Time-domain Impedance Boundary Conditions for Computational Acoustics and Aeroacoustics

This paper reviews the short history, motivation, numerical and theoretical issues, and development of methods for treating a boundary as a reflective/absorptive surface for the time-domain computation of waves in general and acoustic waves in particular. It begins with the extension and implementation of the frequency-domain impedance to a time-domain impedance-equivalent boundary condition (TDIBC), and illustrates how the theoretical, numerical, and implementation issues are addressed and resolved for acoustic/aeroacoustic applications. Comments are also made on the extendibility and applicability of the concept and TDIBC to other fields and types of problems.     

Review of Computational Aeroacoustics Algorithms

This paper presents a review of recent advancements in computational methodology for aeroacoustics problems. High-order finite difference methods for computation of linear and nonlinear acoustic waves are the primary focus of the review. Schemes for numerical simulation of linear waves include explicit optimized and DRP finite-difference operators, compact schemes, wavenumber extended upwind schemes and leapfrog-like algorithms. Both spatial approximations and time-integration techniques, which include low-dissipation low-dispersion Adams-Bashforth and Runge-Kutta (RK) methods, are examined. Wave propagation properties are analysed in the wavenumber and frequency space. Different approaches to eliminate short-wave spurious numerical waves are also reviewed. Methods for simulating nonlinear acoustic phenomena include essentially non-oscillatory (ENO) schemes, numerical adaptive filtering for high-order explicit and compact finite-difference operators, MacCormack and adaptive compact nonlinear algorithms. A literature survey of other CAA methods is provided in the introductory part.     

Absorbing Boundary Conditions

Absorbing boundary conditions for computational aeroacoustics (CAA) are reviewed. Commonly used absorbing zonal techniques, such as sponge layers and buffer zones, as well as perfectly matched layers (PML) are discussed. The basic ideas and central results of these methods are surveyed and summarized. Special attention will be given to the recently emerged PML technique and its application to CAA. Numerical examples are presented for PML in duct acoustics. A comparison of PML and non-PML absorbing boundary conditions will also be given.     

Computational Aeroacoustics: An Overview of Computational Challenges and Applications

The objective of this paper is to present an overview of recent advances in computational aeroacoustics (CAA). During the last decade, CAA has developed quite independent of computational fluid dynamics (CFD). There are computational issues that are unique to CAA and are, generally, not considered in CFD. In this paper, these issues are discussed and explained. In CAA, there is a great need to resolve high-frequency short waves with the minimum number of mesh points per wavelength. There is also a special need to minimize numerical dispersion and dissipation associated with wave propagation computation. All these have led to the development of large-stencil high-resolution schemes for CAA. A careful examination of dispersion and dissipation errors due to spatial and temporal discretization is provided. These errors are quantified and analyzed in wave number space through the use of Fourier-Laplace transforms. At this time, some of the original computational challenges to CAA have been resolved satisfactorily. A discussion of how some of these computational issues are resolved is presented. Several important CAA applications with interesting or unusual computational innovations are highlighted. Finally, a few of the most pressing outstanding computational challenges to CAA are elaborated.     

Cavity Tones by Computational Aeroacoustics

The flow past open cavities is a problem that is encountered in many engineering applications and can result in intense acoustic tones. The flow physics and acoustics of cavity configurations are complex and computational simulation techniques provide an opportunity to gain further understanding and provide a tool to predict not only cavity tone frequencies but their amplitude. In this paper, we describe the available techniques for performing computational aeroacoustic simulations of cavity flows, and review recent applications for the prediction and control of cavity tones in subsonic, transonic and supersonic regimes.     

Development of Computational Aeroacoustics Tools for Airframe Noise Calculations

This paper discusses the development of computational aeroacoustics (CAA) tools for airframe noise analysis and prediction. We review recent progress in this topic, but emphasize our vision for the future development of such tools. Our intention is for this vision to drive future CAA research in directions that will accelerate widespread use of CAA for airframe noise applications. We discuss the needs for accuracy, efficiency, and easy interface with other design tools and illustrate how CAA tools may help future aircraft design. We explain what appears to be achievable in a 20-year time frame, and what goals will probably take longer.

Important barrier issues include the effects of numerical dispersion and dissipation, the treatment of highly curved, irregular boundary surfaces, and grid generation. Beyond these largely numerical issues, we discuss the role of physics-based modeling, including turbulence modeling in unsteady flow computations and the importance of developing sophisticated techniques for analyzing results of computations. Numerical simulations combined with the acoustic analogy methodology to predict noise are also reviewed. Finally, we discuss how to use recent advances in measurement techniques for CAA tool validation, which is an integral part of future development.     

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 Review of Parallel Computing in Computational Aeroacoustics

This paper discusses parallel computing applied to computational aeroacoustics problems. Computer hardware, software and algorithms are also described. A short history of parallel computers is given, along with some discussion of future prospects. We have reviewed much of the literature, but this review is not exhaustive. Finite difference, finite volume, and finite element methods are briefly discussed. There is also a discussion of how aeroacoustic problems scale, and how that relates to computational requirements.     

关于气动声学数值计算的方法与进展

气动声学数值计算是近年才出现的研究领域。本文介绍了气动声学数值计算的方法和有关的问题、边界条件的处理以及计算非线性声波的数值方法和进展。讨论了计算气动声学(CAA)的特性及其与计算流体力学(CFD)的差异，指出气动声学数值方法的关键是建立能保持色散关系的差分方程和正确处理无反射边界条件。对于非线性声波传播的问题，为了得到正确的解，应注意提高差分格式对短波的分辨能力，同时发展能抑制“伪”振荡(短波)而对长波基本不起作用的数值方法。     

Radiation boundary conditions for finite element solutions of generalized wave equations

On the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein-Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two-dimensional example suggests that the 1D findings can generalize to higher dimensions.     

Effective Flux Boundary Conditions for Upscaling Porous Media Equations

We introduce a new algorithm for setting pressure boundary conditions in subgrid simulations of porous media flow. The algorithm approximates the flux in the boundary cell as the flux through a homogeneous inclusion in a homogeneous background, where the permeability of the inclusion is given by the cell permeability and the permeability of the background is given by the ambient effective permeability. With this approximation, the flux in the boundary cell scales with the cell permeability when that permeability is small, and saturates at a constant value when that permeability is large. The flux conditions provide Neumann boundary conditions for the subgrid pressure. We call these boundary conditions effective flux boundary conditions (EFBCs). We give solutions for the flux through ellipsoidal inclusions in two and three dimensions, assuming symmetric tensor permeabilities whose principal axes align with the axes of the ellipse. We then discuss the considerations involved in applying these equations to scale up problems in geological porous media. The key complications are heterogeneity, fluctuations at all length scales, and boundary conditions at finite scales.     

A Non-Newtonian Fluid with Navier Boundary Conditions

We consider in this paper the equations of motion of third grade fluids on a bounded domain of or with Navier boundary conditions. Under the assumption that the initial data belong to the Sobolev space H ², we prove the existence of a global weak solution. In dimension two, the uniqueness of such solutions is proven. Additional regularity of bidimensional initial data is shown to imply the same additional regularity for the solution. No smallness condition on the data is assumed.     

Balance Laws and Weak Boundary Conditions in Continuum Mechanics

A weak formulation of the stress boundary conditions in Continuum Mechanics is proposed. This condition has the form of a balance law, allows also singular measure data and is consistent with the regular case. An application to the Flamant solution in linear elasticity is shown.     

Boundary Conditions for Plate Bending in One-dimensional Hexagonal Quasicrystals

For plate bending in one-dimensional (1D) hexagonal quasicrystals (QCs), the reciprocal theorem and the general solution for QCs media are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order for plates of general edge geometry and loadings. Through generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed data must satisfy these conditions in order that they should generate a decaying state. When a set of stress edge-data or mixed edge-data is imposed on the plate edge, these decaying state conditions for the case of axisymmetric deformation of 1D hexagonal QC plates are derived explicitly. They are then used for the correct formulation of boundary conditions for the plate theory solution (or the interior solution). Furthermore, in the absence of phonon–phason fields coupling effect, corresponding necessary conditions for the case of transversely isotropic elastic plates are derived subsequently, and their isotropic elastic counterparts are also obtained.      

Nonlinear Boundary Conditions in Kirchhoff-Love Plate Theory

Most of the derivations of the mechanical behavior of a plate as the limit behavior of a three-dimensional solid whose thickness tends to zero deal with stationary homogeneous linear boundary conditions on the lateral boundary. Here, in the framework of small strains, we rigorously determine a large class of steady-state or transient nonlinear boundary conditions which provide asymptotic kinematics of Kirchhoff-Love type.      

A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems

We present a new auxiliary variable formulation of high-order radiation boundary conditions for the numerical simulation of waves on unbounded domains. Retaining the flexibility of Higdon’s wave-product conditions, our approach allows arbitrary-order implementations. When applied to the scalar wave equation, the proposed method leads to balanced, symmetrizable systems of wave equations on the boundary. It can also be extended to first-order systems. Corner compatibility conditions are derived for the auxiliary variable equations. They are shown experimentally to lead to stable, accurate results.     

APPLICABILITY OF THE CRACK FACE ELECTRICAL BOUNDARY CONDITIONS IN PIEZOELECTRIC MECHANICS

The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is consi…     

无网格方法中本质边界条件的处理

基于新的离散模定义，采用移动最小二乘近似方法，给出了场变量的近似表达形式；从约束变分原理出发，给出了无网格方法中新的本质边界条件的处理方案——罚函数法；对权函数、罚函数的选择对计算精度的影响进行了研究。数值计算结果表明该方法不仅简单合理，而且具有较高的精度和稳定性。     

Pseudo‐characteristic formulation and dynamic boundary conditions for computational aeroacoustics

The present paper deals with the use of the pseudo‐characteristic formulation of the Navier–Stokes and Euler equations recently introduced by Sesterhenn (Comput. Fluid. 2001; 30 :37–67) for the simulation of acoustic wave propagation. The emphasis is put on the formulation of an efficient method on structured curvilinear grids, along with the definition and implementation of efficient boundary conditions. The cases of inflow, outflow, rigid/compliant walls and walls with prescribed impedance are addressed. The proposed boundary conditions are assessed on generic cases. The pseudo‐characteristic formulation enables a straightforward and optimal use of high‐order upwind dispersion‐relation‐preserving schemes, yielding an efficient method. Copyright © 2006 John Wiley & Sons, Ltd.     

关于线性非局部弹性理论的应力边界条件

应力边界条件的提法是线性非局部弹性理论尚未解决的一个理论问题。文中针对这一问题进行了研究，所导出的应力边界条件包含了物体微观结构的长程相互作用，这个结果不仅解释了在裂纹混合边界值问题中非线性局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以自然地得到裂纹尖端的分子内聚力模型。