An Exactly Mass Conserving and Pointwise Divergence Free Velocity Method: Application to Compositional Buoyancy Driven Flow Problems in Geodynamics

Nathan Sime, Jakob M. Maljaars, Cian R. Wilson, Peter E. van Keken

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

Tracer methods are widespread in computational geodynamics for modeling the advection of chemical data. However, they present certain numerical challenges, especially when used over long periods of simulation time. We address two of these in this work: the necessity for mass conservation of chemical composition fields and the need for the velocity field to be pointwise divergence free to avoid gaps in tracer coverage. We do this by implementing the hybrid discontinuous Galerkin (HDG) finite element (FE) method combined with a mass conserving constrained projection of the tracer data. To demonstrate the efficacy of this system, we compare it to other common FE formulations of the Stokes system and projections of the chemical composition. We provide a reference of the numerical properties and error convergence rates which should be observed by using these various discretization schemes. This serves as a tool for verification of existing or new implementations. We summarize these data in a reproduction of a published Rayleigh-Taylor instability benchmark, demonstrating the importance of careful choices of appropriate and compatible discretization methods for all aspects of geodynamics simulations.

Original languageEnglish
Article numbere2020GC009349
Number of pages32
JournalGeochemistry, Geophysics, Geosystems
Volume22
Issue number4
DOIs
Publication statusPublished - 2021

Keywords

  • buoyancy driven convection
  • finite element analysis
  • mantle convection
  • tracer methods

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