Application of the spectral-element method to the axisymmetric Navier-Stokes equation

Fournier, A., Bunge, H.P., Hollerbach, R. and Vilotte, J.P. (2004) Application of the spectral-element method to the axisymmetric Navier-Stokes equation. Geophysical Journal International, 156, pp. 682-700. (doi: 10.1111/j.1365-246X.2004.02149.x)

Abstract

We present an application of the spectral-element method to model axisymmetric flows in rapidly rotating domains. The primitive equations are discretized in space with local tensorized bases of high-order polynomials and in time with a second-order accurate scheme that treats viscous and rotational effects implicitly. We handle the pole problem using a weighted quadrature in elements adjacent to the axis of rotation. The resulting algebraic systems are solved efficiently using preconditioned iterative procedures. We validate our implementation through comparisons with analytic and purely spectral solutions to laminar flows in a spherical shell. This axisymmetric tool is the kernel on which complexity will be added subsequently in the long-term prospect of building a parallel spectral-element based geodynamo model.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: UNSPECIFIED
• Authors: Fournier, A., Bunge, H.P., Hollerbach, R., and Vilotte, J.P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Geophysical Journal International
• Publisher: Oxford University Press
• ISSN: 1365-246X
• ISSN (Online): 0956-540X