High accuracy mantle convection simulation through modern numerical methods

Kronbichler, Martin; Heister, Timo; Bangerth, Wolfgang

doi:10.1111/j.1365-246x.2012.05609.x

Cited by 366 publications

(439 citation statements)

References 60 publications

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“…In the phase field method (Lenardic and Kaula, 1993;Van Keken et al, 1997;Kronbichler et al, 2012), materials are assigned a number, and the composition of the fluid at a given node of the grid is given by a field containing the various fractions of the different material components. This field is then advected using a stabilized advection equation.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh-Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…It has therefore been implemented in the state-of-the-art open-source code ASPECT 1 (Kronbichler et al, 2012;Heister et al, 2017) and in the ELEFANT 2 code (Thieulot, 2014;Tosi et al, 2015;Lavecchia et al, 2017). Both codes solve the incompressible flow Stokes equations in spherical shell domains but use Cartesian coordinates.…”

Section: Implementation and Resultsmentioning

confidence: 99%

“…Many codes have been developed in the last 30 years (Machetel et al, 1986;Glatzmaier, 1988;Bercovici et al, 1989;Zhang and Christensen, 1993;Zhang and Yuen, 1995;Ratcliff et al, 1996;Iwase, 1996;Zhong et al, 2000;Tabata and Suzuki, 2000;Richards et al, 2001;Kageyama and Sato, 2004;Yoshida and Kageyama, 2004;Choblet et al, 2007;Tackley, 2008;Davies et al, 2013;Kronbichler et al, 2012;Burstedde et al, 2013), and spherical shell numerical benchmarks have been carried out (Zhong et al, 2000;Stemmer et al, 2006;Zhong et al, 2008;Arrial et al, 2014). Semianalytical Stokes flow solutions derived via propagator matrix methods have also been proposed in the past (Busse, 1975;Busse and Riahi, 1982;Hager and O'Connell, 1981;Richards and Hager, 1984), while Tosi and Martinec (2007) derived a semi-analytical solution in the case of two eccentrically nested spheres.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for viscous incompressible Stokes flow in a spherical shell

Thieulot

2017

Solid Earth

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Abstract. I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial and of the power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g., the root mean square velocity, are analytically computed. This forms the basis of a numerical benchmark for convection codes and I have implemented it in two finite-element codes: ASPECT and ELEFANT. I report error convergence rates for velocity and pressure.

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“…A short summary of the governing equations solved by ASPECT is given in Section 2.1 (for more information the reader is 5 referred to Kronbichler et al, 2012). Section 2.2 lists our specific additions to the code.…”

Section: Methodsmentioning

confidence: 99%

“…Artificial diffusivity ν h is used to prevent 15 oscillations due to the advection of the temperature field. It is calculated according to the entropy viscosity method of Guermond et al (2011), as described in Kronbichler et al (2012).…”

Section: Governing Equationsmentioning

confidence: 99%

Implementing nonlinear viscoplasticity in ASPECT: benchmarking and applications to 3D subduction modeling

Glerum

Thieulot

Fraters

et al. 2017

Preprint

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Abstract. ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel finite element code originally designed for modeling thermal convection in the mantle with a Newtonian rheology. The code is characterized by modern numerical methods, high-performance parallelism and extensibility. This last characteristic is illustrated in this work: we have extended the use of ASPECT from global thermal convection modeling to upper mantle-scale applications of subduction.Subduction modeling generally requires the tracking of multiple materials with different properties and with nonlinear 5 viscous and viscoplastic rheologies. To this end, we implemented a frictional plasticity criterion that is combined with a viscous diffusion and dislocation creep rheology. Because ASPECT uses compositional fields to represent different materials (and, since recently, tracers), all material parameters are made dependent on a user-specified number of fields.The goal of this paper is primarily to describe and validate our implementations of complex, multi-material rheology by reproducing the results of four well-known two-dimensional benchmarks: the indentor benchmark, the brick experiment, the 10 sandbox experiment and the slab detachment benchmark. Furthermore, we aim to provide hands-on examples for prospective users by demonstrating the use of multi-material viscoplasticity with three-dimensional, thermomechanical models of oceanic subduction, putting ASPECT on the map as a community code for high-resolution, nonlinear rheology subduction modeling.

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High accuracy mantle convection simulation through modern numerical methods

Cited by 366 publications

References 60 publications

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

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

Analytical solution for viscous incompressible Stokes flow in a spherical shell

Implementing nonlinear viscoplasticity in ASPECT: benchmarking and applications to 3D subduction modeling

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