A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers

T. Yabe; T. Ishikawa; P. Y. Wang; T. Aoki; Y. Kadota; F. Ikeda

doi:10.1016/0010-4655(91)90072-S

A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers

T. Yabe, T. Ishikawa, P. Y. Wang, T. Aoki, Y. Kadota, F. Ikeda

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293 Scopus citations

Abstract

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 a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.

Original language	English
Pages (from-to)	233-242
Number of pages	10
Journal	Computer Physics Communications
Volume	66
Issue number	2-3
DOIs	https://doi.org/10.1016/0010-4655(91)90072-S
State	Published - 1991
Externally published	Yes

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10.1016/0010-4655(91)90072-S

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abstract = "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 a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.",

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AU - Yabe, T.

AU - Ishikawa, T.

AU - Wang, P. Y.

AU - Aoki, T.

AU - Kadota, Y.

AU - Ikeda, F.

PY - 1991

Y1 - 1991

N2 - 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 a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.

AB - 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 a stable and less diffusive result than the old methods without any flux limiter. Extension to nonlinear equations with nonadvection terms is straightforward.

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A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers

Abstract

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