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A Quasi-Conservative Version of the Semi-Lagrangian Advection Scheme

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  • 1 Institute of Computational Fluid Dynamics, Department of Mathematics, University of Reading, Whiteknights, Reading, United Kingdom
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Abstract

The semi-Lagrangian method is now, perhaps, the most widely researched algorithm in connection with numerical weather prediction (NWP) codes. Monotonicity has been added to the basic method by the use of shape-preserving interpolation, and, more recently, by using ideas from flux corrected transport (FCT). In this paper, the authors describe how to make the scheme quasi-conservative. Although the lack of conservation of the semi-Lagrangian method is not widely regarded as a serious problem, for climate studies, where many tens of thousands of time steps are needed, it could become so. The method proposed here is very cheap, and hence is a viable proposition for addition to existing semi-Lagrangian codes. Making the scheme conservative as well as monotone gives the scheme shock-capturing properties, thus making the method much more useful in application areas outside of meteorology.

Abstract

The semi-Lagrangian method is now, perhaps, the most widely researched algorithm in connection with numerical weather prediction (NWP) codes. Monotonicity has been added to the basic method by the use of shape-preserving interpolation, and, more recently, by using ideas from flux corrected transport (FCT). In this paper, the authors describe how to make the scheme quasi-conservative. Although the lack of conservation of the semi-Lagrangian method is not widely regarded as a serious problem, for climate studies, where many tens of thousands of time steps are needed, it could become so. The method proposed here is very cheap, and hence is a viable proposition for addition to existing semi-Lagrangian codes. Making the scheme conservative as well as monotone gives the scheme shock-capturing properties, thus making the method much more useful in application areas outside of meteorology.

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