Several approaches based on the polynomial which approximates the local solutions to the governing equations have been proposed. The polynomial is piecewisely determined by interpolating the physical quantities on a point aimed at solving the equations and an adequate number of surrounding points. The derivatives at the point are evaluated by using this interpolated polynomial. Most of the conventional methods can be classified by the kinds of the polynomial and how to use the interpolation. It may be considered that this basic concept is useful for constructing a method in which the results are independent of grid systems. Also, it seems that to find an appropriate interpolation may contribute to constructing a multi dimensional upwind scheme.
局所的な補間を用いた風上法について
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