Stability Analysis of a Degenerate Hyperbolic System Modelling a Heat Exchanger
2007 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, Vol. 74, no 1, 8-19 p.Article in journal (Refereed) Published
Mathematical modelling of a heat exchanger in a carbon dioxide heat pump, an evaporator, is considered. A reduced model, called the the zero Mach-number limit, is derived from the Euler equations of compressible liquid flow through elimination of time scales associated with sound waves. The well-posedness of the resulting partial differential-algebraic equation (PDAE) is investigated by analysis of a frozen coefficient linearisation as well as by numerical experiments.
The linear stability analysis is done through transformation to a canonical form with one hyperbolic component and one parabolic block of dimension 2. Using this canonical form it is seen how to prescribe boundary and initial data and an energy estimate is derived.
Numerical experiments on the nonlinear PDAE using a finite difference spatial discretisation support the linear stability analysis.
Place, publisher, year, edition, pages
2007. Vol. 74, no 1, 8-19 p.
reduced Euler equations, degenerate hyperbolic equations, zero Mach-number limit, stability analysis, energy estimate, partial differential-algebraic equations
IdentifiersURN: urn:nbn:se:kth:diva-5859DOI: 10.1016/j.matcom.2006.06.027ISI: 000244395300002ScopusID: 2-s2.0-33846519949OAI: oai:DiVA.org:kth-5859DiVA: diva2:10376
QC 20100930. Uppdaterad från Manuskript till Artikel (20100930).2005-08-302005-08-302010-09-30Bibliographically approved