A Spectral-Element Model of Mantle Convection

Anil Deane, Paul Fischer

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter describes the results for modeling mantle convection using the spectral-element method. The model is useful for 2D plane-rectangular geometries as well as fully spherical 3D. The method combines the geometrical flexibility of the FEM and the high accuracy (exponential convergence) of spectral methods. It models the mantle as a high and infinite Prandtl (Pr) number fluid, and obtains steady and unsteady solutions for varying Rayleigh (Ra) numbers. Results for rectangular and for fully spherical geometries are described, relevant to the Earth's mantle. The spherical case has an aspect ratio (gap to radius) equivalent to the mantle convection zone of the Earth. The finite Pr case is unsteady at Ra=105 whereas infinite Pr convection at Ra=105 is found to be steady. At high Pr, the temperature field forms narrow regions of up-welling and down-welling flows.

Original languageEnglish (US)
Title of host publicationParallel Computational Fluid Dynamics 2003
Subtitle of host publicationAdvanced Numerical Methods, Software and Applications
PublisherElsevier Inc.
Number of pages4
ISBN (Electronic)9780080473673
ISBN (Print)9780444516121
StatePublished - May 6 2004
Externally publishedYes


  • Mantle convection
  • Spectral-Element method

ASJC Scopus subject areas

  • General Mathematics


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