On the numerical approximation of a degenerated hyperbolic system

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.