Abstract
This paper presents rational function based fully multi-dimensional advection schemes for structured and unstructured grids of a quadrilateral geometry. For the structured grid, a fully 2D rational interpolation function is constructed by combining two 1D sweeps based on the 1D rational function with 3 degrees of freedoms, and is convexity preserving. For the unstructured, the interpolation function is constructed according to the same procedure as in the structured grid after each control volume is mapped to a rectangle. Numerical tests of advection transport show that the constructed rational interpolation functions effectively eliminate the numerical oscillations and give well-regulated solutions.
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