A spectral finite volume transport scheme on the cubed-sphere

  • Authors:

  • Vani Cheruvu;Ramachandran D. Nair;Henry M. Tufo

  • Affiliations:

  • Department of Computer Science, University of Colorado at Boulder, Boulder, CO 80309, USA;Scientific Computing Division, National Center for Atmospheric Research, Boulder, CO 80305, USA;Department of Computer Science, University of Colorado at Boulder, Boulder, CO 80309, USA and Scientific Computing Division, National Center for Atmospheric Research, Boulder, CO 80305, USA

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2007

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Abstract

Advective processes are of central importance in many applications and their treatment is crucial in the numerical modelling of the transport of trace constituents in atmospheric models. High-order numerical methods offer the promise of accurately capturing these advective processes in atmospheric flows and have been shown to efficiently scale to large numbers of processors. In this paper, a conservative transport scheme based on the nodal high-order spectral finite volume method is developed for the cubed-sphere. A third-order explicit strong stability preserving scheme is employed for the time integration. The reconstruction procedure which we developed avoids the (expensive) calculation of the inverse of the reconstruction matrix. Flux-corrected transport algorithm is implemented to enforce monotonicity in the two-dimensional transport scheme. Two standard advection tests, a solid-body rotation and a deformational flow, were performed to evaluate the spectral finite volume method optionally combined with a flux-corrected transport scheme. Spectral accuracy in space is demonstrated with a linear wave equation.