Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

Hillebrand, Bram; Thieulot, Cédric; Geenen, T.; Berg, A. P. van den; Spakman, Wim

doi:10.5194/sed-6-1523-2014

Cited by 7 publications

(6 citation statements)

References 47 publications

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“…To reduce these errors, numerical filters can be applied (Lenardic & Kaula, ) as well as flux limiters (Harten, ; Roe, ; Sweby, ) and bound‐preserving limiters (He et al, ). It is also possible to track the interface between materials through the advection of level sets (e.g., Hillebrand et al, ) or a hybrid between particle and level set methods (Samuel & Evonuk, ).…”

Section: Introductionmentioning

confidence: 99%

Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

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Lowman

Butler

2020

Geochem Geophys Geosyst

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Modeling the evolution of composition in a convecting mantle is difficult since the associated chemical diffusivity is very small. Consequently, compositional evolution is often modeled using the advection equation which is prone to overdiffusion and spurious oscillations unless special numerical schemes are employed. Similar errors can also occur while modeling the evolution of temperature, since mantle convection is advection dominated. One numerical scheme designed to minimize such errors is the tracer ratio method, in which Lagrangian tracers are used to track each composition in the system in addition to carrying local temperature values that are time dependent. However, tracer spacing may become very uneven during evolution, which can contribute to errors in mass and energy conservation. In this study, a tracer repositioning algorithm designed to promote even tracer coverage is presented and tested using over 400 calculations in a large thermal Rayleigh number/buoyancy ratio parameter space. In particular, the effect of tracer repositioning on mass and energy conservation errors is examined. In most cases, we find that energy errors are roughly an order of magnitude less than mass errors, regardless of tracer repositioning. However, in situations with substantial entrainment of compositionally distinct material, mass errors can be reduced by up to an order of magnitude if tracers are repositioned during model evolution. We also find that for a fixed buoyancy ratio, entrainment of basal material decreases as the thermal Rayleigh number increases.

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Section: Introductionmentioning

confidence: 99%

Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

Trim

Lowman

Butler

2020

Geochem Geophys Geosyst

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“…Finally, Firedrake's flexibility would make exploring different advection schemes straightforward, rendering it very well-suited to level-set approaches (e.g. Hillebrand et al, 2014).…”

Section: Discussionmentioning

confidence: 99%

Towards automatic finite-element methods for geodynamics via Firedrake

et al. 2022

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Abstract. Firedrake is an automated system for solving partial differential equations using the finite-element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means of creating accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software that is ideally suited to simulating a wide range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach are confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12 288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex non-linear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming Firedrake's suitability for addressing research problems at the frontiers of global mantle dynamics research.

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“…From a modeling view point, the influence of rigid inclusions on fluid flow has been explored at the scale of magma-chambers (Suckale et al 2012;Yamato et al 2015;Shibano et al 2013) or at that of the whole mantle (Patočka et al 2020), but seldom at the crustal scale (Deubelbeiss & Kaus 2008). In fact no previous model has explicitly incorporated deformable compositional heterogeneities in a partially molten crust, most probably because numerical codes encounter issues with mass conservation and numerical diffusion at layers interfaces (Deubelbeiss & Kaus 2008;Schmeling et al 2008;Suckale et al 2010;Hillebrand et al 2014;Pusok et al 2017;Heister et al 2017). This motivates the use of a Volume-Of-Fluid (VOF) method, dedicated to the conservation of compositional interfaces.…”

Section: Introductionmentioning

confidence: 99%

Models of convection and segregation in heterogeneous partially molten crustal roots with a VOF method – I: flow regimes

Louis-Napoléon

Bonometti

Gerbault

et al. 2021

Geophysical Journal International

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Summary We investigate numerically some thermo-mechanical conditions for the development of crustal scale diapirism and convection in a heterogeneous continental crust independently from the action of regional tectonics. Here, we consider a hot crust where convection is generated below a melting front, with unmolten and partially molten domains of specific temperature and strain-rate dependent power-law rheologies. We take advantage of the VOF (Volume Of Fluid) method to capture the coalescence and separation of deformable inclusions in the partially molten domain. The inclusions, of several hundred meters in size, are more or less dense and more or less viscous with respect to the ambient medium (they also behave with a power-law rheology). We restrict our study to a 20 Myr time scale, during which gravitational dynamics may dominate over lateral tectonics and lithospheric thermal reequilibration. The motion of these inclusions during the development of gravitational instabilities allows to define distinct flow regimes that depend on two Rayleigh numbers denoted RaUM and RaPM, for the unmolten and partially molten rock properties, respectively. A ’suspension’ regime occurs at high RaUM and high RaPM, in which most of the light compositional heterogeneities remain entrained in the convective cells. In contrast at low RaUM and high RaPM, a ’layering’ regime is characterized by merging of the light inclusions as floating clusters below the rigid upper crustal lid. This regime occurs occurs in association with a sharp viscosity gradient at upper-to-middle crust transitional depths. In these two regimes, the dense inclusions accumulate at the bottom of the partially molten zone. Finally at moderate RaPM, a ’diapiric’ regime reflects the segregation of the heavy and the light inclusions, respectively downward and upward, without global convection. These numerical experiments lead to a first order evaluation of the physical parameters required for the segregation of deformable inclusions of variable densities and convection, in a partially molten crust, and provide insights on the conditions for the development of migmatite domes. Geological data indicate that these processes likely occur in a large number of settings from Archean to Phanerozoic times, and contribute to the differentiation of the continental crust.

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Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

Cited by 7 publications

References 47 publications

Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

Towards automatic finite-element methods for geodynamics via Firedrake

Models of convection and segregation in heterogeneous partially molten crustal roots with a VOF method – I: flow regimes

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