A class of monotone interpolation schemes

Abstract This paper discusses a class of monotone (nonoscillatory) interpolation schemes convenient for applications with a variety of problems arising in computational fluid dynamics. These interpolators derive from the flux-corrected-transport finite difference advection schemes. It is shown that any known dissipative advection algorithm may be implemented as an interpolation scheme. The resulting interpolation procedure retains the formal accuracy of the advection scheme and offers such attractive computational properties as preservation of a sign or monotonicity of the interpolated variable. The derived class of interpolators consists of schemes of different levels of accuracy, efficiency, and complexity reflecting a rich variety of available advection schemes. Theoretical considerations are illustrated with idealized examples and selected applications to atmospheric fluid dynamics problems.

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