## Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows

We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several ingredients: semi-implicit schemes, the gauge decomposition of the velocity field and a second order formulation of the density equation (in the isentropic case) and of the energy equation (in the full Navier-Stokes case). Additionally, we show that our approach corresponds to a micro-macro decomposition of the model, where the macro field corresponds to the incompressible component satisfying a perturbed low Mach number limit equation and the micro field is the potential component of the velocity. Finally, we also use the conservative variables in order to obtain a proper conservative formulation of the equations when the Mach number is order unity. We successively consider the isentropic case, the full Navier-Stokes case, and the isentropic Navier-Stokes-Poisson case. In this work, we only concentrate on the question of the time discretization and show that the proposed method leads to Asymptotic Preserving schemes for compressible flows in the low Mach number limit.

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*Bulletin of the Institute of Mathematics Academia Sinica (New Series)*,

*2*, 851–892.

*Bulletin of the Institute of Mathematics Academia Sinica (New Series)*2 (2007): 851–92.

*Bulletin of the Institute of Mathematics Academia Sinica (New Series)*, vol. 2, 2007, pp. 851–92.