Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows
Abstract 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 num...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-02-01
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| Series: | Geochemistry, Geophysics, Geosystems |
| Subjects: | |
| Online Access: | https://doi.org/10.1029/2019GC008799 |
| _version_ | 1797638060671762432 |
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| author | S. J. Trim J. P. Lowman S. L. Butler |
| author_facet | S. J. Trim J. P. Lowman S. L. Butler |
| author_sort | S. J. Trim |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-03-11T12:58:14Z |
| format | Article |
| id | doaj.art-25bea160ae24478394791300da827544 |
| institution | Directory Open Access Journal |
| issn | 1525-2027 |
| language | English |
| last_indexed | 2024-03-11T12:58:14Z |
| publishDate | 2020-02-01 |
| publisher | Wiley |
| record_format | Article |
| series | Geochemistry, Geophysics, Geosystems |
| spelling | doaj.art-25bea160ae24478394791300da8275442023-11-03T16:55:47ZengWileyGeochemistry, Geophysics, Geosystems1525-20272020-02-01212n/an/a10.1029/2019GC008799Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle FlowsS. J. Trim0J. P. Lowman1S. L. Butler2Department of Geological Sciences University of Saskatchewan Saskatoon Saskatchewan CanadaDepartment of Physical and Environmental Sciences University of Toronto Scarborough Toronto Ontario CanadaDepartment of Geological Sciences University of Saskatchewan Saskatoon Saskatchewan CanadaAbstract 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.https://doi.org/10.1029/2019GC008799mantle convectiontracercompositional variationsnumerical modelingentrainmentRayleigh number |
| spellingShingle | S. J. Trim J. P. Lowman S. L. Butler Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows Geochemistry, Geophysics, Geosystems mantle convection tracer compositional variations numerical modeling entrainment Rayleigh number |
| title | Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows |
| title_full | Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows |
| title_fullStr | Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows |
| title_full_unstemmed | Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows |
| title_short | Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows |
| title_sort | improving mass conservation with the tracer ratio method application to thermochemical mantle flows |
| topic | mantle convection tracer compositional variations numerical modeling entrainment Rayleigh number |
| url | https://doi.org/10.1029/2019GC008799 |
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