Low Mach Number Limit of the Full Navier-Stokes Equations

Low Mach number limit of the full Navier-Stokes equations,

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniform...

Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit

This paper describes a derivation of the adjoint low Mach number equations and their implementation and validation within a global mode solver. The advantage of using the low Mach number equations and their adjoints is that they are appropriate for flows with variable density, such as flames, but do not require resolution of acoustic waves. Two versions of the adjoint are implemented and assess...

A Low Mach Number Limit of a Dispersive Navier-Stokes System

We establish a low Mach number limit for classical solutions over the whole space of a compressible fluid dynamic system that includes dispersive corrections to the Navier-Stokes equations. The limiting system is a ghost effect system [26]. Our analysis builds upon the framework developed by Métivier and Schochet [20] and Alazard [2] for non-dispersive systems. The strategy involves establishin...

Stability of Isentropic Navier–Stokes Shocks in the High-Mach Number Limit∗

By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier–Stokes equations with γ -law pressure (i) in the limit as Mach number M goes to infinity, for any γ ≥ 1 (proved analytically), and (ii) for M ≥ 2, 500, γ ∈ [1, 2.5] or M ≥ 13, 000, γ ∈ [2.5, 3] (demonstrated numerically)....

Nečas Center for Mathematical Modeling Low Mach number limit for the Navier-Stokes system on unbounded domains under strong stratification