The propagation of sound in particle models of compressible fluids

Summary.

The propagation of sound in compressible fluids is described by the acoustic equations that result from the linearization of the Euler equations around a state of constant mass density and velocity zero. In this article, it is shown that a stable and convergent discretization of the acoustic wave equation for the velocity field can be recovered from the particle model of compressible fluids recently developed by the author in [Numer. Math. (1997) 76: 111–142] by linearizing the equations of motion for the particles. For particles of proper shape, this discretization is second order accurate, and with an obvious modification of the basic particle model, one can even reach an arbitrarily high order of convergence.