Nicolas Zerbib

ESI Group

Use of OpenFOAM coupled with a Hybridization of Finite Element-Boundary Element Methods using an Adaptive Absorbing Boundary Condition for Wind Noise Simulation

The design of modern structure exterior like car, train or aircraft is mainly influenced by the aerodynamic performances. In automotive for example, the air flow detached from the A-pillar and impacting the side windows are of particular interest as they are close to the driver’s/passengers’ ears. The geometrical characteristics of the A-pillar can determine the size or strength of the vortex structure. For early optimized determination of the A-pillar, a very fast and accurate numerical methodology to predict the exterior noise due to the aero-acoustic sources, located in the wake of the side mirror and in the large turbulent region close to the side window and the A-pillar is needed. The new simulation method presented in that paper is a two-step approach assuming the decoupling of noise generation and propagation. The first stage consists in an incompressible Detached Eddy Simulation (DES) of the turbulent flow field. In that specific formulation, the equivalent aero-acoustic sources are represented only by the 3D volume hydrodynamic pressure instead of the more standard and well-known Lighthill’s tensor. In the second step, the acoustic propagation of those 3D volume sources is dealt with an hybridization between the Finite Element and the Boundary Element Methods (FEM/BEM) using an Adaptive Absorbing Boundary Condition (AABC) updated iteratively by a matrix-vector-product accelerated by the MultiLevel Fast Multipole Method (MLFMM). This method can be interpreted as a Domain Decomposition Method (DDM) with overlapping taking advantage of every numerical methods. To save CPU time and some space disk to store the aero-acoustic data, the CFD sources term is transferred from the CFD mesh to the acoustic mesh on the fly, i.e. at the end of each converged time step during the CFD computation by using a conservative mapping operator. Using an academic case, we calculate by this new formulation the sound generated by a turbulent flow over a sphere and we compare it to the standard Boundary Element Curle’s analogy.

1. C. Lubich, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer. Math., 67 (1994), pp. 36--389.

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