A Remark on Collocation and Upwinding in First Order Hyperbolic Systems

dc.contributor.authorKeenan, Philip T.en_US
dc.date.accessioned2018-06-18T17:39:42Zen_US
dc.date.available2018-06-18T17:39:42Zen_US
dc.date.issued1992-11en_US
dc.date.noteNovember 1992en_US
dc.description.abstractKeenan[2] defines and analyzes a new numerical method for coupled systems of nonlinear first order hyperbolic partial differential equations with one degenerate eigenvalue. That work extends in a certain direction the collocation method described by Luskin[3], which applies to systems with all the eigenvalues uniformly bounded away from zero. Luskin's method and Keenan's method both have direct application to the study of one dimensional fluid flow through pipelines. The pressure and velocity of an isothermal fluid in a pipeline can be described by a coupled pair of nonlinear first order hyperbolic partial differential equations. When thermal effects are important a third equation for temperature is added. While Luskin's method works well for the isothermal situation he discussed, it does not apply in certain common cases when thermal effects are modeled. The analysis of the new method shows how the difficulties that come from the application of standard collocation can be overcome by using upwinded piecewise constant functions for the degenerate component of the solution. Experiments indicate that this method is a substantial improvement over standard collocation. A number of technical details obscure the analysis presented in Keenan [2], because that work treats the general nonlinear case. The present paper describes and analyzes the method in the context of a linear, constant coefficient system of equations. In this special case the proof simplifies considerably.en_US
dc.format.extent22 ppen_US
dc.identifier.citationKeenan, Philip T.. "A Remark on Collocation and Upwinding in First Order Hyperbolic Systems." (1992) <a href="https://hdl.handle.net/1911/101778">https://hdl.handle.net/1911/101778</a>.en_US
dc.identifier.digitalTR92-38en_US
dc.identifier.urihttps://hdl.handle.net/1911/101778en_US
dc.language.isoengen_US
dc.titleA Remark on Collocation and Upwinding in First Order Hyperbolic Systemsen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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