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Mathematical models for chemically reacting systems have high degrees of freedom (very large) and are computationally expensive to analyse. In this discussion, we present and analyse a model reduction method that is based on stoichiometry and mass balances. This method can significantly reduce the high degrees of freedom of such systems. Numerical simulations are undertaken to validate and establish efficiency of the method. A practical example of acid mine drainage is used as a test case to demonstrate the efficacy of the procedure. Analytical results show that the stoichiometrically-reduced model is consistent with the original large model, and numerical simulations demonstrate that the method can accelerate convergence of the numerical schemes in some cases. [ABSTRACT FROM AUTHOR]

In this paper a general drift-flux model describing a subsonic and isentropic multi-phase fluid in connected pipes is considered. Each phase is assumed to be isentropic with its own sonic speed. The components are gamma-law gases with γ > 1 . For such, a computational challenge at a junction is the computation of rarefaction waves which do not have a readily available analytical form. Firstly, the well-posedness of the Riemann problem at the junction is discussed. It is suggested that rarefaction waves should be linearized in order to obtain a more efficient numerical method for coupling such multi-component flow. Some computational results on the dynamics of the multi-phase gas in the pipes demonstrate the qualitative behavior of this approach. [ABSTRACT FROM AUTHOR]