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The combined Lagrangian advection method

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 by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudospectral 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 finescale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation.
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David Dritschel, Jerome Fontane. The combined Lagrangian advection method. Journal of Computational Physics, Elsevier, 2010, vol. 229, pp. 5408-5417. ⟨10.1016/j.jcp.2010.03.048⟩. ⟨hal-00786319⟩

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