lowMachNumber

Low Mach number, often written as lowMachNumber, describes fluid flows in which the characteristic velocity is much smaller than the speed of sound in the medium (Mach number M = U / c, with M much less than 1). In this regime, pressure perturbations propagate as acoustic waves on a fast time scale, while the bulk flow evolves more slowly. As a consequence, compressibility effects are reduced, and many numerical simulations can operate with larger time steps by filtering out or decoupling acoustic dynamics.

Practically, the compressible Navier-Stokes equations can be simplified by a low Mach number asymptotic limit. This leads to reduced models in which density changes are governed by the equation of state, while the velocity field obeys a divergence constraint that reflects limited compressibility. In many implementations, the pressure is split into a large thermodynamic part and a small dynamic part, and the equations are arranged to remove fast acoustic modes from the time integration.

Several well-known low Mach number frameworks include the Boussinesq approximation, which assumes nearly constant density except in buoyancy terms, and the anelastic approximation, which allows stratified density while enforcing a constrained velocity field (divergence tied to density variation). Pseudo-incompressible models offer a related approach with slightly different constraints. These models aim to balance accuracy of density- and temperature-driven effects with computational efficiency.

Applications include subsonic aerodynamics, atmospheric and oceanic flows, and reacting flows where speed is much less than sound speed but thermal or compositional effects are important. Limitations arise when flows approach transonic or supersonic speeds, when strong shocks or large density variations occur, or when acoustics play a direct role in the dynamics.