Philippe Delorme

hp Discontinuous Galerkin Method for Computational Aeroacoustics

Discontinuous Galerkin Method is commonly used for Computational Waves. It presents a good settlement to solve problems with complex boundary conditions around complex geometries with an accurate numerical precision. Its mathematical foundations are well establish, the method, based on a variational formulation is robust and stability properties are demonstrated. The use of unstructured meshes is possible, thus complex industrial geometries are easily introduced and mesh adaptation is also possible. Programs are easy to parellelize and have good performance on recent super computers (cluster). The Discontinuous Galerkin Method presents a high flexibility. Each cell (element) may be locally profiled with a particular physical model, a particular functional basis... A 2D application dealing with acoustic propagation inside an air-plane engine is presented. It validates and confirms the tremendous potential and the high interest of the flexibility still slightly explored. Finally, a 3D application is presented and shows the method can cope with industrial problem and run on parallel computers.

Gravity and rumble of distant sources

The subject of this paper is the comprehension of this physical phenomenon: Let an atmospheric source emiting an impulsive signal (such as thunder, explosion...). The received signal at short distance is itself impulsive but at long distance one can hear a rumble which can last up to one minute. If one models the propagation of the sound by the traditional equation of the waves, as the Green function is a distribution whose support is the sphere of radius CT (C: speed of sound, T: the travel time), the received signal (calculated by convolution) should last only the duration of emission. If one uses ray tracings to take into account the heterogeneity of the medium, one obtains the same conclusion (only the time of arrival is modified) in contradiction with the experimental results such as those obtained for example during the First World War to detect the position of the enemy batteries. A similar phenomenon can be observed in the study of the propagation of a sonic boom (although less obvious because the...

Optimal hp Dicontinuous Galerkin Method Application to Computational Aeroacoustics

Today, the Discontinuous Galerkin Method (DGM) is commonly used for studying Computational Waves. It presents the best settlement to solve Computational Aeroacoustics (CAA) problems with complex boundary conditions around complex geometries with an accurate numerical precision. Its mathematical foundations are well establish. The method, based on a variational formulation, is robust and convergence properties have been demonstrated. The use of unstructured meshes is possible, thus complex geometries are easily introduced and mesh adaptation is easy. Finally, the DGM presents a high flexibility. Indeed, each cell (element) may be locally profiled with a particular physical model, a particular functional basis... A first application of the flexibilty is presented to optimise the CPU and memory costs of computations. Before making the CAA computation, a mesh and order adaptation steps are introduced. A new discretisation of geometry and CFD datas is realised, the main purpose is to have cells (elements) as big as possible to help the emergence of higher orders during the second step. The elements used are classical lagrangian elements P0 to P8 with sufficient Gauss cubatures. A 2D application dealing with the acoustic propagation inside an airplane engine is presented and it validates and confirms the tremendous potential of the DGM, and the high interest of the flexibility still slightly explored.

Computational fluid dynamics simulations of infrasound generation process by meteorites

The main objective of this work is to model the emission and propagation of infrasound generated by meteorites. This is done by combining CFD simulations of shock waves with acoustic atmospheric propagation models. In a first step the pressure field in the vicinity of the meteorite is simulated using Euler equations, which are solved using a finite volume method (elsA{copyright, serif}, ONERA). The influence of the parameters such as the diameter and the velocity of the meteorite on the pressure signal, at different radial distances away from the trajectory, is quantified and compared to an empirical line-source shock model. The matching of the CFD and acoustics models is performed at a distance where the shock is locally cylindrical and weakly nonlinear. The distance at which this matching is performed is discussed. This computational method is carried out in the case of the meteorite of Carancas, which impacted in Peru the 15th September 2007.

Simulation of linear aeracoustic propagation in lined ducts with discontinuous Galerkin method

The simulation of the acoustic propagation inside a lined duct with nonuniform flow still presents problems when geometry is complex. To handle computations on a complex geometry, without consequential effort, unstructured meshes are required. Assuming irrotational flow and acoustic perturbation, a well‐posed finite element method based on the potential equation is established. But, the effect of the thin boundary layer is then neglected, which is not relevant to the acoustical processes occurring near the lining. Recent works have focused on the tremendous interest of the Galerkin discontinuous method (GDM) to solve Euler’s linearized equations. The GDM can handle computations on unstructured meshes and introduces low numerical dissipation. Very recent mathematical works have established, for the GDM, a well‐posed boundary condition to simulate the lining effect. Results computed with the GDM are presented for a uniform cross section lined duct with a shear flow and are found to be in good agreement with...

A Galerkin discontinuous method for CAA: The reasons of a choice

As for many others disciplines, the numerical simulation is becoming a powerful tool for the study of the propagation of small disturbances in a heterogeneous flow (aero‐acoustics). Some main applications are, on the one hand, aeronautics for the noise of the aircraft and, on the other hand, the propagation of the sound in the atmosphere. In general the development of a computer code goes by four phases: physical modeling, mathematic analysis, strategy of discretization, programming and validation. At each of these stages some specific choices are carried out. For physical modeling, it is necessary to choose a representative model. Then, it should be checked that the problem is well posed in existence and unicity. For the strategy of discretization the choice resides between the different methods and is guided by the geometries to study. Finally, the choice to use or not the possibility of strongly paralleling influences programming of the code. In this paper the reasons are described which led us to use ...