Semi-Lagrangian Piecewise Biparabolic Scheme for Two-Dimensional Horizontal Advection of a Passive Scalar

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Abstract
A conservative semi-Lagrangian algorithm with a snall computational diffusion is presented that may be applied to advection of passive scalars in numerical models of the atmosphere. The technique is preferable for the horizontal semistaggered grids where a scalar point is surrounded by four velocity points. It is a coupling of the semi-Lagrangian approach and the piecewise parabolic method (PPM). Unlike the original PPM when applied to the advection of passive scalars, the new scheme is a fully two-dimensional algorithm. Also, it is not restricted by the linear stability condition. This paper describes the two steps comprising the two-dimensional algorithm. The first one is the interpolation pressure for getting the piecewise biparabolic function, and the second is a conservative remapping from the original grid to the grid made by the departure domains. Several test integrations are presented in which the described scheme performs very successfully.

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