連続モデルに由来しない離散モデルの性質について

概要

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In numerical simulation two kinds of mathematical models are usually used, continuous models and discontinuous models. The continuous models are used to describe the taget phenomena that are numerically computed, but the models can not be directlyused in digital computation. Another kind of models,the discrete models, are needed. The discrete models have been often regarded just as conventional tools to approximate the original continuous models. But the discrete models are also independent models and the viewpoint to consistency between continuous and discrete models with respect to the inheritance of various properties would be useful to establish the reliability of numerical simulation. As an example of discussion on consistency between the both models, we are concerned with the carbuncle phenomenon, a kind of instsbility that happens in numerical computation for compressible Euler equations. Through numerical experiments we show that the occurrence of instsbility is closely related with some linearized stability of discrete temporal evolution
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