Differential DAE Index for Reactive Euler Equations

A. Hmaidi () and P. Rentrop ()
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A. Hmaidi: Munich University of Technology
P. Rentrop: Munich University of Technology

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 777-784 from Springer

Abstract: Abstract For the numerical simulation of a reacting gas flow, we extend the Euler equations to take into account the interaction of the chemical species. Moreover we describe the thermodynamic properties of the gas such as pressure, internal energy and temperature using appropriate closure equations. The system obtained by the combination of the Euler equations and the closure equations is a differential-algebraic system. After modeling the chemical source terms, we focus on the closure relations that complete the Euler equations for an ideal gas and for a real gas mixture. By investigating the DAE-index of such systems for ideal gases, we show the DAE-index for the time integration is 1, whereas this must not be true for real gases.

Keywords: Internal Energy; Euler Equation; Compressibility Factor; Closure Equation; Chemical Source Term (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_93

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