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Stability analysis of a degenerate hyperbolic system modelling a heat exchanger
- Source :
- Mathematics and Computers in Simulation. 74:8-19
- Publication Year :
- 2007
- Publisher :
- Elsevier BV, 2007.
-
Abstract
- 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.
- Subjects :
- Numerical Analysis
General Computer Science
Discretization
Applied Mathematics
Mathematical analysis
Finite difference
Theoretical Computer Science
Euler equations
law.invention
Nonlinear system
symbols.namesake
law
Modeling and Simulation
Heat exchanger
symbols
Canonical form
Evaporator
Heat pump
Mathematics
Subjects
Details
- ISSN :
- 03784754
- Volume :
- 74
- Database :
- OpenAIRE
- Journal :
- Mathematics and Computers in Simulation
- Accession number :
- edsair.doi...........16e7f58ddf3a105d887c78eb8bbf4a3c