Manufacturing an Exact Solution for 2D Thermochemical Mantle Convection Models
Date
2023
Authors
Trim, Sean
Butler, Samuel
McAdam, Shawn S.C.
Spiteri, Raymond
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Wiley Open Access [Commercial Publisher], American Geophysical Union [Society Publisher], Geochemical Society [Society Publisher]
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Article
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Abstract
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 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™, and code is also made available in Fortran and Python. 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.
Description
© 2023. The Authors. Geochemistry, Geophysics, Geosystems published by Wiley Periodicals LLC on behalf of American Geophysical Union.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Keywords
2D Thermochemical Mantle Convection Model, velocity field, Maple™, compositional transport, thermochemical convection
Citation
Trim, S. J., Butler, S. L., McAdam, S. S. C., & Spiteri, R. J. (2023). Manufacturing an exact solution for 2D thermochemical mantle convection models. Geochemistry, Geophysics, Geosystems, 24, e2022GC010807. https:// doi.org/10.1029/2022GC010807
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Citation
Trim, S. J., Butler, S. L., McAdam, S. S. C., & Spiteri, R. J. (2023). Manufacturing an exact solution for 2D thermochemical mantle convection models. Geochemistry, Geophysics, Geosystems, 24, e2022GC010807. https:// doi.org/10.1029/2022GC010807
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DOI
10.1029/2022GC010807