Asymptotic Single and Multiple Scale Expansions in the Low Mach Number Limit

An asymptotic analysis of the Euler equations in the limit of vanishing Mach number is presented, which can be employed to extend the validity of numerical methods from the compressible to the low Mach number regime [R. Klein, J. Comput. Phys., 121 (1995), pp. 213--237], [L. Hoffmann and A. Meister, in Proceedings of the Fourth ECCOMAS Computational Fluid Dynamics Conference, Vol. 1, C. Hirsch et al., eds., Athens, 1998, pp. 567--572]. The work is based on the analysis recently proposed by Klein, whereby the paper is devoted to a rigorous mathematical justification of this asymptotic investigation in order to give reliable statements concerning the assumptions under which the results hold. In contrast to Klein, a single scale as well as multiple scale expansion is used depending on the spatial domain under consideration.

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