  In this paper, the design and analysis of a class of second order accurate
IMEX finite volume schemes for the compressible Euler equations in the zero
Mach number limit is presented. In order to account for the fast and slow
waves, the nonlinear fluxes in the Euler equations are split into stiff and
non-stiff components, respectively. The time discretisation is performed by an
IMEX Runge-Kutta method, therein the stiff terms are treated implicitly and the
non-stiff terms explicitly. In the space discretisation, a Rusanov-type central
flux is used for the non-stiff part, and simple central differencing for the
stiff part. Both the time semi-discrete and space-time fully-discrete schemes
are shown to be asymptotic preserving. The numerical experiments confirm that
the schemes achieve uniform second order convergence with respect to the Mach
number. A notion of accuracy at low Mach numbers, termed as the asymptotic
accuracy, is introduced in terms of the invariance of a well-prepared space of
constant densities and divergence-free velocities. The asymptotic accuracy is
concerned with the closeness of the compressible solution with that of its
incompressible counterpart in a low Mach number regime. It is shown
theoretically as well as numerically that the proposed schemes are
asymptotically accurate.
