The combined Lagrangian advection method

Authors:
David G. Dritschel;Jérôme Fontane
Affiliations:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom;School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, United Kingdom
Venue:
Journal of Computational Physics
Year:
2010

Citing 3
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Abstract

We present and test a new hybrid numerical method for simulating layerwise-two-dimensional geophysical flows. The method radically extends the original Contour-Advective Semi-Lagrangian (CASL) algorithm [5] by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudo-spectral method for large scales, (2) Lagrangian contours for intermediate to small scales, and (3) Lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely fine-scale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation.