Benchmarking multiphysics software for mantle convection

Trim, S. J.; Butler, S. L.; Spiteri, Raymond J.

doi:10.1016/j.cageo.2021.104797

Cited by 7 publications

(3 citation statements)

References 37 publications

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“…These quantities have been used to help quantify the accuracy of numerical solutions in thermochemical convection studies (Samuel & Evonuk, 2010; Tackley & King, 2003; S. J. Trim et al., 2020, 2021; van Keken et al., 1997). We report the RMS velocity and entrainment for the manufactured solution in Section 3.2.…”

Section: Methodsmentioning

confidence: 99%

Manufacturing an Exact Solution for 2D Thermochemical Mantle Convection Models

Trim

Butler

McAdam

et al. 2023

Geochem Geophys Geosyst

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Introduction MotivationBuoyancy is the primary driving force behind convection in the Earth's mantle. Contributing factors to buoyancy in the mantle include lateral contrasts in temperature and composition. In the case of thermochemical flows, mantle buoyancy depends upon both of these factors. Heat sources and sinks affecting the thermal state of the Earth's mantle include radiogenic heating, heating from the outer core, and cooling at the Earth's surface (Turcotte & Schubert, 2002). Thermally driven buoyancy instabilities can arise when the rate of thermal transport via advection exceeds that of diffusion. Such situations include the rise of hot upwellings from the core and the descent of cold downwellings from the surface (e.g., a subducting slab). Buoyancy instabilities can also be caused by lateral variations in thermal boundary conditions. Lateral contrasts in mantle composition can occur for several reasons, including transitions between oceanic and continental lithosphere, rapid subduction of oceanic lithosphere, and deep dense compositional piles. The Earth's Large Low Shear wave Velocity Provinces may also be influenced by thermal and compositional gradients (Davies et al., 2015;McNamara, 2019).Geophysical flows involving sharp compositional contrasts are notoriously difficult to model numerically. Challenges include both spurious oscillations and extraneous diffusion (Lenardic & Kaula, 1993). Numerical methods employed to minimize these errors include the use of particles (Tackley & King, 2003), level sets (Hillebrand et al., 2014), and hybrid methods (Samuel & Evonuk, 2010).Another even more fundamental challenge is to ensure the software that implements the numerical solution has been coded correctly. By definition, model developers produce code to solve problems for which solutions are unknown. The verification and validation process in modeling and simulation often involves qualitative

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Section: Methodsmentioning

confidence: 99%

Manufacturing an Exact Solution for 2D Thermochemical Mantle Convection Models

Trim

Butler

McAdam

et al. 2023

Geochem Geophys Geosyst

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“…In this paper, we use z R = z I . These quantities have been used to help quantify the accuracy of numerical solutions in thermochemical convection studies (van Keken et al, 1997;Tackley & King, 2003;Samuel & Evonuk, 2010;Trim et al, 2020Trim et al, , 2021. We report the RMS velocity and entrainment for the manufactured solution in section 3.2.…”

Section: Diagnosticsmentioning

confidence: 99%

Manufacturing an exact solution for 2D thermochemical mantle convection models

Trim

Butler

McAdam

et al. 2022

Preprint

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In this study, we manufacture an exact solution for a set of 2D thermochemical mantle convection problems. The derivation begins with the specification of a stream function corresponding to a non-stationary velocity field. The method of characteristics is then applied to determine an expression for composition consistent with the velocity field. The stream function formulation of the Navier-Stokes equation is then applied to solve for temperature. The derivation concludes with the application of the advection-diffusion equation for temperature to solve for the internal heating rate consistent with the velocity, composition, and temperature solutions. Due to the large number of terms, the internal heating rate is computed using Maple which is also made available in Fortran. Using the method of characteristics allows the compositional transport equation to be solved without the addition of diffusion or source terms. As a result, compositional interfaces remain sharp throughout time and space in the exact solution. The exact solution presented allows for precision testing of thermochemical convection codes for correctness and accuracy.

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“…In the present study, we investigate the effect of the regularization with the capped porosity on the liquid transport and mass conservation in the two-phase flow model for the Earth's mantle, using the commercial finite element package COMSOL Multiphysics® (COMSOL, hereafter). COMSOL has been used previously in the context of mantle convection and successfully benchmarked (e.g., Lee, 2013;Yu and Lee, 2018;Trim et al, 2021). COMSOL was used to study the liquid transport in the mantle wedge of subduction zones, considering a simplified porous flow model without the incorporation of the effect of matrix compaction (e.g., Wada and Behn, 2015;Lee et al, 2021;Kim et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

Modeling liquid transport in the Earth’s mantle as two-phase flow: Effect of an enforced positive porosity on liquid flow and mass conservation

Lee,

Cerpa,

Han

et al. 2023

Preprint

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Abstract. Fluid and melt transport in the solid mantle can be modeled as a two-phase flow in which the liquid flow is resisted by the compaction of the viscously deforming solid mantle. Given the wide impact of the liquid transport on the geodynamical and geochemical evolution of the Earth, the so-called “compaction equations” are more and more incorporated in geodynamical modeling studies. The implementation of these equations requires a regularization technique to handle the porosity singularity in dry mantle. Moreover, it is also common to enforce a positive porosity (liquid fraction) to avoid unphysical negative values of porosity. However, the effects of this “capped” porosity on the liquid transport and mass conservation have not been quantitatively evaluated. Here, we investigate these effects using a series of 1- and 2-dimensional numerical models using the commercial finite element package COMSOL Multiphysics®. The results of benchmarking experiments against a semi-analytical solution for 1- and 2-D solitary waves illustrate the successful implementation of the compaction equations. We show that the solutions are accurate when the element size is smaller than half of the compaction length. Furthermore, in time-evolving experiments where the solid is stationary (immobile), we show that the mass balance errors are similarly low for both capped and uncapped experiments (i.e., allowing negative porosity). When Couette flow, convective flow, or subduction corner flow of the solid mantle is assumed, the capped porosity leads to overestimations of the mass of liquid in the model domain and mass flux of liquid across the model boundaries, resulting in intrinsic errors in mass conservation even if high mesh resolution is used. Despite the errors in mass balance, however, the general trends of porosity evolution in the capped experiments are similar to those in the uncapped experiments. Hence, the use of the regularization of the compaction equations with the enforced positive porosity is reasonable for modeling fluid and melt transport in a deforming mantle.

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Benchmarking multiphysics software for mantle convection

Cited by 7 publications

References 37 publications

Manufacturing an Exact Solution for 2D Thermochemical Mantle Convection Models

Manufacturing an Exact Solution for 2D Thermochemical Mantle Convection Models

Manufacturing an exact solution for 2D thermochemical mantle convection models

Modeling liquid transport in the Earth’s mantle as two-phase flow: Effect of an enforced positive porosity on liquid flow and mass conservation

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