Paul Ploumhans’s research while affiliated with Mountain View College and other places

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Publications (18)


Fig. 1. One-dimensional discretization.
Fig. 2. Two numerical modes of the 1D DG operator with N = 5, p = 4 and l = 1. Left figures show the mode. Center figures show the result of a fast Fourier transform (power spectrum) applied to the mode. Right figures show the difference between numerical and exact modes.
Fig. 3. Spectrum of Z for different values of p and using the explicit p + 1 À p scheme and using upwind fluxes (l = 1).
Fig. 4. Convergence plots of numerical amplification factors j1 À jZ k i as a function of numerical wave numbers. The Z k 's were calculated using Runge-Kutta only and using RK and DGM with the p + 1 À p scheme.
Fig. 6. Test case for the 2D plane wave propagation (top,left). Geometry and series of sampling points. The series consists of sampling points located on a quarter of a circle centered about the middle of the fan face and whose radius is equal to 2 m (top,right). Mach number of the mean flow (bottom). Mesh of the domain (3921 triangles). Element sizes ranges from 1 cm to 10 cm. Element are colored using levels of grey that are representing polynomial orders used in the optimized run.

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Optimal numerical parametrization of discontinuous Galerkin method applied to wave propagation problems
  • Article
  • Full-text available

April 2007

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118 Reads

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37 Citations

Journal of Computational Physics

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Xavier Gallez

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This paper deals with the high-order discontinuous Galerkin (DG) method for solving wave propagation problems. First, we develop a one-dimensional DG scheme and numerically compute dissipation and dispersion errors for various polynomial orders. An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented. It is shown that using a time stepping scheme with the same formal accuracy as the DG scheme is too expensive for the range of wave numbers that is relevant for practical applications. An efficient implementation of a high-order DG method in three dimensions is presented. Using 1D convergence results, we further show how to adequately choose elementary polynomial orders in order to equi-distribute a priori the discretization error. We also show a straightforward manner to allow variable polynomial orders in a DG scheme. We finally propose some numerical examples in the field of aero-acoustics.

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A New CAA Formulation based on Lighthill's Analogy applied to an Idealized Automotive HVAC Blower using AcuSolve and Actran/LA

May 2005

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895 Reads

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14 Citations

In this paper, we investigate the use of the variational formulation of Lighthill's anal- ogy, implemented in a Finite/Infinite Element framework. We present an innovative way to handle porous boundaries (or equivalently, control surfaces upon which aerodynamic sources are defined). We show how Lighthill's analogy can be used to predict broadband blower noise. Infinite elements are used to enforce the Sommerfeld radiation boundary condition. A derivation of the analogy is presented and is compared with the derivation of Curle's analogy (extended to handle porous boundaries). The implementation is described and is validated on a test case. Preliminary results on a real automotive HVAC blower case are presented.


Efficient Discontinuous Galerkin Methods for solving acoustic problems

May 2005

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582 Reads

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31 Citations

For being the major source of noise pollution in aero-engines, fan forward and rearward noise is of primary importance in the aeronautics industry. With a view to enabling acoustic-based design of engines’ nacelle and bypass ducts, Free Field Technologies has developed a tool, calledActran/TM, over the past fiveyears. Briefly, Actran/TM computes the propagation of harmonic acoustic disturbances in non-uniform, homentropic mean flow and their radiation to the far field. Using Myers’ formulation of acoustic boundary conditions , the effect of acoustic liners in the presence of flow is accurately accounted for. Strong coupling with duct acoustic modes allows one to both specify incident modes and compute the amplitude of reflected ones. The algebraic system of equations resulting from the finite and infinite element discretization of the acoustic potential equation is solved with a parallel, out-of-core, direct solver. While Actran/TM is widely being used in the industry, for example for nacelle liner optimization, the constant need for higher and higher values of the Helmholtz number in numerical simulations and the increasing interest in fan rearward and turbine noise pose new challenges. For example, a three-dimensional nacelle problem with flow at kr= 30 currently requires several Gigabytes of RAM and hundreds of gigabytes of disk space. The limited efficiency and scalability of direct solvers do not make them good candidates for addressing problems where the Helmholtz number is as high as 50, especially on distributed memory computers. Moreover, propagation in rotational, non-isothermal mean flows can not be addressed with an acoustic potential equation. The above aspects of industrial applications motivate the combination of the time-domain linearized Euler equations (LEE) and the quadrature-free Runge-Kutta Discontinuous Galerkin Method (RK-DGM). An advantageous feature of the DGM is that it allows the use of high-order spatial discretization schemes in a natural fashion. While the number of floating-point operations is high in the DGM, a quadrature-free formulation allows efficient algorithms. By organizing data in a matrix fashion and noting that element matrices differ from one element to the next by only a coefficient, the most demanding operations are written in matrix-matrix form and taken care of by BLAS3 functions. Capitalizing on the work of reputed groups, and conducting their own research in collaboration with major research institutes, UCL and Free Field Technologies recently embarked on implementing the RK-DGM for LEE, focusing on large-scale, industrial applications. This paper presents some early results obtained with our code, focusing on performance, efficiency, data structures and parallel scalability.




Simulation of Three-Dimensional Bluff-Body Flows Using the Vortex Particle and Boundary Element Methods

September 2004

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63 Reads

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14 Citations

Flow Turbulence and Combustion

Recent contributions to the 3-D vortex method for bluff-body flows are presented. The numerical method--a vortex method combined with a boundary element method--is briefy reviewed. It is applied to direct numerical simulation (DNS) of the flow past a sphere (Re= 300, 500 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation (LES) for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed.


Comparison Between Measured and Predicted Tonal Noise from a Subsonic Fan Using a Coupled Computational Fluid Dynamics (CFD) and Computational Acoustics (CA) Approach

May 2004

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453 Reads

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5 Citations

The flow through an HVAC blower fan, typical to the automotive industry, was solved using STAR-CD. Time varying pressure data was then exported to ACTRAN/TM where the CFD results were decomposed into acoustic duct modes, using a multiple plane matching method. These duct modes were then propagated to far field locations and compared with experimental data at the blade passing frequency, obtained in the semi-anechoic chamber at Denso Thermal Systems. Good agreement was attained for microphones located downstream of the inlet and outlet ducts. At the other microphone locations there is doubt that the dominant noise generation mechanism is purely aeroacoustic: vibroacoustic noise sources are present. Since aeroacoustic noise sources alone were modeled, there was a deterioration in the simulation/experimental comparison.



Simulation of three-dimensional bluff-body flows using vortex methods: from direct numerical simulation towards large-eddy simulation modelling*

October 2002

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39 Reads

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7 Citations

Journal of Turbulence

Recent contributions to the three-dimensional vortex method for bluff-body flows are presented. The numerical method—a vortex method combined with a boundary element method—is briefly reviewed. It is applied to direct numerical simulation of the flow past a sphere (Re = 300 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed. This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.


Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows: Application to the Sphere at Re=300, 500, and 1000

May 2002

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193 Reads

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230 Citations

Journal of Computational Physics

Recent contributions to the 3-D vortex methods are presented. Following Cottet, the particles strength exchange (PSE) scheme for diffusion is modified in the vicinity of solid boundaries to avoid a spurious vorticity flux and to enforce a zero-normal component of vorticity during the convection/PSE step. The vortex sheet algorithm used to enforce the no-slip boundary condition through a vorticity flux at the boundary and the technique used to perform accurate redistributions in the presence of bodies of general geometry are extended from their 2-D counterpart. To perform simulations with nonuniform resolution, a mapping of the redistribution lattice is used. Computational efficiency is attained through the use of parallel tree codes based on multipole expansions of vortex particles and of vortex panels. The method is validated, by comparisons with other authors' results, on the flow past a sphere at Re=300. It is then applied to compute the flow at Re=500 and 1000.


Citations (14)


... Not only is meshing of the domain avoided, the Lagrangian nature of the method also eliminates numerical discretization of the convective term in the Navier-Stokes equations, thus eliminating associated numerical diffusion. Satisfactory handling of the no-slip boundary conditions at solid boundaries enabled high-resolution spatially adaptive vortex methods [3, 12, 28, 36, 40, 48] to simulate separating flows and accurately predict onset of separation and time evolution of drag and lift. The computational cost and accuracy of vortex methods are continuously improving. ...

Reference:

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains
Recent Advances in High Resolution Vortex Methods for Incompressible Flows
  • Citing Conference Paper
  • June 1997

... When simulating the non-cavitation noise of a pump jet, it is necessary to use the Lighthill acoustic analogy theory. 28 It can perfectly combine the flow field and the acoustic field. The Lighthill acoustic analogy equation is derived from the continuity and N-S equations. ...

Implementation of Lighthill's Acoustic Analogy in a Finite/Infinite Elements Framework

... For instance, compressible and incompressible source terms can yield similar results in CFD calculations when there is negligible air-acoustic coupling. 38 The acoustic mesh in Fig. 6 models both the acoustic propagation domain (volute) and the internal support structure. The acoustic mesh must have at least six elements within a wavelength corresponding to the maximum frequency of interest. ...

Identification of the Appropriate Parameters for Accurate CAA
  • Citing Conference Paper
  • May 2005

... The phenomenon of the flow-related acoustic wave generation is the subject of many works focused on the identification of basic mechanisms of sound generation. In Ref. [6], a numerical analysis is presented of the operation of a typical-geometry Helmholtz resonator placed in a fluid flow. In Ref. [7], an analysis is conducted of the flow along a cavity with a lid, characterized by a geometry similar to the one analysed herein and operating in conditions corresponding to the Helmholtz resonator. ...

Aeroacoustic Simulation of the Noise Radiated by an Helmholtz Resonator Placed in a Duct

... Thus, the excitation can be applied as a distributed random load directly to a standard structural finite element model. In this approach the pressure distribution is described by a matrix of cross power spectral density [13,14,15]. Although the above-mentioned methods are well suited for a wide range of vibro-acoustic problems, the elasto-acoustic FEM-FEM coupling approach is necessary when cavity-structure interactions of light-weight and thin structures are considered [16,17]. ...

Simulation of randomly excited acoustic insulation systems using finite element approaches

... Varying core The traditional PSE scheme rely on the fact that all particles possess the same core size. The method is extended to particles with varying core by Daeninck et al. [37]. Numerical Implementation The numerical implementation is given e.g. in the articles of Winckelmans [104] or Voutsinas [101]. ...

Simulation of three-dimensional bluff-body flows using vortex methods: from direct numerical simulation towards large-eddy simulation modelling*
  • Citing Article
  • October 2002

Journal of Turbulence

... This problem can be somewhat mitigated by employing massive parallelization for the evaluation of the N 2 Biot-Savart equations. Moreover, a tree-code [100,101] or multi-level [46,102] 20 approach can be used to reduce the computational cost for large problems, through the implementation of a hierarchic mesh. Tree-codes or multi-level codes, depending on their implementation, can reduce the computational cost from O(N 2 ) to O(Nlog(N)) or even O(N). ...

Vortex particles and tree codes: I. flows with arbitrary crossing between solid boundaries and particle redistribution lattice; II. vortex ring encountering a plane at an angle

ESAIM Proceedings

... The Discontinuous Galerkin Method (DGM) is the dominant unstructured approach for the LEE [44, 45, 46] and has been customised as a commercial product for CAA [47]. DGM allows variable orders of approximation within an unstructured grid and achieves an accuracy commensurate with local element order [48]. ...

Efficient Discontinuous Galerkin Methods for solving acoustic problems

... Since the aeroacoustic noise is the consequence of turbulent flow, it is important to consider a proper model accordingly. Various models have considered this issue [77][78][79], and in almost all of them, the distribution along with the grid density has been taken into account. The fact is that the calculation time and cost should be evaluated to reduce the time and cost for calculations. ...

Comparison Between Measured and Predicted Tonal Noise from a Subsonic Fan Using a Coupled Computational Fluid Dynamics (CFD) and Computational Acoustics (CA) Approach