Finite volume schemes optimized for low numerical dispersion and their aeroacoustic applications.

摘要

The field of computational aeroacoustics is concerned with the calculation of acoustic fluctuations in an aerodynamic flow field. Moreover, it is desirable to resolve the spectral content and directivity of the aeroacoustic field with high accuracy. For the purposes of the designer, it is preferable to endow a computational fluid dynamics code with some capability for predicting aeroacoustic information. If the prediction algorithm can be written within the current flow solver's structure, the costly acquisition of a new code is not necessary. In an effort to provide designers with this option, a new finite volume methodology is developed in the present work.;Three families of upwind, finite volume schemes are developed and demonstrated for a series of aeroacoustics problems. These new low dispersion finite volume schemes are designed to mitigate numerical dispersion and dissipation errors in the computational space while achieving high formal orders of accuracy. Variable extrapolation stands as the framework for these methods. In this case, the cell face variables are interpolated from cell nodes by using a procedure that optimizes the stencil representation of flow field properties in terms of sinusoidal waves. This procedure renders an accurate representation of these properties for a higher range of numerical wavenumbers. In addition, an unsteady, farfield boundary treatment is proposed. This low reflectivity farfield boundary treatment is designed as an integral part of the finite volume discretization procedure. This technique is very robust and causes only minimal reflection at the farfield boundary.;The low dispersion finite volume schemes have been applied to a number of aeroacoustics problems. The numerical results are shown and compared either to exact solutions or to the results computed by other schemes. Good agreement with the exact solutions is evident. Results are also shown for the problem of laminar vortex-shedding from a circular cylinder. The associated simulations are performed for Reynolds number 200 and Mach number 0.2.;These methods are easily applied on arbitrary grids. The results demonstrate that these schemes are well suited for the prediction of acoustic levels at sampling points located more than twenty chord lengths away from the body.