An extension of Glimm's method to the gas dynamical model of transonic flows

Ying Chin Su; John M. Hong; Shih Wei Chou

doi:10.1088/0951-7715/26/6/1581

An extension of Glimm's method to the gas dynamical model of transonic flows

Ying Chin Su, John M. Hong, Shih Wei Chou

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We extend Glimm's method for conservation laws to a larger class of sources so that it can be applied to the compressible Euler equations in transonic flow. Our approximate solutions to the Cauchy problem are constructed by combining the Glimm scheme with the splitting algorithm. We study the nonlinear interaction between wave patterns and the perturbations, and establish the stability of our scheme. Therefore, a more general Glimm-type argument is developed.

Original language	English
Pages (from-to)	1581-1597
Number of pages	17
Journal	Nonlinearity
Volume	26
Issue number	6
DOIs	https://doi.org/10.1088/0951-7715/26/6/1581
State	Published - Jun 2013

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abstract = "We extend Glimm's method for conservation laws to a larger class of sources so that it can be applied to the compressible Euler equations in transonic flow. Our approximate solutions to the Cauchy problem are constructed by combining the Glimm scheme with the splitting algorithm. We study the nonlinear interaction between wave patterns and the perturbations, and establish the stability of our scheme. Therefore, a more general Glimm-type argument is developed.",

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AU - Hong, John M.

AU - Chou, Shih Wei

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N2 - We extend Glimm's method for conservation laws to a larger class of sources so that it can be applied to the compressible Euler equations in transonic flow. Our approximate solutions to the Cauchy problem are constructed by combining the Glimm scheme with the splitting algorithm. We study the nonlinear interaction between wave patterns and the perturbations, and establish the stability of our scheme. Therefore, a more general Glimm-type argument is developed.

AB - We extend Glimm's method for conservation laws to a larger class of sources so that it can be applied to the compressible Euler equations in transonic flow. Our approximate solutions to the Cauchy problem are constructed by combining the Glimm scheme with the splitting algorithm. We study the nonlinear interaction between wave patterns and the perturbations, and establish the stability of our scheme. Therefore, a more general Glimm-type argument is developed.

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DO - 10.1088/0951-7715/26/6/1581

M3 - 期刊論文

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VL - 26

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JO - Nonlinearity

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An extension of Glimm's method to the gas dynamical model of transonic flows

Abstract

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