Analysis and approximation of multicomponent gas mixtures
Klaus Schenk, Georg Bader, Guntram Berti
Technical University Cottbus, Institute of Mathematics
03013 Cottbus, PF 101344, Germany
We consider theoretical aspects as well as the numerical approximation
of a generalized system of Euler equations that describes the inviscid
flow for a mixture of ideal gases in one and two space dimensions.
The system arises from the standard Euler equations by replacing
the continuity equation by
corresponding conservation laws for each chemical species.
Furthermore there is a general thermodynamical representation
of the pressure as a function of the species densities and of the temperature.
For each species the specific
enthalpy depends on the temperature by a caloric equation of state.
We are interested in realistic situations where the
various chemical species have different molecular weights as well as
different specific heat functions.
Systems of conservation laws of the described type occur for example
in the context of the numerical simulation of chemical reacting flows.
At first we present results concerning the mathematical properties of the
above system. The Jacobian matrices of the
flux vectors, their eigenvalues and the corresponding eigenspaces are
investigated for general equations of state.
It turns out that a simple property of the thermodynamical equation of state
ensures the hyperbolicity of the system.
In addition we investigate the behaviour of the different physical quantities
at discontinuities or rarefaction waves.
Our theoretical results are complemented by numerical evaluations
in one and two space dimensions.