Accuracy of Multiply-Upstream Semi-Lagrangian Advective Schemes II

Abstract

The degree of accuracy of various multiply-upstream semi-Lagrangian schemes is examined by analyzing the driven one-dimensional advection equation. The relationship between the order of accuracy of a given scheme and the order of the interpolations used, both of find the position of, and the value of the fields at, the departure point is established. In the process, it is shown how to construct a semi-Lagrangian scheme which is accurate to third-order.