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A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver

✍ Scribed by T. Yabe; T. Aoki

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 767 KB
Volume: 66
Category: Article
ISSN: 0010-4655
DOI: 10.1016/0010-4655(91)90071-r

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✦ Synopsis

A new numerical method is proposed for general hyperbolic equations. The scheme uses a spatial profile interpolated with a cubic polynomial within a grid cell, and is described in an explicit finite-difference form by assuming that both a physical quantity and its spatial derivative obey the master equation. The method gives stable and less diffusive results even without any flux limiter. It is successfully applied to the KdV equation, a one-dimensional shock-tube problem and a cylindrically converging shock wave.

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✍ T. Yabe; T. Ishikawa; P.Y. Wang; T. Aoki; Y. Kadota; F. Ikeda 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 592 KB

A new numerical method is proposed for multidimensional hyperbolic equations. The scheme uses a cubic spatial profile within grids, and is described in an explicit finite-difference form by assuming that both the physical quantity and its spatial derivative obey the master equation. The method gives