A new numerical method is proposed for multidimensional linear advection equations. The scheme uses a cubic spatial profile within grids, and is described in an explicit form by assuming that both a physical quantity and its spatial derivative obey the given equation. The method gives a stable and less diffusive result without any flux limiter. Its extension to nonlinear equations with nonadvection term is straightforward.
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Yabe et al. (1990) studied this question.