Development of optimized interpolation schemes with spurious modes minimization

This work constitutes a fraction of a more extensive effort, which ultimate objective is the development of advanced aeroacoustics hybrid methods. Within this framework, we here focus on the interpolation step, on which generally rely all coupling processes that link altogether the various stages constituting any given hybrid method. In that regard, previous works by the present authors had revealed the intrinsic limitations and subsequent side effects (e.g., signal degradation) that weight on usual high‐order interpolation schemes, whether the latter are of centered or noncentered nature, as well as optimized in an acoustic sense or not. Based on the outcomes of such study, here, a novel optimization technique for interpolation schemes is proposed. Such a technique, which is designed hereafter as the interpolation by parts (IBP), allows interpolating accurately a given signal, while minimizing its possible degradation. As a result, compared with its standard counterpart, any IBP‐optimized interpolation scheme exhibits improved characteristics, such as a spurious modes generation that is greatly reduced (up to a 99% factor). Such improved characteristics are here validated on the basis of three test cases (of 1D, 2D and 3D nature), which illustrates the potentialities offered by the IBP optimization technique. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical investigation of a spectral‐type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations

In this paper, we focus on the applicability of spectral‐type collocation discontinuous Galerkin methods to the steady state numerical solution of the inviscid and viscous Navier–Stokes equations on meshes consisting of curved quadrilateral elements. The solution is approximated with piecewise Lagrange polynomials based on both Legendre–Gauss and Legendre–Gauss–Lobatto interpolation nodes. For the sake of computational efficiency, the interpolation nodes can be used also as quadrature points. In this case, however, the effect of the nonlinearities in the equations and/or curved elements leads to aliasing and/or commutation errors that may result in inaccurate or unstable computations. By a thorough numerical testing on a set of well known test cases available in the literature, it is here shown that the two sets of nodes behave very differently, with a clear advantage of the Legendre–Gauss nodes, which always displayed an accurate and robust behaviour in all the test cases considered.Copyright © 2012 John Wiley & Sons, Ltd.     

Computer-aided evaluation method for interferograms

For the quantitative evaluation of interferograms a video camera is used to digitize the interferograms in frames up to 512 by 512 pixels which are transmitted to a host computer. Quantitative data of the whole field are obtained by the following procedure: First the fringes are extracted with the help of binarization methods. Then to each fringe boundary a value is assigned in a certain point. Starting from this point the boundaries are traced through the whole pattern. Finally the data between the fringe boundaries are determined by linear interpolation. Other operations like smoothing can be done before the results are printed.     

High order schemes for the scalar transport equation

A finite volume hybrid scheme for the spatial discretization that combines a fixed stencil and a stencil determined by the classical essentially non‐oscillatory (ENO) scheme is presented. Evolution equations are obtained for the mean values of each cell by means of piecewise interpolation. Time discretization is accomplished by a classical fourth‐order Runge–Kutta. Interpolation polynomials are determined using information of adjacent cells. While smooth regions are interpolated by means of a fixed molecule, discontinuous or sharp regions are interpolated by the classical ENO algorithm. The algorithm estimates the interpolation error at each time step by means of two interpolants of order q and q+1. The main computational load of the resultant scheme is in the interpolation, which is performed by the divided differences table. This table involves O(qN) operations, where q is the interpolation order and N is the number of cells. Finally, linear test cases of continuous and discontinuous initial conditions are integrated to see the goodness of the hybrid scheme. It is well known that, for some particular initial conditions, the classical ENO scheme does not perform properly, not attaining the truncation error of the scheme. It is shown that, for the smooth initial condition, sin⁴(x), the classical ENO scheme does not preserve the character of stability of the initial value problem, giving rise to unstable eigenvalues. The proposed hybrid scheme solves this problem, choosing a fixed stencil over the whole computational domain. The resultant schemes are equivalent to the classical finite difference schemes, which preserve the character of stability. It is also known that the same degeneracy of the error can be encountered for discontinuous solutions. It is shown for the initial discontinuous solution, e^−x, that the classical ENO algorithm does not perform properly due to the conflict between the selection of the stencil to smoother regions (downwind region) and the hyperbolic character of the problem, which obliges us to take information from downwind. The proposed hybrid scheme solves this problem by choosing a fixed stencil over the whole computational domain except at the discontinuity. Copyright © 2001 John Wiley & Sons, Ltd.     

Contributions of Computational Aeroacoustics to Jet Noise Research and Prediction

A brief review of recent progress in the field of computational aeroacoustics (CAA) is proposed. This paper is complementary to the previous reviews of Tam [(1995a) “Computational aeroacoustics: issues and methods”, AIAA J. 33(10), 1788–1796], Lele [(1997) “Computational Aeroacoustics: a review”, AIAA Paper 97–0018, 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada] and Glegg [(1999) “Recent advances aeroacoustics: the influence of computational fluid dynamics”, 6th International Congress on Sound and Vibration, Copenhagen, Danemark, 5–8 July, 43–58] on advances in CAA. After a short introduction concerning the current motivations of jet noise studies, connections between computational fluid dynamics (CFD) and CAA using hybrid approaches are discussed in the first part. The most spectacular advances are probably provided by the direct computation of jet noise, and some recent results are shown in the second part.     

A hybrid approach for nonlinear computational aeroacoustics predictions

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier–Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier–Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.     

A Three-Dimensional Hybrid LES-Acoustic Analogy Method for Predicting Open-Cavity Noise

A three-dimensional (3D) hybrid LES-acoustic analogy method for computational aeroacoustics (CAA) is presented for the prediction of open-cavity noise. The method uses large-eddy simulation (LES) to compute the acoustic source while the Ffowcs Williams-Hawkings (FW-H) acoustic analogy is employed for the prediction of the far-field sound. As a comparison, a two-dimensional (2D) FW-H analogy is also included. The hybrid method has been assessed in an open-cavity flow at a Mach number of 0.85 and a Reynolds number of Re=1.36×10⁶, where some experimental data are available for comparison. The study has identified some important technical issues in the application of the FW-H acoustic analogy to cavity noise prediction and CAA in general, including the proper selection of the integration period and the modes of sound sources in the frequency domain. The different nature of 2D and 3D wave propagation is also highlighted, which calls for a matching acoustic solver for each problem. The developed hybrid method has shown promise to be a feasible, accurate and computationally affordable approach for CAA.     

Numerical modeling of the self-oscillation onset near a three-dimensional backward-facing step in a transonic flow

The results of a numerical investigation of the nature of self-oscillation processes occurring in transonic flow past a backward-facing step and a cavity with a flow of the open type are presented. The turbulent flow past the above-mentioned bodies is modeled using the NOISEtte software package intended for solving problems of aerodynamics and aeroacoustics on unstructured grids. The modeling is performed using the eddy-resolving IDDES method that belongs to the class of hybrid RANS-LES approaches. The adequacy of the calculations is confirmed by means of comparing the results obtained with the available experimental data. The structure and the salient features of the self-oscillatory, hydrodynamic-in-nature process, which arises in flow past a cavity and a backward-facing step, are established.     

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 2: Application to Complex Flows

The paper summarises the validation activity performed with the Scale-Adaptive Simulation turbulence model (SAS model) using the two commercial CFD solvers, ANSYS-FLUENT and ANSYS-CFX. Both the KSKL-SAS and the SST-SAS model variants have been tested, although most cases have been computed with the second. The turbulence-resolving capability of the SAS method has been validated with a representative set of test cases, covering both underlying generic flows as well as practical engineering applications. In addition to the purely aerodynamic flows with massive separation and heat transfer they include also such physical phenomena as turbulent combustion and aeroacoustics. The illustrating results show the potentials of the SAS approach for industrial flow simulations. Most of the test case simulations were conducted during the recent EU project “DESider”.     

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Aeroacoustics simulations require much more precise boundary conditions than classical aerodynamics. Two classes of non‐reflecting boundary conditions for aeroacoustics are compared in the present work: the characteristic analysis‐based methods and the Tam and Dong approach. In the characteristic methods, waves are identified and manipulated at the boundaries, whereas the Tam and Dong approach use modified linearized Euler equations in a buffer zone near outlets to mimic a non‐reflecting boundary. The principles of both approaches are recalled, and recent characteristic methods incorporating the treatment of transverse terms are discussed. Three characteristic techniques—the original Navier–Stokes characteristic boundary conditions (NSCBC) of Poinsot and Lele and two versions of the modified method of Yoo and Im—are compared with the Tam and Dong method for four typical aeroacoustics problems: vortex convection on a uniform flow, vortex convection on a shear flow, acoustic propagation from a monopole, and acoustic propagation from a dipole. Results demonstrate that the Tam and Dong method generally provides the best results and is a serious alternative solution to characteristic methods even though its implementation might require more care than the usual NSCBC approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Advanced numerical method for a thermally induced slug flow: application to a capillary closed loop pulsating heat pipe

An advanced hybrid lumped parameter code for the simulation of Pulsating Heat Pipes is developed. Being able to simulate transient operative conditions and removing common physical simplified assumptions, it represents a step forward with respect to the present models of passive two‐phase systems. Mass, momentum and energy balances account for the thermal and fluid‐dynamics phenomena. Heterogeneous and homogeneous phase changes are directly integrated. In addition, a fitting correlation for the wall/vapour heat transfer coefficient is implemented and tuned against experimental data in order to evaluate the influence of the liquid film on conjugate heat transfer. The resulting numerical tool have been validated against experimental data achieved testing a copper pulsating heat pipe during the 58th ESA Parabolic Flight Campaign in several operative conditions and transient gravity levels. The predicted results show very good matching with the actual thermo‐physical behaviour of the system. Copyright © 2016 John Wiley & Sons, Ltd.     

The effects of the irregular sample and missing data in time series analysis

Human self-report time series data are typically marked by irregularities in sampling rates; furthermore, these irregularities are typically natural outcomes of the data generation process. Relatively little has been published to assist the analysis of irregularly sampled data. We report the results of a series of computational experiments on synthetic data sets designed to assess the utility of techniques for handling irregular time series data. The behavior of a conservative quasiperiodic, a dissipative chaotic, and a self-organized critical dynamics were sampled regularly in time and the regular sampling was disrupted by data point removal or by stochastic shifts in time. Missing data segments were then patched by means of segment concatenation, by segment filling with average data values, or by local interpolation in phase space. We compared results of nonlinear analytical tools such as autocorrelations and correlation dimensions using complete and patched sets, as well as power spectra with Lomb periodograms of the decimated sets. Local interpolation in phase space was particularly successful at preserving key features of the original data, but required potentially impractical quantities of intact data as a primer. While the other patching methods are not limited by the need for intact data, they distort results relative to the intact series. We conclude that irregularly sampled data sets with as much as 15 percent missing data can potentially be re-sampled or repaired for analysis with techniques that assume regular sampling without introducing substantial errors.     

格子玻尔兹曼法多块网格的交界结构优化研究

基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。     

Recent advances of computational aeroacoustics

Computational aeroacoustics (CAA) is an interdiscipline of aeroacoustics and computational fluid dynamics (CFD) for the investigation of sound generation and propagation from various aeroacoustics problems. In this review, the foundation and research scope of CAA are introduced firstly. A review of the early advances and applications of CAA is then briefly surveyed, focusing on two key issues, namely, high order finite difference scheme and non-reflecting boundary condition. Furthermore, the advances of CAA during the past five years are highlighted. Finally, the future prospective of CAA is briefly discussed.     

On the controlled propagation of wave signals in a sinusoidally forced two-dimensional continuous Frenkel-Kontorova model

The nonlinear processes of supratransmission and infratransmission are employed here in order to show numerically that binary information may be transmitted into (2 + 1)-dimensional, continuous Frenkel-Kontorova media spatially defined on a square, by perturbing harmonically two adjacent boundaries by means of Neumann conditions. The presence of these nonlinear phenomena is established numerically through a computational method that preserves the positivity of the energy operators, and that consistently approximates the solution of the model, the local energy density, the total energy and its dissipation; the existence of a region of bistability where two regimes coexist (conducting and insulating) is established as a corollary. The transmission of binary information is accomplished by fixing a frequency in the forbidden band-gap of the system, and modulating the amplitude of the signals as the sum of a seed (whose amplitude oscillates sinusoidally between the supratransmission and infratransmission thresholds) and small, positive, constant perturbations associated to nonzero bits. Our simulations show that a reliable transmission of information is indeed feasible.     

A quasi diffusive reflective method for the calculation of radiative heat transfer in semitransparent media between parallel planes with angle dependent reflection behaviour

 The problem of radiation heat transfer in a semitransparent infinite plane parallel layer with purely diffusive reflection, emission and transmission behaviour (referred to as optical boundary conditions), in which the temperature depends only on the coordinate perpendicular to the boundaries, can be solved exactly by using exponential integrals of different orders. On the other hand the attenuation for the reflected, emitted and transmitted heat currents in the case of specular reflecting, emitting and transmitting boundaries has to be described by more complicate functions or the problem has to be treated by different methods as the discrete ordinates method (DOM). Within this work, a new method to describe radiation heat transfer for this geometry especially in the case of strongly angle dependent optical boundary conditions, including total reflection as described by Fresnel's equations, is developed. This method uses discrete angle ranges with averaged optical properties of the boundaries as well as the exponential integral formalism and is therefore referred to as quasi-diffusive reflective method (QDR-method). Exact solutions and solutions by means of the QDR-method including heat transfer by conduction are compared. The results of the QDR-method are sufficiently accurate in the most practical cases and allow calculations with a temperature dependent absorption coefficient in a much easier way. Received on 13 March 2000     

Measurements and treatment of LDA signals, comparison with hot-wire signals

 An experimental investigation was carried out in the wind tunnel F2 of the ONERA Fauga centre for the measurement of the characteristics of a turbulent wake behind a wing. As these measurements require the calculation of time and space correlations, two different types of acquisition means are used : a pair of crossed hot wires and a one-dimensional laser-Doppler anemometer. The non-intrusive characteristics of laser anemometry allow the measurement of fluid velocity upstream of a hot wire probe without disrupting the flow. It is well known that LDA generates individual realisations of randomly sampled velocity data because the random arrival of seeding particles in the measurement volume is nonperiodic. A detailed study of this random sampling quantifies the deviations from the theoretical lows, shows the limiting factors of this sampling, and gives a characterisation of the particles arrival law. The simultaneous acquisition of the two velocity signals at very close points allows a good comparison between the signals. A statistical analysis of the two signals enables us to precisely measure the error value of the velocity estimation made by the anemometer. The spectrum analysis of the laser signal coupled with one of the hot wire signals requires resampling the signal at constant steps. Two different methods of interpolation are analysed: the sample and hold interpolation method and the linear interpolation method. The influence of these interpolation methods on the spectrum of LDA signals is studied. Different estimators are then calculated to evaluate the convection velocities and the coherence length of the turbulence. Received: 9 December 1997/Accepted: 19 March 1999     

Comments on the relation between surface wave theory and the theory of reflection

The sextic Stroh formalism, previously extensively used in the analysis of subsonic phenomena, has been used for the analysis of reflection phenomena and leaky surface waves in the first transsonic range of velocities. In particular the behaviour of the reflection problem at the limiting velocity is studied. It is shown that when the condition of free surface can be satisfied without the inhomogeneous partial wave, a situation which would appear to be the natural limiting case of a surface wave of infinite penetration, the body wave alone satisfies the condition of free surface. This result illuminates the Barnett-Lothe existence theorem for subsonic surface waves. The close connection between the reflection problem and the leaky surface wave problem becomes very apparent in the formalism used. It is shown that for a point on a branch of leaky waves where the solution is undamped, the conditions for simple reflection, i.e. reflection only involving the two body waves, are also present. In the vicinity of such a point reflection is accompanied by resonance excitation of leaky waves. The paper concludes with some explicit calculations for transversely isotropic solids.     

固定网格下的特征线法求解溃坝问题

溃坝问题是典型的非线性双曲方程的Riemann问题，其数值求解的难点在于对间断面的捕捉以及避免间断面处在数值计算过程中产生数值色散，因而为求解此问题所产生的各种数值计算方法的优劣也体现在这两个方面。本文针对溃坝问题提出一种新的计算方法。该方法基于对偶变量推导的浅水波方程，根据方程的特点，从方程的特征值和黎曼不变量出发，采用高精度的激波捕捉方法计算黎曼不变量的位置随时间的变化，然后映射至不随时间变化的固定网格。根据黎曼不变量的位置，采用保形分段三次Hermite插值将物理量映射至网格节点。计算结果显示，该方法不仅操作简单，计算量小，而且结果准确。     

高速列车车体长度对气动噪声影响的数值研究

高速列车具有细长形状, 数值评估气动噪声往往需要巨大的计算量.目前对高速列车气动噪声的数值模拟大多基于对简化短编组列车的评估,而实际列车通常具有较长的8$\sim$16节编组.如何基于现有条件合理评价真实长度列车的气动噪声,是一个急需探讨的问题. 本文应用非线性声学求解器(NLAS)和FW--H声学比拟法的混合算法, 先求解噪声积分面上的声场脉动,再进行远场积分, 引入多噪声面积分技术,通过对三种不同长度(3节、4节、6节)列车模型的气动性能和噪声数值模拟,分析了车体长度对列车气动噪声的影响. 结果表明,同一列车模型的各节车厢具有相似的沿线噪声分布,其噪声曲线在量值上十分接近,只是主峰位置会随着车厢空间位置的不同而相应地发生偏移;不同长度编组列车对应部位之间的远场噪声特性具有较强的关联性,它们的远场噪声具有接近的总声压级和噪声频谱.通过利用短编组计算数据进行分解、平移和叠加,成功重构了4编组和6编组列车远场噪声特性,与直接计算结果相比误差在可接受范围内.由此发展了基于短编组列车噪声的数值结果,重构长编组列车沿线噪声的近似评估方法.