Acoustic damping for explicit calculations of fluid flow at low Mach number

A method is proposed for damping the sound waves in explicit calculations of fluid flow at low Mach number, where sound waves are usually not of interest but may distract attention from other flow features. The method is based on the introduction of an artificial pressure q of the form q = - q0rhoc2Δt(del x u - del x u0), where q0 is a coefficient of order unity, rho is the density, c is the sound speed, Δt is the time step, and u0 is the velocity field that would obtain at zero Mach number. When del x u0 is zero, the method becomes equivalent to the use of an artificial bulk viscosity q0rhoc2Δt. However, del x u0 can be substantially different from zero in problems with heat or mass sources (e.g., combustion), and its inclusion is then essential to obtain the correct pressure field. The method is well suited for use in conjunction with explicit numerical schemes that employ acoustic subcycling or artificial reduction of the sound speed for improved efficiency at low Mach number. The beneficial effects of the method are illustrated by means of calculations with an acoustic subcycling computer program. 9 refs., 1 fig