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It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz-type instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as the Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of the TIMIBC for scattering of acoustic waves by lined surfaces are carried out, and its effectiveness is demonstrated by a numerical example. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. As such, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition. Moreover, time domain implementation of the TIMIBC is also discussed and illustrated with a numerical example using a finite difference scheme. In particular, a minimization procedure for finding the poles and coefficients of a broadband multipole expansion for the impedance function is formulated by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. [ABSTRACT FROM AUTHOR]

Acoustic liners are an effective tool for noise reduction and are characterized by a frequency-dependent impedance value. In this paper, a time-domain boundary element method for acoustic scattering coupled with a broadband impedance boundary condition is studied for the case of no mean flow. A Burton-Miller reformulation of the time domain boundary element method for acoustic scattering is carried out with both the pressure and its surface normal derivative terms retained. A multipole impedance model is converted into the time domain and used for enforcing an impedance boundary condition over a wide range of frequencies. Discretization of the coupled system is described. In particular, the time-domain impedance boundary condition is discretized by the third-order implicit backward difference scheme. Stability of the coupling is assessed by an eigenvalue analysis. Scattering solutions that demonstrate the validity and stability of the numerical method are presented. [ABSTRACT FROM AUTHOR]

Abstract It is well-known that the convective wave equation with a uniform mean flow can be transformed into a standard wave equation without flow by a Prandtl-Glauert-Lorentz type transformation. This paper examines the boundary condition to be used in the transformed coordinates for acoustic scattering by rigid bodies. Recently, based on the energy conservation equation for acoustic waves propagating in a uniform flow, a new solid wall boundary condition, dubbed the Zero Energy Flux (ZEF) solid surface boundary condition, has been proposed. Instead of the commonly used solid surface boundary condition that the normal acoustic velocity be zero, the ZEF condition requires that the acoustic energy flux be zero. In this paper, we point out that when formulated in the acoustic velocity potential and under the ZEF boundary condition, the normal derivative of the velocity potential remains to be zero when computed in the transformed coordinates. As such, numerical methods developed for solving the standard wave equation can be directly applied to the convective wave equation through a use of the Prandtl-Glauert-Lorentz transformation. Utilization of the transformation is particularly beneficial for numerical methods based on the boundary integral formulation because of the simplified kernel function in the transformed coordinates, for both the time domain and the frequency domain approaches. Useful relations for applying the transformation are derived and numerical examples that demonstrate the effectiveness of the transformation and ZEF boundary condition are presented. [ABSTRACT FROM AUTHOR]

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source or sink points on solid surfaces. An alternative solid wall boundary condition, termed zero energy flux boundary condition, is proposed that conserves the acoustic energy and a time domain boundary integral equation is derived. Furthermore, stabilization of the integral equation by Burton-Miller type reformulation is presented. The stability is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the current formulation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we formulate a numerical method that is high order with strong accuracy for numerical wave numbers, and is adaptive to non-uniform grids. Such a method is developed based on the discontinuous Galerkin method (DGM) applied to the hyperbolic equation, resulting in finite difference type schemes applicable to non-uniform grids. The schemes will be referred to as DGM-FD schemes. These schemes inherit naturally some features of the DGM, such as high-order approximations, applicability to non-uniform grids and super-accuracy for wave propagations. Stability of the schemes with boundary closures is investigated and validated. Proposed scheme is demonstrated by numerical examples including the linearized acoustic waves and solutions of non-linear Burger’s equation and the flat-plate boundary layer problem. For non-linear equations, proposed flux finite difference formula requires no explicit upwind and downwind split of the flux. This is in contrast to existing upwind finite difference schemes in the literature. [Copyright &y& Elsevier]

Abstract: Absorbing boundary conditions for the nonlinear Euler and Navier–Stokes equations in three space dimensions are presented based on the perfectly matched layer (PML) technique. The derivation of equations follows a three-step method recently developed for the PML of linearized Euler equations. To increase the efficiency of the PML, a pseudo mean flow is introduced in the formulation of absorption equations. The proposed PML equations will absorb exponentially the difference between the nonlinear fluctuation and the prescribed pseudo mean flow. With the nonlinearity in flux vectors, the proposed nonlinear absorbing equations are not formally perfectly matched to the governing equations as their linear counter-parts are. However, numerical examples show satisfactory results. Furthermore, the nonlinear PML reduces automatically to the linear PML upon linearization about the pseudo mean flow. The validity and efficiency of proposed equations as absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations are demonstrated by numerical examples. [Copyright &y& Elsevier]

Abstract: A Perfectly Matched Layer (PML) for linearized Euler equations with a parallel non-uniform mean flow is presented. The PML is formulated by utilizing a proper space–time transformation in its derivation so that in the transformed coordinates all dispersive waves supported by the non-uniform flow have consistent phase and group velocities. The space–time transformation is determined through a study of dispersion relations of all the linear waves. The proposed PML equations are applicable to both bounded and unbounded flows and given in unsplit physical variables. Furthermore, the stability of the PML is also considered. It is shown that the proposed PML is stable for a finite range of the absorption coefficient. Numerical examples that demonstrate the validity and effectiveness of PML as an absorbing boundary condition are presented. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

We present a detailed study of spatially propagating waves in a discontinuous Galerkin scheme applied to a system of linear hyperbolic equations. We start with an eigensolution analysis of the semidiscrete system in one space dimension with uniform grids. It is found that for any given order of the basis functions, there are at most two spatially propagating numerical wave modes for each physical wave of the partial differential equations (PDE). One of the modes can accurately represent the physical wave of the PDE and the other is spurious. The directions of propagation of these two numerical modes are opposite, and, in most practical cases, the spurious mode has a large damping rate. Furthermore, when an exact characteristics split flux formula is used, the spurious mode becomes nonexistent. For the physically accurate mode, it is shown analytically that the numerical dispersion relation is accurate to order 2p+2, where p is the highest order of the basis polynomials. The results of eigensolution analysis are then utilized to study the effects of a grid discontinuity, caused by an abrupt change in grid size, on the numerical solutions at either side of the interface. It is shown that due to “mode decoupling,” numerical reflections at grid discontinuity, when they occur, are always in the form of the spurious nonphysical mode. Closed-form numerical reflection and transmission coefficients are given and analyzed. Numerical examples that illustrate the analytical findings of the paper are also presented. [Copyright &y& Elsevier]

Presents information on a study which examined the effectiveness of absorbing layers as nonreflecting computational boundaries for the Euler equations. Description of the numerical models; Applicability of the absorbing condition technique to shock-turbulence and shock-vortex interaction problems; Results of the study; Conclusions.

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained. [ABSTRACT FROM AUTHOR]

It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier–Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. This ensures that the instability is, indeed, tied to the presence of the Mach waves. It is proposed that enhanced mixing of supersonic shear layers may be achieved by the use of such a periodic Mach wave system through the inducement of parametric instabilities in the flow. [ABSTRACT FROM AUTHOR]

This paper intends to explore the rationality and feasibility of modeling dispersed submicron particles in air by a kinetic-based method called the unified gas-kinetic scheme (UGKS) and apply it to the simulation of particle concentration under a transverse standing wave. A gas-particle coupling scheme is proposed where the gas phase is modeled by the two-dimensional linearized Euler equations (LEE) and, through the analogous behavior between the rarefied gas molecules and the air-suspended particles, a modified UGKS is adopted to estimate the particle dynamics. The Stokes' drag force and the acoustic radiation force applied on particles are accounted for by introducing a velocity-dependent acceleration term in the UGKS formulation. To validate this methodology, the computed concentration patterns are compared with experimental results in the literature. The comparison shows that the adopted LEE-UGKS coupling scheme could well capture the concentration pattern of suspended submicron particles in a channel. In addition, numerical simulations with varying standing wave amplitudes, different acoustic radiation force to drag force ratios, and mean flow velocities are conducted. Their respective influences on the particle concentration pattern and efficiency are analyzed. [ABSTRACT FROM AUTHOR]

Abstract: With many superior features, Runge–Kutta discontinuous Galerkin method (RKDG), which adopts Discontinuous Galerkin method (DG) for space discretization and Runge–Kutta method (RK) for time integration, has been an attractive alternative to the finite difference based high-order Computational Aeroacoustics (CAA) approaches. However, when it comes to complex physical problems, especially the ones involving irregular geometries, the time step size of an explicit RK scheme is limited by the smallest grid size in the computational domain, demanding a high computational cost for obtaining time accurate numerical solutions in CAA. For computational efficiency, high-order RK method with nonuniform time step sizes on nonuniform meshes is developed in this paper. In order to ensure correct communication of solutions on the interfaces of grids with different time step sizes, the values at intermediate-stages of the Runge–Kutta time integration on the elements neighboring such interfaces are coupled with minimal dissipation and dispersion errors. Based upon the general form of an explicit p-stage RK scheme, a linear coupling procedure is proposed, with details on the coefficient matrices and execution steps at common time-levels and intermediate time-levels. Applications of the coupling procedures to Runge–Kutta schemes frequently used in simulation of fluid flow and acoustics are given, including the third-order TVD scheme, and low-storage low dissipation and low dispersion (LDDRK) schemes. In addition, an analysis on the stability of coupling procedures on a nonuniform grid is carried out. For validation, numerical experiments on one-dimensional and two-dimensional problems are presented to illustrate the stability and accuracy of proposed nonuniform time-step RKDG scheme, as well as the computational benefits it brings. Application to a one-dimensional nonlinear problem is also investigated. [ABSTRACT FROM AUTHOR]