Evaluation of the successive approximations method for acoustic streaming numerical simulations

Abstract

This work evaluates the successive approximations method commonly used to predict acousticstreaming by comparing it with a direct method. The successive approximations method solvesboth the acoustic wave propagation and acoustic streaming by solving the first and second orderNavier-Stokes equations, ignoring the first order convective effects. This method was applied toacoustic streaming in a 2D domain and the results were compared with results from the directsimulation of the Navier-Stokes equations. The velocity results showed qualitative agreementbetween both methods, which indicates that the successive approximations method can describethe formation of flows with recirculation. However, a large quantitative deviation was observedbetween the two methods. Further analysis showed that the successive approximation method solution is sensitive to the initial flow field. The direct method showed that the instantaneous flowfield changes significantly due to reflections and wave interference. It was also found that convective effects contribute significantly to the wave propagation pattern. These effects must be takeninto account when solving the acoustic streaming problems, since it affects the global flow. Byadequately calculating the initial condition for first order step, the acoustic streaming predictionby the successive approximations method can be improved significantly.