On the numerical approximation of a degenerated hyperbolic system

On the numerical approximation of a degenerated hyperbolic system

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Article ID: iaor201527009
Volume: 79
Issue: 5
Start Page Number: 1585
End Page Number: 1602
Publication Date: Jan 2009
Journal: Mathematics and Computers in Simulation
Authors: ,
Keywords: approximation, stability
Abstract:

The heat exchanger in a heat pump system may be conveniently described by a degenerated hyperbolic system, namely the zero Mach‐number limit of the Euler equations. This leads to a mixed hyperbolic/parabolic system with coupled time‐dependent boundary conditions. We propose a method‐of‐lines discretisation by using an upwinding scheme. We derive stability estimates for the linearisation with frozen coefficients. The resulting differential–algebraic equation has a perturbation index of 2 and a weak instability with respect to the space step size. The latter property is validated experimentally even for the nonlinear system. In contrast, the perturbation index did not exceed one in the numerical experiments.

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