An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension

By T. Yabe, R. Tanaka, T. Nakamura, F. Xiao. 2001

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A conservative local interface sharpening scheme for the constrained interpolation profile method (2012, methodology): “The conservative scheme is abbreviated CIP-CSL (conservative semi-Lagrangian) and the different abbreviations are used in accordance with the accuracy in space; CIP-CSL2 the third-order scheme [3], CIP-CSL3 the fourth-order [5], and CIP-CSL4 the fifth-order [4,6].”
Construction of the SILAM Eulerian atmospheric dispersion model based on the advection algorithm of Michael Galperin (2015, methodology): “For instance, the conservative semi-Lagrangian schemes (Yabe and Aoki, 1991; Yabe et al., 2001) use a semi-Lagrangian step to evaluate the mixing ratio at cell interfaces, and then use the interface values along with the cell integrals to derive an interpolant representing the sub-grid distribution.”
The Evolution of Dynamical Cores for Global Atmospheric Models(125th Anniversary Issue of the Meteorological Society of Japan) (2007, methodology): “As water vapor began to play a more dominant role in the parameterizations, dissatisfaction arose with the spectral transform method for transport of scalars such as water vapor and chemical constituents.”