transparent acoustic source condition applied to the euler equations it can be concluded from the present calculations that the transparent source model proposed here is useful to numerically simulate an acoustic source in the computational domain that is located far downstream thus it is possible to simulate a complex acoustic problem such as the reflection and transmission of an incident wave

practical aspects of higher order numerical schemes for wave propagation phenomena this paper examines practical issues related to the use of compact difference based fourth and sixth order schemes for wave propagation phenomena with focus on maxwell s equations of electromagnetics an outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches transformed plane method and physical space differencing in the first technique the truncation error expansion for the sixth order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available physical space differencing formulas are derived for the five point stencil by expressing the coefficients in terms of local spacing ratios the order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes to ensure stability for a broad range of problems fourier analysis is employed to develop a single parameter family of up to tenth order tridiagonal based spatial filters the implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1 d cavity where they are employed to suppress a late time instability the paper concludes after demonstrating the application of the scheme to several 3 d canonical problems utilizing cartesian as well as curvilinear meshes published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

multigrid acceleration of a high resolution computational aeroacoustics scheme a multigrid method is applied to a fourth order accurate spatially and temporally nite difference runge kutta time marching scheme thisisusedto solvethenonlineareulerequationsfortheef cientprediction ofnoise radiation from turbofan engine inlets this noise prediction approach computes a steady state solution rst and thenasourceisturnedonandtheunsteadysolutioniscomputed thishastheadvantageofusingthesamenumerical scheme to evaluate the residuals of the governing equations in both the steady and unsteady calculations which meansthatthesteady statesolutionissmoothand nonumericalerrorscontaminatetheacousticsolution thehigh

a time domain method for duct acoustics this paper reports the development of a time accurate method for prediction of acoustics in lined ducts the multi dimensional euler equations are dimensionally split into a system of uni directional simple wave equations which are discretized and solved using an implicit compact high order finite difference scheme the split equations are closed and coupled through the concept of impedance at domain boundaries time domain extensions of the impedance boundary condition and their efficient implementation are introduced for broadband and monotone waves the method is benchmarked by the modal solution of a monopole in the lined duct and used to investigate wall interference on the acoustic fields of realistic sources excellent agreement is found in the comparison with classical solutions and the discrepancy found in the comparison with experiment is ascribable to experimental uncertainty

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

broadband time domain impedance models the modeling of a set of impedance values given either experimentally or heuristically for implementation as a time domain impedance equivalent boundary condition tdibc is discussed it is shown that impedance as defined by the reflection of plane harmonic waves when extended for broadband time domain applications can correspond to mathematically feasible but physically unacceptable noncausal reflection processes given a set of impedance data on a finite positive and real frequency range it is possible to construct causal time domain models that render efficient implementation of tdibc for broadband reflections however these models defined by measurement of harmonic waves may not be valid for the reflection of impulses for which measurement of transient reflections is warranted

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

obtaining holonomy from curvature in physical applications of differential geometry one sometimes wishes to compute the holonomy group of a riemannian manifold from local data such as the curvature tensor in general this can be a complicated problem but we show that in cases of most interest in physics the holonomy group can be obtained directly from the lie algebras generated by the curvature tensor

backlund transformations and explicit solutions of certain inhomogeneous nonlinear schrodinger type equations shows that the darboux bargmann method can be used to derive backlund transformations and construct explicit soliton solutions for certain inhomogeneous nonlinear schrodinger type equations

on the robust flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations the accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries in the present study we discuss time domain impedance boundary conditions tdibc the formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries our formulation is an extension of the well known navier stokes characteristic boundary conditions the frequency dependent reflections at the boundaries are implemented with a state space model in the time domain we provide a comprehensive discussion on how such state space models can be constructed and interpreted this discussion shows that the state space description allows a robust and flexible implementation it allows to consider complex reflection coefficients and account for non constant cfd time steps in a straight forward manner furthermore we prove analytically and demonstrate numerically that the formulation proposed is consistent i e the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately as long as the waves impinging on the boundary are plane and it prohibits drift of the mean flow variables finally the boundary conditions are tested successfully for laminar and turbulent flows

an improved γ riccati backlund transformation and its applications for the inhomogeneous nonlinear schrodinger model from plasma physics and nonlinear optics abstract the inhomogeneous nonlinear schrodinger type nls model from certain plasmas and optical fibers is investigated with symbolic computation an improved riccati backlund transformation r bt is presented which can generate successively a hierarchy of solutions through algebraic manipulations based on the improved r bt the darboux transformation is obtained the analytic one two soliton like solutions are presented and the physical characteristics of the influences of the coefficient parameters on the propagation of the soliton pulses are discussed graphically

holonomy groups and holonomy representations the holonomy group of a riemannian manifold always arises in geometry through a particular representation not as an abstract group one can therefore ask whether there exist pairs of compact locally irreducible manifolds with holonomy groups which are isomorphic yet distinct because the holonomy representations are not equivalent a theorem of besse asserts that this is not possible in the simply connected case however it is possible for certain nonsimply connected manifolds here we identify all of these manifolds up to space form problems in the case where the ricci curvature is not negative this allows us to solve the holonomy classification problem for all compact locally irreducible riemannian manifolds of positive ricci curvature

frequency domain prediction of turbofan noise radiation this paper describes a frequency domain numerical method for predicting noise radiation from ducted fans including acoustic treatment and non uniform background flow effects the method solves the euler equations linearized about a mean flow in the frequency domain a pseudo time derivative term is added to the frequency domain equations so that a time marching technique can be employed to drive the acoustic field to steady state explicitly this approach makes distributed parallel computing more viable for equations of this type and will allow for future use of well known convergence acceleration techniques such as multigrid to obtain the solutions efficiently simulations of the jt15d static test inlet are performed including the effects of liners and the results are compared with experimental data a generic engine geometry is used for demonstrating further the prediction capability of the code calculating the attenuation effects of different liner impedances and liner installation locations on the radiated sound fields

finite difference solution to the parabolic wave equation in this article an implicit finite difference ifd scheme is introduced for solving underwater acoustic wave propagation problems this scheme is applied to the parabolic wave equation model for the acoustic problem with a free surface and arbitrary bottom and bottom boundary conditions the mathematical theory of the implicit finite difference method as applied to the parabolic equation is developed and a computer model to implement the ifd is introduced representative problems are presented to demonstrate the capability of the ifd model advantages and limitations of the ifd are discussed

fundamental problems with the model of uniform flow over acoustic linings abstract the walls of ducts containing flow are often acoustically lined in order to reduce sound many simple models of acoustic linings assume the lining to be linear and locally reacting examples considered here include the three parameter mass spring damper helmholtz resonator and enhanced helmholtz resonator models all of these models have been found to have stability issues with uniform mean grazing flow and there has been some confusion over the existence of hydrodynamic instability surface waves over such linings mathematically the standard proven briggs bers stability analysis is not applicable computationally the hydrodynamic modes are routinely ignored in the frequency domain and instabilities filtered out in the time domain this confusion also causes significant problems for mode matching green functions and scattering analyses in this paper it is shown that any situation not capable of being analysed using the briggs bers criterion is illposed and that this is the root cause of the confusion over hydrodynamic instabilities a large class of lining models including all those mentioned above are shown to be illposed with uniform mean flow an explanation is given of the effects of this illposedness in practice and it is argued that illposed models should not be used an alternative stability criterion to briggs bers has been occasionally used in the literature this alternative criterion involving analytic continuation to purely imaginary frequencies was recently christened the crighton leppington stability criterion however this stability criterion is incorrect and several counter examples are given here

impedance boundary condition for truncated open spaces the propagation of waves governed by hyperbolic systems at a surface is in general reflective the numerical solution of many problems in mechanics necessitates the truncation of an open space to a finite domain the reflectivity of the boundary of a truncated domain can be effectively characterized by a few parameters and implemented as a time domain impedance boundary condition it is shown that the concept of a time domain impedance boundary condition affords a simple and effective treatment of waves allowing them to exit the surfaces of a truncated domain as a causal local space time continuation rather than a global boundary confinement we presentanddiscusstheopen spaceimpedancesofradiativeandconvective fields theirmodeling analyticstructures implementation and solution effectiveness as an open space impedance boundary condition we further propose a generalmethodologyfornumericaldefinitionofopen spaceimpedanceanditsapplicationwithinexistingschemesto reduce truncated domains and computational resources

time domain numerical simulation of a flow impedance tube an efficient method has been developed for the application of the surface acoustic impedance condition in time domain solutions of aeroacoustic problems such as the broadband frequency simulation of a flow impedance tube the basis for this method is the standard impedance condition stated in the frequency domain as the particle displacement continuity equation the development of the time domain impedance condition follows the relations among the frequency z and discrete time domains and a rational function representation of the impedance in thez domain the resultant impedance condition consists of finite infinite impulse response type digital filter operations in the time domain which is very suitable to computational aeroacoustics algorithms this paper describes the present approach and discusses the time domain numerical simulations of the nasa langley flow impedance tube with a constant depth ceramic tubular liner both single and broadband frequency simulations are performed excellent agreement is shown with experimental data at various frequencies and flow conditions

an improved method for darboux transformation for the coupled inhomogeneous nonlinear schrodinger system from plasma physics and nonlinear optics abstract the coupled inhomogeneous nonlinear schrodinger type system which can be used to control soliton propagation and interaction in certain plasmas and optical fibers is investigated an improved method for darboux transformation dt is presented in more general forms by constructing an improved riccati type backlund transformation r bt with the n th iterated r bt or the n th iterated dt which is a compact representation for the n soliton like solutions and can generate a series of analytic solutions from a pair of the seed solutions through algebraic manipulations the analytic one two soliton like solutions are provided with the choice of parameters for the soliton solutions the dynamical characteristics of the influences of the inhomogeneous parameters on the propagation of the soliton pulses are discussed graphically

a controllable canonical form implementation of time domain impedance boundary conditions for broadband aeroacoustic computation a new method which can be effectively and efficiently applied in the simulations of broadband noise problems is proposed for time domain impedance boundary condition implementations by using the so called controllable canonical form that is well known in linear system usually the impedance boundary condition can be defined in frequency domain as a rational polynomial function with poles in the negative half of the complex plane to guarantee stability otherwise causality might be violated in the corresponding time domain implementation to address this issue various methodologies have been proposed previously that usually lead to complicated polynomials whose numerical implementations are often indirect and intricate the proposed method with a controllable canonical form on the other hand directly transforms the frequency domain transfer function a quotient of rational polynomials to an equivalent state space model which consists of a series of first order ordinary differential equations that can be numerically implemented in a straightforward way the proposed method is demonstrated by using two benchmark problems a two dimensional gaussian pulse propagating in a uniform flow with a lined wall and the test cases from the nasa langley grazing incidence tube experiments good agreements demonstrate the potential of the proposed computational method

a compact difference scheme for the navier stokes equations in vorticity velocity formulation this paper presents a new numerical method for solving the incompressible unsteady navier stokes equations in vorticity velocity formulation the method is applicable to spatial simulations of transitional and turbulent boundary layer flows it is based on a compact difference discretization of the streamwise and wall normal derivatives in cartesian coordinates a fourier collocation approach is used for the spanwise derivatives important new features of the numerical method are the use of nonequidistant differences in the wall normal direction the use of split compact differences in the streamwise direction a new fast iteration for a semi implicit time integration of the wall normal diffusion terms and an improvement of the buffer domain technique to prevent reflections of waves at the outflow boundary results of test calculations are presented to verify the improvements obtained by the use of these new techniques

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

efficient implementation of tam and auriault s time domain impedance boundary condition a new and efficient time domain implementation is proposed for the impedance model originally introduced by tam and auriault tam c k w and auriault l time domain impedance boundary conditions for computational aeroacoustics aiaa journal vol 34 no 5 may 1996 pp 917 923 in the frequency domain the pressure can be calculated from the product of the impedance with the normal velocity in the time domain a convolution is needed which may become a costly operation present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency domain models to time domain formulations involving time derivatives the former approach is very costly in terms of memory and cpu time the latter makes the implementation discretization specific and vulnerable to stability issues a new formulation based on recursive convolution results in an efficient implementation that stores only one accumulator which can be updated at each time step with minimal addition and multiplication it allows for the exact representation of the impedance at a given frequency the formulation is validated by a comparison with the measurement data from the nasa langley grazing flow impedance tube the simulations are performed by introducing a plane wave at a single frequency in the tube and this is done for six frequencies and five different mean flow speeds

broadband impedance boundary conditions for the simulation of sound propagation in the time domain an accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband frequency simulation in aeroacoustic problems to show the capability of this method two kinds of numerical simulations are performed and compared with the analytical experimental results one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall both single frequency and broadband frequency simulations are performed within the framework of linearized euler equations a high order dispersion relation preserving finite difference method and a low dissipation low dispersion runge kutta method are used for spatial discretization and time integration respectively the results show excellent agreement with the analytical experimental results at various frequencies the method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well posedness of the broadband time domain impedance boundary condition

time domain implementation of an impedance boundary condition with boundary layer correction a time domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary based on the asymptotic frequency domain boundary condition of brambley 2011 25 a finite difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case the discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities the cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite difference schemes it is suggested that these are general properties of any numerical discretization of an unstable system existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band the properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general these filters are capable of removing only the artificial numerical instabilities allowing the reference implementation to correctly reproduce the stability properties of the analytic solution

fast euler solver for transonic airfoils i theory ii applications equations written in terms of generalized riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices using an implicit euler solver that is based on the lambda formulation the solution is found on a c grid whose boundaries are very close to the airfoil the fast solver is then applied to the computation of several flowfields on a naca 0012 airfoil at various mach number and alpha values yielding results that are primarily concerned with transonic flows the effects of grid fineness and boundary distances are analyzed the code is found to be robust and accurate as well as fast

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

an algorithm to implement a surface impedance boundary condition for fdtd em scattering two models for numerically simulating a surface impedance boundary condition in fdtd are presented the resulting algorithm is easy to implement requiring only trivial modification to a code written for a perfect electrical conductor boundary condition

an extension of complex modes for the resolution of finite element poroelastic problems a new modal synthesis technique inspired from complex modes is presented in this paper the purpose of this method is to find an alternative to the weakness of usual modal techniques in order to improve resolution of finite element poroelastic problems firstly the construction of modes and the synthesis for a general forcing is explained secondly the approach is applied to a one dimensional poroelastic problem finally the approach is numerically tested and its performance is investigated by comparison with solutions obtained with a direct resolution of the system

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

time domain impedance boundary conditions for computational aeroacoustics it is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance impedance is a complex quantity as such it is designed primarily for frequency domain analysis time domain boundary conditions that are the equivalent of the frequency domain impedance boundary condition are proposed both single frequency and model broadband time domain impedance boundary conditions are provided it is shown that the proposed boundary conditions together with the linearized euler equations form well posed initial boundary value problems unlike ill posed problems they are free from spurious instabilities that would render time marching computational solutions impossible

parallel computation of forward radiated noise of ducted fans with acoustic treatment forward radiated noise of ducted fans is computed numerically on parallel processors solving the three dimensional time dependent euler equations in body conformed coordinates with a fourth order accurate finite difference runge kutta time integration scheme sound attenuation effects of inlet wall acoustic treatment are included in computations employing a time discrete form of the standard impedance condition a distributed computing approach with domain decomposition is used for integrating the equations in parallel using the message passing interface library routines the abilities of the method are demonstrated with hard and soft wall simulations of the jt15d inlet including flow effects

on the effect of the dispersion error when updating acoustic models abstract in the frame of predicting acoustic pressure fields by means of numerical simulations many tools are already available making mostly use of the finite or boundary element techniques in order to get simulated acoustic pressure fields closer to the reality updating techniques can be used particularly one focuses on a validation method based on the constitutive law error cle which was initially proposed by p ladeveze new advances in adaptative computational methods in mechanics elsevier 1998 pp 135 151 in structural dynamics and was recently applied to acoustics v decouvreur et al in h mang f rammerstorfer j eberhardsteiner eds wccm v fifth world congress on computational mechanics vienna austria vienna university of technology 2002 isbn 3 9501554 0 6 these works use the fem as numerical approximation method when increasing the frequency the validation quality decreases due to the growing discretization error of the linear fem therefore to diminish the discretization error another approximation method is used namely the element free galerkin method a case study is presented where the discretization error is controlled and the effects on the updating parameters the admittance coefficients is evaluated comparing the results coming from the validation when using both fem and efgm shows that a numerical method with robust frequency behaviour is more suited for updating setups with highly frequency dependent parameters

using high order methods on adaptively refined block structured meshes derivatives interpolations and filters block structured adaptive mesh refinement amr is used for efficient resolution of partial differential equations pdes solved on large computational domains by clustering mesh points only where required by large gradients previous work has indicated that fourth order convergence can be achieved on such meshes by using a suitable combination of high order derivative interpolation and filter stencils and can deliver significant computational savings over conventional second order methods at engineering error tolerances in this paper we explore the interactions between the errors introduced by the discretized operators for derivatives interpolations and filters we develop general expressions for high order derivative interpolation and filter stencils applicable in multiple dimensions using a fourier approach to facilitate high order block structured amr implementations these stencils are derived under the assumption that the fields that they are applied to are smooth for a given derivative stencil and thus a given order of accuracy the necessary interpolation order is found to be dependent on the highest spatial derivative in the pde being solved this is demonstrated empirically using one and two dimensional model equations by observing the increase in delivered accuracy as the order of accuracy of the interpolation stencil is increased we also examine the empirically observed order of convergence as the effective resolution of the mesh is increased by successively adding levels of refinement with different orders of derivative interpolation and filter stencils the procedure devised here is modular and its various pieces i e the derivative interpolation and filter stencils can be extended independently to higher orders and dimensions in the case of interpolation stencils the application of these methods often requires nontrivial logic especially near domain boundaries this logic along with the stencils used in this study are available as a freely downloadable software library

low dispersion finite difference methods for acoustic waves in a pipe a new algorithm for computing one dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial boundary value problem conventional dissipation free second order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength using the signal generated by a piston in a duct as an example transient acoustic computations are presented using a new compact three point algorithm which allows about 60 fewer mesh points per wave length both pulse and harmonic excitation are considered coupling of the acoustic signal with the pipe resonant modes are shown to generate a complex transient wave with rich harmonic content

time domain numerical computation of noise reduction by diffraction and finite impedance of barriers a new time domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers high order finite difference schemes conventionally used for computational aeroacoustics and time domain impedance boundary conditions are utilized for the development of the time domain method compared with other methods this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise linearized euler equations in cartesian co ordinates are considered and solved numerically straight and t shaped barriers with and without surface admittance are calculated in order to assess the accuracy of this time domain method comparison with the results of sysnoise software ver 5 3 are made there are very good agreements between the results of the present time domain numerical method and the boundary element method of the sysnoise software

implicit high order compact algorithm for computational acoustics accurate solution of the linearized multidimensional euler equations for aeroacoustics as a system of simple wave equations is demonstrated if organized this system has unambiguous easily implemented boundary conditions allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions thus the task of designing a complex multidimensional scheme with approximate boundary conditions reduces to the design of accurate schemes for the simple wave equation in particular an implicit compact finite difference scheme and a characteristically exact but numerically nth order accurate boundary condition are used this low dispersion scheme has a third order spatial accuracy for various types of nonuniform meshes fourth order accuracy on uniform meshes and by choice a temporal accuracy of second order for algorithmic simplicity as the crank nicolson scheme the robustness and accuracy of the scheme and the validity of the system decoupling are demonstrated through a series of numerical experiments and comparisons with published results including the recent institute for computer applications in science and engineering nasa langley research center benchmark problems of acoustic and convective wave propagation in cartesian and cylindrical domains and reflection at stationary and or moving boundaries

a finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields a propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented the method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function a finite element propagation model is combined with a coarse fine grid impedance plane search technique to extract the impedance of the material results are presented for three different materials for which the impedance is known for each material the input data required for the prediction scheme were computed from modal theory and then contaminated by random error the finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments thus the method developed here provides a means for determining the impedance of materials in a nonprogressive wave environment such as that usually encountered in a commercial aircraft engine and in most laboratory settings

spatial fourier transform method of measuring reflection coefficients at oblique incidence i theory and numerical examples a new method using spatial fourier transform has been developed to measure reflection coefficients at oblique incidence the method involves the measurement of complex pressure distributions on two parallel planes lying close to the surface of a test material and decomposing each of the complex pressure distributions into plane wave components by using two dimensional spatial fourier transform the incident and reflected plane wave components on the surface of the test material can be mathematically separated by the use of plane wave propagation theory this separation leads to the determination of reflection coefficients at arbitrary angles of incidence investigation has been made into the error due to the finite size of the measurement area to show that the magnitude of the error can be reduced by using a dipole source instead of a monopole source numerical examples are given to illustrate the validity of the method

treatment of frequency dependent admittance boundary conditions in transient acoustic finite infinite element models the paper addresses the handling of frequency dependent local admittance boundary conditions in acoustic transient finite infinite element models the proposed approach avoids the evaluation of a convolution integral along the related boundary based on a similar technique developed in an aeroacoustic finite difference context the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before the incorporation of such a discrete in time boundary condition in a finite infinite element context is addressed the infinite element scheme selected for that purpose relies on the conjugated astley leis formulation implementation aspects cover the handling of frequency dependent boundary conditions along both finite and infinite element edges numerical examples waveguide single source in a half space bounded by an impedance plane diffraction by an acoustically treated screen are presented in order to demonstrate the efficiency of the proposed approach

energy analysis and discretization of nonlinear impedance boundary conditions for the time domain linearized euler equations time domain impedance boundary conditions tdibcs can be enforced using the impeda nce the admittance or the scattering operator this article demonstrates the computational advantage of the last even for nonlinear tdibcs with the linearized euler equations this is achieved by a systematic semi discrete energy analysis of the weak enforcement of a generic nonlinear tdibc in a discontinuous galerkin finite element method in particular the analysis highlights that the sole definition of a discrete model is not enough to fully define a tdibc to support the analysis an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube then the derivation of time delayed broadband tdibcs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners a high order discretization of the derived time local formulation which consists in composing a set of ordinary differential equations with a transport equation is applied to two flow ducts

well posed boundary condition for acoustic liners in straight ducts with flow doi 10 2514 1 j050723 the myers boundary condition for acoustics within flow over an acoustic lining has been shown to be ill posed leading to numerical stability issues in the time domain and mathematical problems with stability analyses this paper gives a modification for flat or cylindrical straight ducts to make the myers boundary condition well posed and indeed more accurate by accounting for a thin inviscid boundary layer over the lining and correctly deriving the boundary condition to first order in the boundary layer thickness the modification involves two integraltermsovertheboundarylayer the firstmaybewrittenintermsofthemass momentum andkinetic energy thicknessesoftheboundarylayer whichareshownto physicallycorrespondtoamodifiedboundarymass modified grazingvelocity andatensionalongtheboundary thesecondintegral termisrelatedtothecriticallayerwithinthe boundary layer a time domain version of the new boundary condition is proposed although not implemented the modified boundary condition is validated against high fidelity numerical solutions of the pridmore brown equation for sheared inviscid flow in a cylinder absolute instability boundaries are given for certain examples though convective instabilities appear to always be present at certain frequencies for any boundary layer thickness

impedance and its time domain extensions the classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex valued quantity akin to plane harmonic waves and the analysis of their ree ections a new look at this classical quantity irrespective of the type of incident waves is presented it points out that a direct operational inversion of impedance into time domain boundary operators will in general lead to an unstable system whereas the inversion of the corresponding ree ection coefe cient will result in stable easily implementable boundary operators for time domain prediction of wave ree ection it reveals the equivalent pulselike causal process of time convoluting the incident wave into the ree ected wave excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

optimized prefactored compact schemes the numerical simulation of aeroacoustic phenomena requires high order accurate numerical schemes with low dispersion and dissipation errors in this paper we describe a strategy for developing high order accurate prefactored compact schemes requiring very small stencil support these schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes the prefactorization strategy splits the central implicit schemes into forward and backward biased operators using fourier analysis we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components this ensures that when the forward and backward stencils are added the original central compact scheme is recovered to extend the resolution characteristic of the schemes an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh the resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth and eighth order compact schemes making them more suitable for high resolution numerical simulations in gas dynamics and computational aeroacoustics the efficiency accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems

einstein metrics on s 3 r 3 and r 4 bundles starting from a 4n dimensional quaternionic kahler base space we construct metrics of cohomogeneity one in 4n 3 dimensions whose level surfaces are thes 2 bundle space of almost complex structures on the base manifold we derive the conditions on the metric functions that follow from imposing the einstein equation and obtain solutions both for compact and non compact 4n 3 dimensional spaces included in the non compact solutions are two ricci flat 7 dimensional metrics withg 2 holonomy we also discuss two other ricci flat solutions one on ther 4 bundle overs 3 and the other on anr 4 bundle overs 4 these haveg 2 and spin 7 holonomy respectively

an adjoint based method for liner impedance eduction validation and numerical investigation abstract an inverse method for liner acoustic impedance eduction in a duct is presented the determination of adjoint equations allows to make explicit the directional derivatives of the objective function needed by the search algorithm direct and adjoint system of equations are spatially discretized by a discontinuous galerkin scheme the propagation model and the eduction process are successfully validated on nasa benchmark data extracted from literature in a no flow configuration objective functions written in terms of acoustic pressure and acoustic velocity are considered successively special attention is given to the possibilities offered by the method such as multiparameter identification with the study of a non homogeneous liner convergence history of the process is also examined revealing interesting properties for the velocity based objective function compared to the pressure based objective function in further developments the method is planned to be used with acoustic velocity fields obtained by laser doppler velocimetry

a potential theoretic method for far field sound radiation calculations abstract the far field acoustic radiation due to the interaction of upstream unsteady vortical disturbances with an airfoil in subsonic compressible flow is calculated using potential theory a kirchhoff surface is placed in the near field surrounding the airfoil and the pressure on this surface is calculated from the unsteady flow field obtained using a second order finite difference code the governing equation is reduced to the helmholtz equation in the frequency domain and the solution is written in terms of an integral over the kirchhoff surface involving the free space green s function and an unknown single layer density function the single layer density is then determined from the boundary condition on the kirchhoff surface this method is presented as an alternative to classical kirchhoff methods it has the advantage of being able to accommodate arbitrarily shaped kirchhoff surfaces and is also readily extendable to three dimensional problems numerical results are presented for thin symmetric and loaded airfoils thin airfoil results are compared to the analytical solution and thick airfoil results are checked for numerical convergence and compared to results obtained from a time domain euler solver

numerical prediction of aft radiation of turbofan tones through exhaust jets this paper describes a numerical methodology for calculating tonal noise propagation and radiation through turbomachinery exhaust ducts including non uniform background jet flows the numerical method is based on solution of the linearized euler equations directly in the frequency domain employing a direct sparse matrix solver in parallel acoustic sources are introduced into the computational domain via the perfectly matched layer equations various test cases including propagation through infinite ducts and propagation and radiation through semi infinite ducts with and without liners are solved and results are compared with analytical solutions it is demonstrated that solutions even with thin shear layers separating the exterior and jet streams at reasonably high mach numbers can be obtained quite successfully the method is also validated by simulating the radiated sound waves from two actual engine exhaust cowl geometries and the results are compared with experimental data

a new efficient algorithm for computational aeroacoustics on parallel processors one of the great challenges in computational physics is the prediction of flow associated noise where the quantities of interest namely the sound waves can be at high frequencies and are usually orders of magnitude smaller in magnitude than the mean quantities in order to numerically resolve such small scales governed by the fluid dynamics equations high resolution schemes are required thus solutions of flow noise problems are computationally intensive an efficient hybrid data parallel computational aeroacoustics algorithm has been developed for the prediction of noise radiation and scattering from three dimensional geometries the algorithm solves the euler navier stokes equations in the interior and nonreflecting boundary conditions on the outer boundaries a moving surface kirchhoff method is coupled to the flow solver for far field predictions the algorithm uses standard time and spatial discretization techniques but utilizes several new optimization strategies that are highly suitable for single zone solutions on data parallel processors one strategy for example enables simultaneous residual evaluations of the interior and far field nonreflecting boundary conditions equations reducing the computational effort spent on them by approximately 60 cpu time savings the algorithms for the flow solver and the kirchhoff method and their coupling are described in this paper and results for some example radiation and scattering problems are presented

geometrical and gauge equivalence of the generalized hirota heisenberg and wkis equations with linear inhomogeneities integrable evolution equations can take several equivalent forms in a geometrical sense here we consider the equivalence of generalized versions involving linear inhomogeneities of three important nonlinear evolution equations namely the hirota heisenberg ferromagnetic spin and wadati konno ichikawa shimizu wkis equation through a moving helical space curve formalism and stereographic representation from the geometrical consideration we also construct suitable 2 2 matrix linear eigenvalue equations involving however non isospectral flow the eigenvalues evolve in time however these systems are also gauge equivalent we briefly analyse the scattering problem and show that infinite number of constants of motion can exist for these systems

acoustic propagation on irrotational mean flows using transient finite and infinite elements a formulation is presented for the computation of transient wave fields propagating on unbounded irrotational mean flows the numerical scheme is based on an inner mesh of conventional finite elements which is matched to high order multipole infinite elements in the far field the scheme is validated against simple transient test solutions and shown to be effective for large three dimensional problems provided that iterative solvers are used to advance the solution at each time step