CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011

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4 Finite element simulation of acoustic scattering in a subsonic flow 4.1 A full coupling between acoustics and hydrodynamics A.-S. Bonnet-Ben Dhia, F. Millot, S. Pernet and E. Peynaud We focus now our attention on the acoustic scattering in a subsonic flow. Our objective is to develop a numerical method to solve linearized problem in time-harmonic regime in an unbounded domain and in a quite general case, in the sense that the geometry and therefore the mean flow can be complex. Contrary to the classical case when the fluid is at rest, the obtained problem is now vectorial since the presence of the mean flow generally couples two different phenomena : acoustic propagation and convection of vortices. Up to our knowledge, only the potential case, which leads to a Helmholtz like scalar equation has been completely handled. But it is only available in specific cases when the flow and also the source are irrotational. This means that there is no coupling between acoustic and hydrodynamic pertubations. For more general cases for instance for an arbritrary flow, the problem is much more difficult to solve. Generally, it is modeling by using the Linearized Euler equations whose unknowns are the perturbation of velocity v and of pressure p. An alternative is to consider a less well-known equation called the Galbrun Equation where the unknown is the Lagrangian displacement u. These two approaches are equivalent and the classical quantities v and p can be easily recovered from u. Although the second is less usual, it has several advantages : in particular, it allows a very simple treatment of the boundary conditions, which are generally expressed with respect to the displacement (see paragraph 4.2). One difficulty is that a direct discretization of Galbrun equation by a Galerkin finite element method does not work, due to the lack of coerciveness. We have proposed to write an augmented equation by adding a term relative to a new unknown ψ. This term corresponds to the hydrodynamic phenomena and is obtained by solving a time-harmonic advection equation. Firstly, we have focused on this time-harmonic advection equation [EMA25]. We have proved the well posedness of this problem for a class of flows which fill the bounded domain [12]. Two different approachs have been studied to solve this kind of equation. The first method is a finite element method based on a finite element method based on a least-squares formulation. The second approach is a Discontinuous Galerkin (DG) method [15] which turns out to be well-suited for advection equations as it naturally takes into account the transport phenomenon. The analysis of these two approaches which can be found in [EMA23], has led us to choose the DG approach. Secondly, we come back to the coupled system where the unknowns are u,ψ. For that, we use the Lagrange Finite Element for the displacement u and a Discontinuous Galerkin scheme for the new unknown ψ. When the flow and the source are irrotational,the potential approach can be done and is implemented. And the results obtained form the Galbrun coupled system are compared with those obtained from the potential method ( see Fig. 4.2 in a complex flow). 4.2 Treatment of the lined walls A.-S. Bonnet-Ben Dhia, F. Millot, S. Pernet and E. Peynaud 62 Jan. 2010 – Dec. 2011
ELECTROMAGNETISM AND ACOUSTICS TEAM FIG. 4.1: Mean flow. FIG. 4.2: Real part the components of Euler velocity ( on left obtained form the Galbrun system, on right with the potential approach. CERFACS ACTIVITY REPORT 63
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CERFACS Scientific Activity Report
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Table des matières 1 Foreword xiii
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9 Publications 40 9.1 Books . . . .
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3 The OpenPALM coupler 104 3.1 Intr
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Table des figures CERFACS chart as
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TABLE DES FIGURES 6 Computational F
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Foreword Welcome to the 2010-2011 S
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CERFACS STRUCTURE CERFACS organizat
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CERFACS STAFF NAME POSITION PERIOD
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CERFACS STAFF SILVA GARZON Ph.D stu
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CERFACS STAFF NAME POSITION PERIOD
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CERFACS Wide-Interest Seminars Pete
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1 Introduction 1.1 Introduction The
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PARALLEL ALGORITHMS PROJECT success
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PARALLEL ALGORITHMS PROJECT Visitor
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3 List of Members of HiePACS HiePAC
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Page 71 and 72: 1 Overview presentation The main ex
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Page 97 and 98: 1 Introduction Data assimilation is
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5 Climate Variability and Global Ch
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2 Climate variability and predictab
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CLIMATE VARIABILITY AND PREDICTABIL
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PUBLICATIONS [CM15] Y. Kwon, C. Des
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1 Introduction The CFD (Computation
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2 Combustion The research activity
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COMPUTATIONAL FLUID DYNAMICS rate-o
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COMPUTATIONAL FLUID DYNAMICS FIG. 2
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7 Aviation and Environment
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INTRODUCTION instead of regular ker
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SIMULATIONS OF AIRCRAFT WAKES AND R
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LARGE SCALE ATMOSPHERIC COMPOSITION
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LARGE SCALE ATMOSPHERIC COMPOSITION
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PUBLICATIONS 4.2 Technical Reports
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CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011

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CERFACS CERFACS Scientific Activity Report Jan. 2010 â Dec. 2011