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Author(s):
M. Ida and T. Yabe
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Title:
Implicit CIP (Cubic-Interpolated Propagation) Method in One Dimension
Date of publication:
May 1995
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Key words:
Numerial solver, Hyperbolic equation, CIP method, Implicit scheme, Two-points connected systems
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Abstract:
A new implicit numerical solver for hyperbolic equations is proposed. This method is based on the CIP (Cubic-Interpolated Propagation) method that was propose in an explicit form. Both a physical quantity and its spatial derivative are determined so as to obey the given equation. Just same as the CIP method, this method provides a stable and less diffusive result although it has an implicit form. Most importantly, this method, like other implicit schemes, is stable even in a high-CFL computation. In addition, this scheme can be directly solved by non-iterative procedure because of the two-points connected systems although it has third-order accuracy. The scheme is applied to a one-dimensional shock-tube problem accompanied by a region expanding with quite a high velocity.
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