The HyperCASL algorithm: A new approach to the numerical simulation of geophysical flows

Jérôme Fontane*, David G. Dritschel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We describe a major extension to the Contour-Advective Semi-Lagrangian (CASL) algorithm [D.G. Dritschel, M.H.P. Ambaum, A contour-advective semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields, Quart. J. Roy. Meteorol. Soc. 123 (1997) 1097-1130; D.G. Dritschel, M.H.P. Ambaum, The diabatic contour advective semi-Lagrangian algorithm, Mon. Weather Rev. 134 (9) (2006) 2503-2514]. The extension, called 'HyperCASL' (HCASL), uses Lagrangian advection of material potential vorticity contours like CASL, but a Vortex-In-Cell (VIC) method for the treatment of diabatic forcing or damping. In this way, HyperCASL is fully Lagrangian regarding advection. A grid is used as in CASL to deal with 'inversion' (computing the velocity field from the potential vorticity field). First, the novel aspects of the algorithm are described including several improvements to the underlying CASL algorithm. All numerical parameters are chosen so as to minimise the computational cost while improving conservation properties. Finally, a thorough inter-code comparison is conducted using a two-dimensional inviscid unforced turbulence test-case. This enables us to point out the advantages of this new algorithm in terms of resolution, computational cost and numerical diffusion compared to other existing methods, namely CASL, VIC and Pseudo-Spectral (PS) methods.

Original languageEnglish
Pages (from-to)6411-6425
Number of pages15
JournalJournal of Computational Physics
Issue number17
Publication statusPublished - 20 Sept 2009


  • Contour advection
  • Contour dynamics
  • Geophysical flows
  • Vortex methods


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