The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell

H. Neishlos; M. Israeli; Y. Kivity

doi:10.1016/0045-7825(83)90002-6

The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell

H. Neishlos, M. Israeli, Y. Kivity

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Abstract

A mathematical model for describing the interaction between a compressible fluid and an elastic shell is formulated as an initial boundary value problem. The partial differential equations of the model are discretized both in time and space by a finite-difference method. The stability of the resulting explicit difference schemes is analyzed by Kreiss' theory for the stability analysis of difference schemes in initial boundary value problems. It is shown that the stability properties of the schemes for the interaction problem may be influenced by the type of discretization in space used for the contact condition on the interface between the fluid and the shell and also by the approximation of the hydrodynamic pressure on the surface of the shell. A simple sufficient condition is found that will ensure the best possible stability properties of the schemes. Several of these, which are of practical interest, are analyzed.

Original language	English
Pages (from-to)	129-143
Number of pages	15
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/0045-7825(83)90002-6
State	Published - Dec 1983
Externally published	Yes

Bibliographical note

Funding Information:
Parts of this work were carried out by the authors at the Technion, Israel Institute of Technology, Haifa, and others by the first author at the National Research Institute for MathematicalS ciencesa nd at the National Institute for Aeronautics and SystemsT echnology at the Council for Scientific and Industrial Research,P retoria.

Funding

Parts of this work were carried out by the authors at the Technion, Israel Institute of Technology, Haifa, and others by the first author at the National Research Institute for MathematicalS ciencesa nd at the National Institute for Aeronautics and SystemsT echnology at the Council for Scientific and Industrial Research,P retoria.

Funders	Funder number
Israel Institute of Technology, Haifa
National Institute for Aeronautics and SystemsT echnology
National Research Institute for MathematicalS ciencesa
Technion-Israel Institute of Technology

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10.1016/0045-7825(83)90002-6

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title = "The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell",

abstract = "A mathematical model for describing the interaction between a compressible fluid and an elastic shell is formulated as an initial boundary value problem. The partial differential equations of the model are discretized both in time and space by a finite-difference method. The stability of the resulting explicit difference schemes is analyzed by Kreiss' theory for the stability analysis of difference schemes in initial boundary value problems. It is shown that the stability properties of the schemes for the interaction problem may be influenced by the type of discretization in space used for the contact condition on the interface between the fluid and the shell and also by the approximation of the hydrodynamic pressure on the surface of the shell. A simple sufficient condition is found that will ensure the best possible stability properties of the schemes. Several of these, which are of practical interest, are analyzed.",

author = "H. Neishlos and M. Israeli and Y. Kivity",

note = "Funding Information: Parts of this work were carried out by the authors at the Technion, Israel Institute of Technology, Haifa, and others by the first author at the National Research Institute for MathematicalS ciencesa nd at the National Institute for Aeronautics and SystemsT echnology at the Council for Scientific and Industrial Research,P retoria.",

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AU - Kivity, Y.

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N2 - A mathematical model for describing the interaction between a compressible fluid and an elastic shell is formulated as an initial boundary value problem. The partial differential equations of the model are discretized both in time and space by a finite-difference method. The stability of the resulting explicit difference schemes is analyzed by Kreiss' theory for the stability analysis of difference schemes in initial boundary value problems. It is shown that the stability properties of the schemes for the interaction problem may be influenced by the type of discretization in space used for the contact condition on the interface between the fluid and the shell and also by the approximation of the hydrodynamic pressure on the surface of the shell. A simple sufficient condition is found that will ensure the best possible stability properties of the schemes. Several of these, which are of practical interest, are analyzed.

AB - A mathematical model for describing the interaction between a compressible fluid and an elastic shell is formulated as an initial boundary value problem. The partial differential equations of the model are discretized both in time and space by a finite-difference method. The stability of the resulting explicit difference schemes is analyzed by Kreiss' theory for the stability analysis of difference schemes in initial boundary value problems. It is shown that the stability properties of the schemes for the interaction problem may be influenced by the type of discretization in space used for the contact condition on the interface between the fluid and the shell and also by the approximation of the hydrodynamic pressure on the surface of the shell. A simple sufficient condition is found that will ensure the best possible stability properties of the schemes. Several of these, which are of practical interest, are analyzed.

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The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell

Abstract

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