Direct numerical calculation of acoustics: solution evaluation through energy analysis

Abstract

The propagation of acoustic energy from a sound source to the far field is a fundamental problem of acoustics. In this paper the use of computational fluid dynamics (CFD) to directly calculate the acoustic field is investigated. The two-dimensional, compressible, inviscid flow about an accelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder surface to the fluid, as the cylinder is moved from rest to some non-negligible velocity, is shown. Energy is the quantity of interest in the calculations since various components of energy have physical meaning. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy following the body. In the calculations, entropy generation is due to a combination of physical mechanisms and numerical error. In the case of propagating acoustic waves, entropy generation seems to be a measure of numerical damping associated with the discrete flow solver.