Comparison of high-order numerical schemes and several filtering methods applied to Navier-Stokes equations with applications to computational aeroacoustics

Lai, L.S., Djambazov, Georgi, Lai, Choi-Hong and Pericleous, Koulis A. (2009) Comparison of high-order numerical schemes and several filtering methods applied to Navier-Stokes equations with applications to computational aeroacoustics. Journal of Algorithms & Computational Technology, 3 (3). pp. 443-459. ISSN 1748-3018

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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 nearfield
of the unsteady flow are solved by using a Computational Fluid
Dynamics (CFD) technique, such as Direct Numerical Simulation (DNS),
Large Eddy Simulation (LES) or unsteady Reynolds averaged Navier-
Stokes equations (RANS) the CFD predictions are then used to
calculate sound sources using the acoustic analogy or 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 a
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 size. 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 statistical similarities.

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