×

An ALE-based numerical technique for modeling sedimentary basin evolution featuring layer deformations and faults. (English) Zbl 1214.86005

Summary: We present a numerical tool to simulate dynamics of stratified sedimentary basins, i.e. depressions on the Earth’s surface filled by sediments. The basins are usually complicated by crustal deformations and faulting of the sediments. The balance equations, the non-Newtonian rheology of the sediments, and the depth-porosity compaction laws describe here a model of basin evolution. We propose numerical schemes for the basin boundary movement and for the fault tracking. In addition, a time splitting algorithm is employed to reduce the original model into some simpler mathematical problems. The numerical stability and the other features of the developed methodology are shown using simple test cases and some realistic configurations of sedimentary basins.

MSC:

86A60 Geological problems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76A05 Non-Newtonian fluids

Software:

El-Topo
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Longoni, M.; Malossi, A.; Villa, A., A robust and efficient conservative technique for simulating three-dimensional sedimentary basins, Comput. Fluids, 39, 1964-1976 (2010) · Zbl 1245.76050
[2] Ismail-Zadeh, A.; Tsepelev, I.; Talbot, C.; Korotkii, A., Three-dimensional forward and backward modelling of diapirism: numerical approach and its applicability to the evolution of salt structures in the Pricaspian basin, Tectonophysics, 387, 81-103 (2004)
[3] Ismail-Zadeh, A.; Krupskii, D., Extrusion and gravity current of a fluid: Implications for salt tectonics, Phys. Solid Earth, 42, 999-1006 (2006)
[4] Poliakov, A.; Podladchikov, Y.; Dawson, E.; Talbot, C., Salt diapirism with simultaneous brittle faulting and viscous flow, Geol. Soc. London Spec. Pub. (Salt Tectonics), 100, 291-302 (1996)
[5] Zaleski, S.; Julien, P., Numerical simulation of Rayleigh-Taylor instability for single and multiple salt diapirs, Tectonophysics, 206, 55-69 (1992)
[6] Collins, I., Associated and non-associated aspects of constitutive laws for coupled elastic - plastic materials, Int. J. Geomech., 2, 259-267 (2002)
[7] van Keken, P.; Spiers, C.; van den Berg, A.; Muyzert, E., The effective viscosity of rocksalt: implementation of steady-state creep laws in numerical models of salt diapirism, Tectonophysics, 225, 457-476 (1993)
[8] Turcotte, D.; Schubert, G., Geodynamics (2001), Cambridge University Press
[9] Peric, D.; Crook, A., Computational strategies for predictive geology with reference to salt tectonics, Comput. Methods Appl. Mech. Eng., 193, 5195-5222 (2004) · Zbl 1112.74534
[10] Lefton, L.; Wei, D., A penalty method for approximations of the stationary power-law Stokes problem, Electron. J. Diff. Equat., 7, 1-12 (2001) · Zbl 0972.65096
[11] Cloetingh, S.; Podladchikov, Y., Perspectives in tectonic modeling, Tectonophysics, 320, 169-173 (2000)
[12] Massimi, P.; Quarteroni, A.; Scrofani, G., An adaptive finite element method for modeling salt diapirism, Math. Mod. Methods Appl. Sci., 16, 587-614 (2007) · Zbl 1136.76389
[13] Massimi, P.; Quarteroni, A.; Saleri, F.; Scrofani, G., Modeling of salt tectonics, Comput. Methods Appl. Mech. Eng., 197, 281-293 (2007) · Zbl 1169.76326
[14] Bey, J., Tetrahedral grid refinement, Computing, 55, 355-378 (1995) · Zbl 0839.65135
[15] Liu, A.; Joe, B., Quality local refinement of tetrahedral meshes based on bisection, SIAM J. Sci. Comput., 16, 1269-1291 (1995) · Zbl 0841.65098
[16] Liu, A.; Joe, B., Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision, SIAM J. Sci. Comput., 65, 1183-1200 (1996) · Zbl 0858.65120
[17] Plaza, A.; Carey, G., Local refinement of simplicial grids based on the skeleton, Appl. Numer. Math., 32, 195-218 (2000) · Zbl 0940.65142
[18] W. Wessner, Mesh refinement techniques for TCAD Tools, Ph.D. Thesis, Technische Universität Wien, 2006.; W. Wessner, Mesh refinement techniques for TCAD Tools, Ph.D. Thesis, Technische Universität Wien, 2006.
[19] Onate, E.; Idelsohn, S.; Pin, F. D.; Aubry, R., The particle finite element method. An overview, Int. J. Comput. Methods, 1, 267-307 (2004) · Zbl 1182.76901
[20] Moresi, L.; Dufour, F.; Muhlhaus, H., A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials, J. Comput. Phys., 184, 476-497 (2003) · Zbl 1047.74540
[21] O’Neill, C.; Moresi, L.; Muller, D.; Albert, R.; Dufour, F., Ellipsis 3D. a particle-in-cell finite-element hybrid code for modelling mantle convection and lithosperic deformation, Comput. Geosci., 1, 1769-1779 (2006)
[22] Darlington, R.; McAbee, T.; Rodrigue, G., A study of ALE simulations of Rayleigh-Taylor instability, Comput. Phys. Commun., 135, 58-73 (2001) · Zbl 0987.76061
[23] Villa, A.; Formaggia, L., Implicit tracking for multi-fluid simulations, J. Comput. Phys., 229, 5788-5802 (2010) · Zbl 1346.76156
[24] Armero, F.; Love, E., An arbitrary Lagrangian-Eulerian finite element method for finite strain plasticity, Int. J. Num. Methods Eng., 57, 471-508 (2003) · Zbl 1062.74604
[25] Formaggia, L.; Nobile, F., Stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Numer. Math., 7, 105-131 (1999) · Zbl 0942.65113
[26] Huerta, A.; Rodriguez-Ferran, A.; Diez, P.; Sarrate, J., Adaptive finite element strategies based on error assessment, Int. J. Num. Methods Eng., 46, 1803-1818 (1999) · Zbl 0968.74066
[27] Lesoinne, M.; Farhat, C., Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact in aeroelastic computations, Comput. Methods Appl. Mech. Eng., 134, 71-90 (1996) · Zbl 0896.76044
[28] M. Murayama, K. Nakahashi, K. Matsushima, Unstructured dynamic mesh for large movement and deformation, AIAA Paper 2002-0122, 2002.; M. Murayama, K. Nakahashi, K. Matsushima, Unstructured dynamic mesh for large movement and deformation, AIAA Paper 2002-0122, 2002.
[29] Peery, J.; Carrol, D., Multi-material ALE methods in unstructured grids, Comput. Methods Appl. Mech. Eng., 187, 591-619 (2000) · Zbl 0980.74068
[30] Smith, R., Ausm(ale): a geometrical conservative arbitraary Lagrangian-Eulerian flux splitting scheme, J. Comput. Phys., 150, 268-286 (1999) · Zbl 0936.76046
[31] Askes, H.; Rodriguez-Ferran, A., A combined rh-adaptivity scheme based on domain subdivision. Formulation and linear examples, Int. J. Num. Methods Eng., 51, 253-273 (2001) · Zbl 1031.74047
[32] Askes, H.; Rodriguez-Ferran, A.; Huerta, A., Adaptive analysis of yeld line patterns in plates with the arbitrary Lagrangian-Eulerian method, Comput. Struct., 70, 257-271 (1999) · Zbl 0958.74055
[33] Masud, A.; Bhanabhagvanwala, M.; Khurram, R., An adaptive mesh rezoning scheme for moving boundary flows and fluid-structure interaction, Comput. Fluids, 36, 77-91 (2007) · Zbl 1181.76108
[34] Aymone, J. F., Mesh motion technique for the ALE formulation in 3D large deformation problems, Comput. Methods Appl. Mech. Eng., 59, 1879-1908 (2004) · Zbl 1060.74625
[35] Blom, F., Consideration on the spring analogy, Int. J. Numer. Methods Fluids, 32, 647-668 (1998) · Zbl 0981.76067
[36] Bottasso, C.; Detomi, D.; Serra, R., The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes, Comput. Methods Appl. Mech. Eng., 194, 4244-4264 (2005) · Zbl 1151.74429
[37] Johnson, A.; Tezduyar, T., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Comput. Methods Appl. Mech. Eng., 119, 73-94 (1994) · Zbl 0848.76036
[38] Audet, D.; Fowler, A., A mathematical model for compaction in sedimentary basins, Geophys. J. Int., 110, 577-590 (1992)
[39] Zlotnik, S.; Diez, P., Hierarchical X-FEM for n-phase flow \((n>2)\), Comput. Methods Appl. Mech. Eng., 198, 2329-2338 (2009) · Zbl 1229.76060
[40] Zlotnik, S.; Fernandez, M.; Diez, P.; Verges, J., Modelling gravitational instabilities: slab break-off and Rayleigh-Taylor diapirism, Pure Appl. Geophys., 165, 1491-1510 (2008) · Zbl 1191.86031
[41] Fowler, A.; Yang, X., Fast and slow compaction in sedimentary basins, SIAM J. Appl. Math., 59, 365-385 (1998) · Zbl 0923.35124
[42] Neto, J. C.; Wawrzynek, P.; Carvalho, M.; Martha, L.; Ingraffea, A., An algorithm for three-dimensional mesh generation for arbitrary regions with cracks, Eng. Comput., 17, 75-91 (2001) · Zbl 1002.68527
[43] Quarteroni, A., Numerical Models for Differential Problems (2009), Springer-Verlag
[44] Quarteroni, A.; Valli, A., Numerical Approximation of Partial Differential Equations (1997), Springer-Verlag
[45] May, D.; Moresi, L., Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics, Phys. Earth Planet In., 171, 33-47 (2008)
[46] Moresi, L.; Zhong, S.; Gurnis, M., The accuracy of finite element solution of Stokes flow with strongly varying viscosity, Phys. Earth Planet In., 97, 83-94 (1996)
[47] Olshanskii, M.; Reusken, A., Analysis of a Stokes interface problem, Numer. Math., 103, 129-149 (2006) · Zbl 1092.65104
[48] W. Huang, Anisotropic mesh adaptation and movement, Lecture Notes for the Workshop on: Adaptive Method, Theory and Application, Peking University, Beijing, China, 2005.; W. Huang, Anisotropic mesh adaptation and movement, Lecture Notes for the Workshop on: Adaptive Method, Theory and Application, Peking University, Beijing, China, 2005.
[49] Huang, W.; Sun, W., Variational mesh adption 2: error estimates and monitor functions, J. Comput. Phys., 184, 619-648 (2003) · Zbl 1018.65140
[50] Adams, R.; Fournier, J., Sobolev Spaces (2003), Elsevier Science · Zbl 1098.46001
[51] Ern, A.; Guermond, J., Theory and Practice of Finite Elements (2000), Springer
[52] Brochu, T.; Bridson, R., Robust topological operations for dynamic explicit surfaces, SIAM J. Sci. Comput., 31, 2472-2493 (2009) · Zbl 1195.65017
[53] Osher, S.; Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces (2003), Springer · Zbl 1026.76001
[54] Sethian, A., Level Set Methods and Fast Marching Methods (1999), Cambridge University Press · Zbl 0929.65066
[55] Ciarlet, P., Introduction to Numerical Linear Algebra and Optimization (1988), Cambridge University Press
[56] Lions, J., Optimal Control of Systems Governed by Partial Differential Equations (1971), Springer · Zbl 0203.09001
[57] Ismail-Zadeh, A.; Talbot, C.; Volozh, Y., Dynamic restoration of profiles across diapiric salt structures: numerical approach and its applications, Tectonophysics, 337, 21-36 (2001)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.