Comparison of higher-order numerical schemes and several filtering methods applied to navier - Stokes equations with applications to computational acoustics

Abstract

In computational acoustics, fluid-acoustic coupling methods for the computation of sound have been widely used by researchers for the last five decades. In the first part of the coupling procedure, the fully unsteady incompressible or compressible flow equations for the near-field of the unsteady flow are solved by using a Computational Fluid Dynamics (CFD) technique, i.e., Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) or unsteady Reynolds averaged Navier-Stokes equations (RANS); results of these simulations are then used to calculate sound sources using the acoustic analogy or by solving a set of acoustic perturbation equations (APE) leading to the solution of the acoustic field. It is possible to use a 2-D reduced problem to provide preliminary understanding of many acoustic problems. Unfortunately 2-D CFD simulations using a fine-mesh-small-time-step-LES-alike numerical method cannot be considered as LES which applies to 3-D simulations only. Therefore it is necessary to understand the similarities and the effect between filters applied to unsteady compressible Navier-Stokes equations and the combined effect of high-order schemes and mesh sizes. The aim of this study is to provide suitable LES-alike methods for 2-D simulations. An efficient software implementation of high order schemes is also proposed. Numerical examples are provided to illustrate these empirical similarities.