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Stability Analysis of a Degenerate Hyperbolic System Modelling a Heat Exchanger
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0003-4950-6646
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2007 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 74, no 1, 8-19 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
reduced Euler equations, degenerate hyperbolic equations, zero Mach-number limit, stability analysis, energy estimate, partial differential-algebraic equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-5859DOI: 10.1016/j.matcom.2006.06.027ISI: 000244395300002Scopus ID: 2-s2.0-33846519949OAI: oai:DiVA.org:kth-5859DiVA: diva2:10376
Note
QC 20100930. Uppdaterad från Manuskript till Artikel (20100930).Available from: 2005-08-30 Created: 2005-08-30 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Model Order Reduction with Rational Krylov Methods
Open this publication in new window or tab >>Model Order Reduction with Rational Krylov Methods
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. Both methods are designed for generalised state space systems---the former for multiple-input-multiple-output (MIMO) systems from finite element discretisations and the latter for single-input-single-output (SISO) systems---and applied to relevant test problems. The dual rational Arnoldi method is designed for generating real reduced order systems using complex shift points and stabilising a system that happens to be unstable. For the rational Krylov method, a forward error in the recursion and an estimate of the error in the approximation of the transfer function are studie.

A stability analysis of a heat exchanger model is made. The model is a nonlinear partial differential-algebraic equation (PDAE). Its well-posedness and how to prescribe boundary data is investigated through analysis of a linearised PDAE and numerical experiments on a nonlinear DAE. Four methods for generating reduced order models are applied to the nonlinear DAE and compared: a Krylov based moment matching method, balanced truncation, Galerkin projection onto a proper orthogonal decomposition (POD) basis, and a lumping method.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. v, 21 p.
Series
Trita-NA, ISSN 0348-2952 ; 0522
Keyword
Model order reduction, dual rational Arnoldi, rational Krylov, moment matching, eigenvalue computation, stability analysis, heat exchanger model
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-401 (URN)91-7178-126-9 (ISBN)
Public defence
2005-09-26, Salongen, KTHB, Osquars backe 31, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20101013Available from: 2005-08-30 Created: 2005-08-30 Last updated: 2010-10-13Bibliographically approved

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Hanke, Michael

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