AMS Classification: References [1] F. Nicoud. Conservative High-Order Finite-Difference Schemes for Low-Mach Number

Numerical dissipation, often used in collocated mesh schemes to enforce stability or to avoid odd-even decoupling problem, may be undesirable, for example to compute turbulent fluid flows in DNS or LES. Unfortunately, on the other hand, central discretization suffers from loss of stability problems, in particular when the Reynolds number increases. Therefore, an important attention has been devoted to find criteria that could ensure the stability without any addition of non-physical dissipation into the numerical schemes (see e.g. Nicoud [1]). It appears experimentally that the discrete kinetic energy conservation in the “incom-pressible limit ” is one of these criteria [2]. In the particular case of an “all-Mach ” algorithm suggested by Nerinckx et al. [3], the present study deals with (1) the asymptotic signifi-cation of this conservation property; (2) the physical conditions under which the discrete kinetic energy is conserved; (3) some computational benefits that can be expected from this conservation property and the numerical problems that it does not prevent