oblique convergence. Geology 1993, 21:153-156.
10. Braun J. Three-dimensional numerical simulations of crustal-scale wrenching using a non-linear failure criterion. Journal of Structural Geology 1994, 16:1173-1186.
11. Braun J. Pecube: a new finite-element code to solve the 3D heat transport equation including the effects of a time-varying, finite amplitude surface topography. Computers and Geosciences 2003, 29:787-794.
12. Braun J., Beaumont C. Three-dimensional numerical experiments of strain partitioning at oblique plate boundaries: implications for contrasting tectonic styles in the southern Coast Ranges, California, and central South Island, New Zealand. Journal of Geophysical Research 1995, 100:18,059-18,074.
13. Braun J., Sambridge M. Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretisation. Basin Research 1997, 9:27-52.
14. Braun J., Thieulot C., Fullsack P., DeKool M., Huismans R. DOUAR: a new three-dimensional creeping flow model for the solution of geological problems. Physics of the Earth and Planetary Interiors 2008, 171:76-91.
15. Braun J., Yamato P. Structural evolution of a three-dimensional, finite-width crustal wedge. Tectonophysics 2009, 484:181-192. 10.1016/j.tecto.2009.08.032.
16. Brun J.P. Narrow rifts versus wide rifts: inferences for the mechanics of rifting from laboratory experiments. Philosophical Transactions of the Royal Society A 1999, 357:695-712.
17. Buiter S., Babeyko A., Ellis S., Gerya T., Kaus B., Kellner A., et al. The numerical sandbox: comparison of model results for a shortening and an extension experiment. Analogue and numerical modelling of crustal-scale processes. Geological Society, London. Special Publications 2006, 253:29-64.
18. Burov E., Poliakov A. Erosion and rheology controls on synrift and postrift evolution: verifying old and new ideas using a fully coupled numerical model. Journal of Geophysical Research 2001, 106:16,461-16,481.
19. Burov E., Cloetingh S. Erosion and rift dynamics: new thermomechanical aspects of post-rift evolution of extensional basins. Earth and Planetary Science Letters 1997, 150:7-26.
20. Chemenda A. The formation of shear-band/fracture networks from a constitutive instability: theory and numerical experiment. Journal of Geophysical Research 2007, 112. 10.1029/2007JB005026.
21. Chen X., Phoon K. Some numerical experiences on convergence criteria for iterative finite element solvers. Computers and Geotechnics 2009, 36:1272-1284.
22. Choi E., Lavier L., Gurnis M. Thermomechanics of mid-ocean ridge segmentation. Physics of the Earth and Planetary Interiors 2008, 171:374-386.
23. Coulomb C.A. Essai sur une application des règles de maximis et minimis àquelques problèmes de statique relatifs à l'architecture. Mémoires de l'Académie Royale prés. Divers Savants 1773, 7:343-382.
24. Cruz L., Malinski J., Wilson A., Take W., Hilley G. Erosional control of kinematics and geometry of fold-and-thrust belts imaged in a physical and numerical sandbox. Journal of Geophysical Research 2010, 115. 10.1029/2010JB007472.
25. Cuvelier C., Segal A., van Steenhoven A. Finite Element Methods and Navier-Stokes Equations 1986, D. Reidel Publishing Company.
26. Dabrowski M., Krotkiewski M., Schmid D. Milamin: Matlab based finite element solver for large problems. Geochemistry Geophysics Geosystems 2008, 9:Q04030. 10.1029/2007GC001719.
27. Davies D.R., Wilson C.R., Kramer S.C. Fluidity: a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics. Geochemistry Geophysics Geosystems 2011, 12:Q06001. 10.1029/2011GC003551.
28. Davis R., Selvadurai A. Plasticity and Geomechanics 2002, Cambridge University Press.
29. Deubelbeiss Y., Kaus B. Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of strongly varying viscosity. Physics of the Earth and Planetary Interiors 2008, 171:92-111.
30. Donea J., Huerta A. Finite Element Methods for Flow Problems 2003, John Wiley & sons.
31. Drucker D., Prager W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics 1952, 10:157-165.
32. Dunbar J., Sawyer D. Three-dimensional dynamical model of continental rift propagation and margin plateau formation. Journal of Geophysical Research 1996, 101:27,845-27,863.
33. Egholm D.L. A new strategy for discrete element numerical models: 1. Theory. Journal of Geophysical Research 2007, 112:B05203. 10.1029/2006JB004557.
34. Egholm D.L., Sandiford M., Clausen O.R., Nielsen S.B. A new strategy for discrete element numerical models: 2. Sandbox applications. Journal of Geophysical Research 2007, 112:B05204. 10.1029/2006JB004558.
35. Elesin Y., Gerya T., Artemieva I., Thybo H. Samovar: a thermomechanical code for modeling of geodynamic processes in the lithosphere - application to basin evolution. Arabian Journal of Geosciences 2010, 3:477-497.
36. England P. Some numerical investigations of large scale continental deformation. Mountain Building Processes 1982, 129-189. Academic Press.
37. Fortin M. Old and new finite elements for incompressible flows. International Journal for Numerical Methods in Fluids 1981, 1:347-364.
38. Fuller C.W., Willett S.D., Brandon M.T. Formation of forearc basins and their influence on subduction zone earthquakes. Geology 2006, 34:65-68.
39. Fullsack P. An arbitrary Lagrangian-Eulerian formulation for creeping flows and its application in tectonic models. Geophysical Journal International 1995, 120:1-23.
40. Geenen T., ur Rehman M., MacLahlan S., Segal G., Vuik C., van den Berg A., et al. Scalable robust solvers for unstructured FE geodynamic modeling applications: solving the Stokes equation for models with large localized viscosity contrasts. Geochemistry Geophysics Geosystems 2009, 10:Q09002. 10.1029/2009GC002526.
41. Gerbault M., Cembrano J., Mpodozis C., Farias M., Pardo M. Continental margin deformation along the Andean subduction zone: thermo-mechanical models. Physics of the Earth and Planetary Interiors 2009, 177:180-205.
42. Gerya T. Dynamical instability produces transform faults at mid-ocean ridges. Science 2010, 329:1047-1050.
43. Gerya T. Numerical Geodynamic Modelling 2010, Cambridge University Press.
44. Gerya T., Yuen D. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties. Physics of the Earth and Planetary Interiors 2003, 140:293-318.
45. Gerya T., Yuen D. Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems. Physics of the Earth and Planetary Interiors 2007, 163:83-105.
46. Glowinski R. Handbook of Numerical Analysis, Vol IX: Numerical Methods for Fluids 2003, North-Holland.
47. Gunzburger M. Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice and Algorithms 1989, Academic, Boston.
48. Gupta, A., 2000. WSMP: Watson Sparse Matrix Package (Part-I: Direct Solution of Symmetric Sparse Systems). Technical Report RC 21886. IBM T.J. Watson Research Center. Yorktown Heights, NY. http://www.cs.umn.edu/~agupta/wsmp.
49. Gupta A., Karypis G., Kumar V. Highly scalable parallel algorithms for sparse matrix factorization. IEEE Transactions on Parallel and Distributed Systems 1997, 8:502-520.
50. Gupta, A., Koric, S., George, T., 2009. Sparse matrix factorization on massively parallel computers. In: SC09 (International Conference for High Performance Computing, Networking, Storage and Analysis).
51. Hansen D. A meshless formulation for geodynamic modeling. Journal of Geophysical Research 2003, 108. 10.1029/2003JB002460.
52. Hassani R., Jongmans D., Chéry J. Study of plate deformation and stress in subduction processes using two-dimensional numerical models. Journal of Geophysical Research 1997, 102:17,951-17,960.
53. Hetényi G., Godard V., Cattin R., Connolly J. Incorporating metamorphism in geodynamic models: the mass conservation problem. Geophysical Journal International 2011, 186:6-10.
54. Hirt C., Amsden A., Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 1974, 14:227-253.
55. Houseman G., England P. Crustal thickening versus lateral expulsion in the Indian-Asian continental collision. Journal of Geophysical Research 1993, 98(B7). 12, 333-12, 249.
56. Hughes T.J. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis 2000, Dover Publications, Inc.
57. Huismans, R., Beaumont, C., 2007. Roles of lithospheric strain softening and heterogeneity in determining the geometry of rifts and continental margins. In: Karner, G.D., Manatschal, G., Pinheiro, L.M. (Eds.), Imaging, Mapping and Modelling Continental Lithosphere Extension and Breakup, vol. 282. Geological Society, London, Special Publications, pp. 111-138. doi:10.1144/SP282.6.
58. Huismans R., Buiter S., Beaumont C. Effect of plastic-viscous layering and strain softening on mode selection during lithospheric extension. Journal of Geophysical Research 2005, 110:B02406.
59. Huismans R.S., Beaumont C. Symmetric and asymmetric lithospheric extension: relative effects of frictional-plastic and viscous strain softening. Journal of Geophysical Research 2003, 108(B10). 10.1029/2002JB002026.
60. Ismail-Zadeh A., Tackley P. Computational Methods for Geodynamics 2010, Cambridge University Press.
61. Kachanov L. Fundamentals of the Theory of Plasticity 2004, Dover Publications, Inc.
62. Karato S.I. Deformation of Earth Materials 2008, Cambridge University Press.
63. Kaus, B., 2005. Modelling approaches to geodynamic processes. Ph.D. Thesis, ETH Zurich.
64. Kaus B. Factors that control the angle of shear bands in geodynamic numerical models of brittle deformation. Tectonophysics 2010, 484:36-47. 10.1016/j.tecto.2009.08.042.
65. Kaus B., Mühlhaus H., May D. A stabilization algorithm for geodynamic numerical simulations with a free surface. Physics of the Earth and Planetary Interiors 2010, 181:12-20.
66. Kaus B., Steedman C., Becker T. From passive continental margin to mountain belt: insights from analytical and numerical models and application to Taiwan. Physics of the Earth and Planetary Interiors 2008, 171:235-251.
67. Kurfess D., Heidbach O. CASQUS: a new simulation tool for coupled 3D finite element modeling of tectonic and surface processes based on ABAQUS and CASCADE. Computers and Geosciences 2009, 35:1959-1967.
68. Levin D. The approximation power of moving least-squares. Mathematics of Computation 1998, 67:1517-1531.
69. Lewis R., Nithiarasu P., Seetharamu K. Fundamentals of the Finite Element Method for Heat and Fluid Flow 2004, John Wiley & Sons Ltd.
70. Loiselet C., Braun J., Husson L., Le Carlier de Veslud C., Thieulot C., Yamato P., et al. Subducting slabs: jellyfishes in the Earth's mantle. Geochemistry, Geophysics and Geosystems 2010, 11. 10.1029/2010GC003172.
71. May D., Moresi L. Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics. Physics of the Earth and Planetary Interiors 2008, 171:33-47.
72. von Mises R. Mechanik der festen korper im plastisch deformablen zustand. Nachrichten der Koniglichen Gesellschaft der Wissenchaften 1913, 582.
73. Moresi L., Dufour F., Muhlhaus H. A Lagrangian integration point finite element method for large deformation modeling of visco-elastic geomaterials. Journal of Computational Physics 2003, 184:476-497.
74. Moresi L., Quenette S., Lemiale V., Mériaux C., Appelbe B., Mühlhaus H.B. Computational approaches to studying non-linear dynamics of the crust and mantle. Physics of the Earth and Planetary Interiors 2007, 163:69-82.
75. Moresi L.N., Solomatov V. Numerical investigation of 2D convection with extremely large viscosity variations. Physics of Fluids 1995, 7:2154-2162.
76. O'Neill C., Moresi L., Müller D., Albert R., Dufour F. Ellipsis 3D: a particle-in-cell finite element hybrid code for modelling mantle convection and lithospheric deformation. Computers and Geosciences 2006, 32:1769-1779.
77. Owen D., Hinton E. Finite Elements in Plasticity 1980, Pineridge Press.
78. OzBench M., Regenauer-Lieb K., Stegman D., Morra G., Farrington R., Hale A., et al. A model comparison study of large-scale mantle-lithosphere dynamics driven by subduction. Physics of the Earth and Planetary Interiors 2008, 171:224-234.
79. Pelletier J. Quantitative Modelling of Earth Surface Processes 2008, Cambridge University Press.
80. Petrunin A., Sobolev S. Three-dimensional numerical models of the evolution of pull-apart basins. Physics of the Earth and Planetary Interiors 2008, 171:387-399.
81. Poliakov A., Cundall P., Podlachikov P., Lyakhovsky V. An explicit inertial method for the simulation of viscoelastic flow: an evaluation of elastic effects on diapiric flow in two- and three-layers models. Flow and Creep in the Solar System: Observations, Modeling and Theory 1993, 175-195. Kluwer Academic Publishers.
82. Popov A., Sobolev S. SLIM3D: a tool for three-dimensional thermomechanical modelling of lithospheric deformation with elasto-visco-plastic rheology. Physics of the Earth and Planetary Interiors 2008, 171:55-75.
83. Pysklywec R. Surface erosion control on the evolution of the deep lithosphere. Geology 2006, 34:225-228.
84. Quinquis M.E., Buiter S.J., Ellis S. The role of boundary conditions in numerical models of subduction zone dynamics. Tectonophysics 2011, 497:57-70.
85. Ramberg H. Instability of layered systems in the field of gravity. Physics of the Earth and Planetary Interiors 1968, 1:427-447.
86. Ranalli G. Rheology of the Earth 1995, Springer.
87. Reddy J. On penalty function methods in the finite element analysis of flow problems. International Journal for Numerical Methods in Fluids 1982, 2:151-171.
88. Renka R.J. Multivariate interpolation of large sets of scattered data. ACM Transactions on Mathematical Software 1988, 14:139-148.
89. Samuel H., Evonuk M. Modeling advection in geophysical flows with particle level sets. Geochemistry Geophysics Geosystems 2010, 11. 10.1029/2010GC003081.
90. Sani R., Gresho P., Lee R., Griffiths D. The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations: part 1. International Journal for Numerical Methods in Fluids 1981, 1:17-43.
91. Schenk O., Bollhoefer M., Roemer R. On large-scale diagonalization techniques for the anderson model of localization. SIAM Review 2008, 50:91-112.
92. Schenk O., Wächter A., Hagemann M. Matching-based preprocessing algorithms to the solution of saddle-point problems in large-scale nonconvex interior-point optimization. Computational Optimization and Applications 2007, 36:321-341.
93. Schmeling H., Babeyko A., Enns A., Faccenna C., Funiciello F., Gerya T., et al. A benchmark comparison of spontaneous subduction models - towards a free surface. Physics of the Earth and Planetary Interiors 2008, 171:198-223.
94. Schmeling H., Babeyko A., Enns A., Faccenna C., Funiciello F., Gerya T., et al. A benchmark comparison of spontaneous subduction models - towards a free surface. Physics of the Earth and Planetary Interiors 2008, 171:198-223.
95. Schöberl, J., 1999. Robust multigrid methods for parameter dependent problems. Ph.D. Thesis, Johannes Kepler Universität Linz.
96. Selzer C., Buiter S., Pfiffner O. Numerical modeling of frontal and basal accretion at collisional margins. Tectonics 2008, 27. 10.1029/2007TC002169.
97. Sobolev S., Petrunin A., Garfunkel Z., Babeyko A. Thermo-mechanical model of the dead sea transform. Earth and Planetary Science Letters 2005, 238:78-95.
98. Stadler G., Gurnis M., Burstedde C., Wilcox L., Alisic L., Ghattas O. The dynamics of plate tectonics and mantle flow: from local to global scales. Science 2010, 329:1033-1038.
99. Steer, P., Cattin, R., Lavé, J., Godard, V., in press. Surface Lagrangian Remeshing: a new tool for studying long term evolution of continental lithosphere from 2D numerical modelling. Computers and Geosciences. doi:10.1016/j.cageo.2010.05.023.
100. Tezduyar T.E., Osawa Y. Finite element stabilization parameters computed from element matrices and vectors. Computer Methods in Applied Mechanics and Engineering 2000, 190:411-430.
101. Thieulot C., Fullsack P., Braun J. Adaptive octree-based finite element analysis of two- and three-dimensional indentation problems. Journal of Geophysical Research 2008, 113:B12207.
102. Tresca H. Sur l'écoulement des corps solides soumis à de fortes pressions. Comptes Rendus de l'Académie des Sciences (Paris) 1864, 59:754.
103. Tucker G., Hancock G. Modelling landscape evolution. Earth Surface Processes and Landforms 2010, 35:28-50.
104. Turcotte G.S.D.L., Olson P. Mantle Convection in the Earth and Planets 2001, Cambridge University Press.
105. Willett S. Dynamic and kinematic growth and change of a coulomb wedge. Thrust Tectonics 1992, 19-31. Chapman and Hall. K. McClay (Ed.).
106. Willett S.D. Rheological dependence of extension in wedge models of convergent orogens. Tectonophysics 1999, 305:419-435.
107. Willett S.D., Pope D.C. Thermo-mechanical models of convergent orogenesis: thermal and rheologic dependence of crustal deformation. Rheology and Deformation of the Lithosphere at Continental Margins 2003, 166-222. Columbia University Press.
108. Yamato P., Burov E., Agard P., Pourhiet L.L., Jolivet L. HP-UHP exhumation during slow continental subduction: self-consistent thermodynamically and thermomechanically coupled model with application to the Western Alps. Earth and Planetary Science Letters 2008, 271:63-74.
109. Yamato P., Husson L., Braun J., Loiselet C., Thieulot C. Influence of surrounding plates on 3D subduction dynamics. Geophysical Research Letters 2009, 36. 10.1029/2008GL036942.
110. Zhu G., Gerya T., Yuen D., Honda S., Yoshida T., Connolly T. Three-dimensional dynamics of hydrous thermal-chemical plumes in oceanic subduction zones. Geochemistry, Geophysics, Geosystems 2009, 10. 10.1029/2009GC002625.
111. Zienkiewicz O., Cormeau I. Visco-plasticity and creep in elastic solids - a unified numerical solution approach. International Journal for Numerical Methods in Engineering 1974, 8:821-845.
112. Zienkiewicz O., Taylor R. The Finite Element Method 2002, vols. 1-3, Butterworth and Heinemann.