The application of a finite volume multigrid method to three-dimensional flow problems in a highly viscous fluid with a variable viscosity

Trompert, R. A.; Hansen, Ulrich

doi:10.1080/03091929608208968

Cited by 66 publications

(68 citation statements)

References 37 publications

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“…This method has been applied successfully to a variety of convection problems, e.g., [20][21][22], including calculations with extremely variable viscosity [23]. Trompert and Hansen [24] have presented a different multigrid method, though they have used a similar discretization scheme. By modifying the multigrid smoother they have been able to treat viscosity variations up to 10 9 , but convergence of the multigrid method becomes slow if viscosity varies strongly.…”

Section: Introductionmentioning

confidence: 98%

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A Local Mesh Refinement Multigrid Method for 3-D Convection Problems with Strongly Variable Viscosity

Albers¹

2000

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 98%

“…I solve 3-D convection problems with variable viscosity in Cartesian geometry, following the approaches given by Tackley [19] and Trompert and Hansen [24]. I have improved these approaches by the implementation of a different multigrid scheme which can handle local grid refinements.…”

Section: Introductionmentioning

confidence: 99%

A Local Mesh Refinement Multigrid Method for 3-D Convection Problems with Strongly Variable Viscosity

Albers¹

2000

Journal of Computational Physics

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“…6^8 is solved on a cell-centered grid by using a second-order ¢nite volume multigrid method. Details of the method are given by Trompert and Hansen [27], where it was used for free convection at in¢nite Prandtl number.…”

Section: Formulationmentioning

confidence: 99%

Chaotic thermohaline convection in low-porosity hydrothermal systems

Schoofs

Spera

Hansen

1999

Earth and Planetary Science Letters

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Fluids circulate through the Earth's crust perhaps down to depths as great as 5^15 km, based on oxygen isotope systematics of exhumed metamorphic terrains, geothermal fields, mesozonal batholithic rocks and analysis of obducted ophiolites. Hydrothermal flows are driven by both thermal and chemical buoyancy; the former in response to the geothermal gradient and the latter due to differences in salinity that appear to be ubiquitous. Topographically driven flows generally become less important with increasing depth. Unlike heat, solute cannot diffuse through solid matrix. As a result, temperature perturbations advect more slowly than salinity fluctuations by the factor P, but diffuse more rapidly by the factor U/D and are so smoothed out more efficiently. Here, P is porosity, while U and D denote the thermal and chemical molecular diffusivity, respectively. Double-advective instabilities may play a significant role in solute and heat transport in the deep crust where porosities are low. We have studied the stability and dynamics of the flow as a function of P and thermal and chemical buoyancy, for situations where mechanical dispersion of solute dominates over molecular diffusion in the fluid. In the numerical experiments, a porous medium is heated from below while solute provides a stabilizing influence. For typical geological parameters, the thermohaline flow appears intrinsically chaotic. We attribute the chaotic dynamical behavior of the flow to a dominance of advective and dispersive chemical transfer over the more moderate convective heat transfer, the latter actually driving the flow. Fast upward advective transport and lateral mixing of solute leads to formation of horizontal chemical barriers at depth. These gravitationally stable interfaces divide the domain in several layers of distinct composition and lead to significantly reduced heat flow for thousands of years. The unsteady behavior of thermochemical flow in low-porosity regions has implications for heat transport at mid-ocean ridges, for ore genesis, for metasomatism and metamorphic petrology, and the diagenetic history of sediments in subsiding basins. ß 1999 Elsevier Science B.V. All rights reserved.

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“…These studies include Christensen and Harder (1991), Weinberg and Schmeling (1992), Bercovici (1993), Poliakov et al (1993), Braun and Sambridge (1994), Bunge and Baumgardner (1995), Fullsack (1995), Trompert and Hansen (1996), Zhong and Gurnis (1996), Schmalholz et al (2001), Babeyko et al (2002), Tackley and Xie (2003), Moresi et al (2003), Sobolev et al (2005), Muhlhaus and Regenauer-Lieb (2005), Petrunin and Sobolev (2006), O'Neil et al (2006), Gerya and Yuen (2007), Braun et al (this issue), and Petrunin and Sobolev (this issue), which have all contributed to the development of geodynamic modeling techniques.…”

Section: Introductionmentioning

confidence: 99%

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

Popov

Sobolev

2008

Physics of the Earth and Planetary Interiors

187

159

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We describe a new technique for three-dimensional lithospheric-scale modeling of solid state deformation including strain localization processes. The new code, SLIM3D, includes a coupled thermo-mechanical treatment of deformation processes and allows for an elasto-visco-plastic rheology with diffusion, dislocation and Peierls creep mechanisms and Mohr-Coulomb plasticity. The code incorporates an Arbitrary Lagrangian Eulerian formulation with free surface and Winkler boundary conditions. SLIM3D is developed and implemented using the C++ objectoriented programming language. We describe aspects of physical models as well as details of the numerical implementation, including the Newton-Raphson solver, the stress update procedure, and the tangent operator. The applicability of the code to lithospheric-scale modeling is demonstrated by a number of benchmark problems that include: (i) the bending of an elastic plate, (ii) the sinking of a rigid cylinder into a viscous fluid, (iii) the initiation of shear bands in the brittle crust, (iv) triaxial compression test, and (v) lithospheric transpressional deformation. Finally, we discuss possible directions of further development.

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The application of a finite volume multigrid method to three-dimensional flow problems in a highly viscous fluid with a variable viscosity

Cited by 66 publications

References 37 publications

A Local Mesh Refinement Multigrid Method for 3-D Convection Problems with Strongly Variable Viscosity

A Local Mesh Refinement Multigrid Method for 3-D Convection Problems with Strongly Variable Viscosity

Chaotic thermohaline convection in low-porosity hydrothermal systems

SLIM3D: A tool for three-dimensional thermomechanical modeling of lithospheric deformation with elasto-visco-plastic rheology

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