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

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

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

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

linearizing non linear inverse problems and an application to inverse backscattering we propose an abstract approach to prove local uniqueness and conditional holder stability to non linear inverse problems by linearization the main condition is that in addition to the injectivity of the linearization a we need a stability estimate for a as well that condition is satisfied in particular if a a is an elliptic pseudo differential operator we apply this scheme to show uniqueness and holder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed

inverse problems for lorentzian manifolds and non linear hyperbolic equations we study two inverse problems on a globally hyperbolic lorentzian manifold m g the problems are 1 passive observations in spacetime consider observations in an open set v subset m the light observation set corresponding to a point source at q in m is the intersection of v and the light cone emanating from the point q let w subset m be an unknown open relatively compact set we show that under natural causality conditions the family of light observation sets corresponding to point sources at points q in w determine uniquely the conformal type of w 2 active measurements in spacetime we develop a new method for inverse problems for non linear hyperbolic equations that utilizes the non linearity as a tool this enables us to solve inverse problems for non linear equations for which the corresponding problems for linear equations are still unsolved to illustrate this method we solve an inverse problem for semilinear wave equations with quadratic non linearities we assume that we are given the neighborhood v of the time like path mu and the source to solution operator that maps the source supported on v to the restriction of the solution of the wave equation to v when m is 4 dimensional we show that these data determine the topological differentiable and conformal structures of the spacetime in the maximal set where waves can propagate from mu and return back to mu

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

on scattering by time dependent potentials the 2 d case abstract we consider a real potential q x t which has compact support in space x r2 and it is damped we study the solutions of utt u q x t u 0 showing that under additional technical assumptions on q the scattering operator exists our proofs are elementary

stable recovery of time dependent coefficient from arbitrary measurements for wave equation abstract this paper concerns the stability in the inverse problem of determining the time dependent coefficient in the wave equation from partial knowledge of the dirichlet to neumann map at the boundary of a bounded domain of interest we first establish a stability estimate in the determination of the time dependent coefficient from partial boundary observations then we prove that by enlarging the set of data the unknown coefficient can be stably determined in larger regions

determining the wind driven surface currents for prediction of movements of oil slicks in the arabian gulf abstract proposed is a computational algorithm for determination of surface currents under given wind conditions for prediction of oil slick trajectories in the arabian gulf the algorithm interpolates a prespecified set of current velocities obtained from the three dimensional hydrodynamic model of the arabian gulf the three dimensional hydrodynamic model of the arabian gulf computes surface currents for any given wind velocity the prespecified wind velocities are combinations of the eight cardinal wind directions and seven wind speeds ranging from 5 to 35 knots at 5 knot increments a database of surface current velocities for the selected wind conditions is created the interpolation algorithm developed in this study uses the database to compute the surface currents for various wind conditions the proposed algorithm provides the many prospective users an opportunity to utilize the three dimensional hydrodynamic models without the requirement for large computing resources numerical results indicate the feasibility of such an approach

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

a vertical horizontal splitting algorithm for three dimensional tidal and storm surge computations an algorithm is described for the computation of the three dimensional velocity fields due to tides and storm surges the surface elevation and depth averaged velocity components are first computed from the shallow water equations these equations are then used as part of the input to the second part of the algorithm in which the velocity profiles are computed from the momentum equations the nonlinear terms in the momentum equations and both the advective terms and the bottom friction terms in the shallow water equations are fully included the shallow water equations are solved by a finite difference scheme that achieves third order local truncation errors in all the dominant terms and that permits correct parallel flow on coastal boundaries of any orientation two alternative algorithms are discussed for computation of the velocity profiles one based on finite elements in the vertical coordinate direction the other based on a generalized crank nicolson scheme the complete algorithm has been tested on several model problems and has been found to be accurate and fast

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

resonances for non trapping time periodic perturbations for time periodic perturbations of the wave equation in given by a potential q t x we obtain an upper bound of the number of the resonances we establish for m n large enough a trace formula relating the iterations of the monodromy operator u mt 0 t 0 and the sum jzmj of all resonances counted with their multiplicities

stability in the determination of a time dependent coefficient for wave equations from partial data let be a c2 bounded domain of rn n 2 and fix q 0 t with t 0 we consider the stability in the inverse problem of determining a time dependent coefficient of order zero q appearing in a dirichlet initial boundary value problem for a wave equation t2u xu q t x u 0 in q from partial observations on q the observation is given by a boundary operator associated to the wave equation using suitable geometric optics solutions and carleman estimates we prove a stability estimate in the determination of q from the boundary operator

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

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

acoustics in variable area duct finite element and finite difference comparisons to experiment plane wave sound propagation without flow in a rectangular duct with a converging diverging area variation is studied experimentally and theoretically the area variation was of sufficient magnitude to produce large reflections and induce modal scattering the rms pressure and phase angle on both the flat and curved surface were measured and tabulated the steady state finite element theory of astley and eversman and the transient finite difference theory of white are in good agreement with the data it is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations f h j k l p p p0 s t u

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

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

mapped transient infinite elements for heat transfer problems in infinite media abstract based on the fundamental solutions of transient heat transfer problems in infinite media a mapped transient infinite element is presented and the so called heat transfer function of the element has been derived in this paper in order to express the property matrices of the present mapped transient infinite element a mapping technique in which the infinite element in a global coordinate system is mapped into a strip element of finite width and infinite length in a local coordinate system has also been developed using the variable substitution technique the general integral involved in the evaluation of the property matrices of the element has been changed into a standard one for which the conventional gauss legendre integration scheme can be employed since the heat transfer function of the present mapped transient infinite element is dependent on both space and time variables the mechanism of heat transfer problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis finally the accuracy and efficiency of the present mapped transient infinite element have been verified through the analysis of a 1d heat conduction problem in a semi infinite medium and a 2d transient heat transfer problem in a full plane

inflow outflow boundary conditions for two dimensional acoustic waves in channels with flow an analysis of the number and form of the required inflow outflow boundary conditions for the full two dimensional time dependent nonlinear acoustic system in subsonic mean flow is performed the analysis is performed in a rectangular channel with rigid walls and is extendable to more complicated geometries and wall conditions the explicit predictor corrector method of maccormack is used to integrate the acoustic system coupled with the derived boundary conditions the methodology is tested on both uniform and sheared mean flows with plane and nonplanar sources

computation of exponentials in transient data prony s method is widely used to identify the poles of a time series a numerical implementation of prony s method based on the properties of the least squares solution of the transient data matrices is described and a practical indicator of the accuracy of the computational results that is based on the singular values of the transient data matrices is derived this algorithm can be applied to time series which contain simple or multiple poles

global strichartz estimates for the wave equation with time periodic potentials abstract we obtain global strichartz estimates for the solutions u of the wave equation t 2 x v t x u f t x for time periodic potentials v t x with compact support with respect to x our analysis is based on the analytic properties of the cut off resolvent r z u t z i 1 1 where u t u t 0 is the monodromy operator and t 0 the period of v t x we show that if r z has no poles z c z 1 then for n 3 odd we have a exponential decal of local energy for n 2 even we obtain also an uniform decay of local energy assuming that r z has no poles z c z 1 and r z remains bounded for z in a small neighborhood of 0

an algorithm for three dimensional convection and diffusion with very different horizontal and vertical length scales an algorithm is developed and tested for the numerical solution of the three dimensional convection diffusion equation appropriate for the marine environment in which the horizontal and vertical scales differ by one or two orders of magnitude the algorithm splits the horizontal and vertical parts of the process treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable the overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known

an inverse problem of the wave equation this paper is organized as follows in sect 1 the statement of the inverse problem is formulated the basic results are formulated and proved in sect 2 some auxiliary material on the x ray transform is given in a self contained way for convenience of the reader this material is used in section one

a rigorous derivation of the miracle identity of three dimensional inverse scattering the large energy asymptotic behavior of scattering solutions of the three dimensional time dependent schrodinger equation is investigated the second term of the expansion leads to the miracle of newton s three dimensional inverse scattering theory

accurate petrov galerkin methods for transient convective diffusion problems the petrov galerkin method is applied to transient convective diffusion problems with convection dominance weighting functions are used which differ from the shape functions by both symmetric and non symmetric modifications it is proved that the symmetric modifications largely influence the accuracy by a one dimensional and a two dimensional example it is shown how to choose this modification to maximize accuracy

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

finite difference model for tidal flows in the arabian gulf abstract a two dimensional hydrodynamical model for tidal flows in the arabian gulf is developed the model uses variable mesh sizes to handle a more detailed tidal current filed in selected sub regions in this study a three block model scheme is developed in which the deep areas are covered by a relatively coarse grid and the shallow coastal areas by a finer grid the third block which is a super fine mesh in the area of dhahran bahrain and the west coast of qatar is included in the model to predict the more detailed tidal current field in this area a finite difference model is utilized to solve the partial differential equations considered in the model

the leading singularity of a wave reflected by a moving boundary the propagation of singularities of waves in the presence of an impenetrable body is a well studied phenomenon on the formal level of rays snell s law states that the incident and reflected rays reflect at equal angles with the normal analytically the simplest singularity to study is the leading wavefront before multiple reflections can take place its precise nature has been derived rigorously by majda 6 and others in the case of a smooth stationary body of arbitrary shape when the body is moving the theory is less highly developed the rays no longer reflect at equal angles with the normal the reflected angle is greater if the body is locally advancing and less if the body is locally receding uniformly moving plane boundaries are studied in classical textbooks a general theory of scattering with emphasis on the resonant frequencies the scattering amplitude and the decay of the transient waves has been given by us in 3 in the present paper we calculate the wavefront which is reflected when a delta function plane wave impinges upon a three dimensional moving body our body may move or change its shape in any smooth manner as long as it remains in a fixed sphere and moves slower than the wave speed we consider only the simplest kind of wave solutions of the scalar wave equation in r4 which vanish on the space time boundary of the moving body specifically we consider the incident traveling plane wave

numerical solution of the two dimensional tidal equations using the method of characteristics abstract two dimensional shallow water equations which are obtained from the full three dimensional equations by averaging over the vertical coordinate were solved using the method of characteristics the solution technique which utilizes a first order computational scheme is presented in detail and an analysis of the tidal currents in the arabian gulf and the gulf of salwa is given as an example of the method the advantages of using the method of characteristics are discussed

a special adi model for the laplace tidal equations abstract an efficient method for numerical integration of the time dependent laplace tidal equations for a flat or curved earth is described the method is implicit uses alternating directions in two space dimensions with time staggering and a split sea height variable some special auxiliary features of the method are described and stability is discussed

a formulation for higher dimensional inverse problems for the wave equation abstract two particular inverse scattering problems are of special interest the first concerns the discovery of a perturbation in the speed of sound by analyzing the return signal from a blast wave set off above it the second concerns the determination of a potential from the back scattering of plane waves in one dimensional problems the two cases are very closely related in higher dimensions the situation becomes much more complicated we present here a new approach to four such classical higher dimensional inverse problems for determining the coefficients of a partial differential equation including the two mentioned the idea stems from the work of deift and trubowitz 1 in one space dimension no conclusive theorem is found but the approach provides an algorithm for iteration which might lead to an existence theorem and which will be explored numerically elsewhere

numerical study of sound generation due to a spinning vortex pair a numerical approach for the calculation of an acoustic field is applied to the case of a spinning vortex pair to investigate the sound generation by quadrupole sources in unsteady vortical flows based on the unsteady hydrodynamic information from the known incompressible flowfield the perturbed compressible acoustic terms derived from the euler equations are calculated nonreflecting boundary conditions are developed to obtain highly stable solutions calculated results are compared with analytical solutions obtained by the method of matched asymptotic expansions the possibility of predicting the effect of convective mean flow is also tested it is concluded that the sound generated by the quadrupole sources of unsteady vortical flows without a sound generating body or surface can be calculated by using the source terms of hydrodynamic flow fluctuations

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

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

scattering of waves by periodically moving bodies abstract we consider solutions of the scalar wave equation vanishing on the boundary of an obstacle which undergoes periodic motion in analogy with the lax phillips theory we show that the scattering matrix as a function of frequency is holomorphic in a lower half plane and meromorphic in an upper half plane provided rays are not trapped the poles of the scattering matrix correspond to certain outgoing eigenfunctions and there is a near field expansion of finite energy solutions in terms of these eigenfunctions

two step method for evolving nonlinear acoustic systems to a steady state a two step method for evolving two dimensional nonlinear acoustic systems with flow to a periodic steady state is presented in the first step of the method the full nonlinear system governing acoustic disturbances is integrated numerically starting with arbitrary initial conditions using the explicit predictor corrector method developed by maccormack in the second step the fourier time transform of the computed field is calculated to determine its frequency components the transient wave field is then filtered from the spectrum and the inverse transform taken to provide an approximation to the steady state wave field this approximate field provides a new initial condition for subsequent iterations on the method the method is tested on a benchmark acoustic problem for which exact steady state solutions are known and on a nonlinear problem for which a steady state solution has not been given before excellent agreement with the benchmark acoustic solution was obtained within four iterations for planar and nonplanar sources convergence to a steady state for the nonlinear problem occurred in six iterations the two step method eliminates the need to develop nonreflecting boundary conditions in order to obtain periodic steady state solutions of two dimension al acoustic problems and is easily extended to any number of spatial dimensions and to other hyperbolic systems the procedure is shown to be numerically stable and may provide the only alternative for obtaining steady state solutions to problems for which nonreflecting boundary conditions are not known or are physically incorrect

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

scattering frequencies for the wave equation with a potential term abstract the existence of an infinite sequence of scattering frequencies for the equation u qu 0 is established where q is a real valued potential which may assume negative values this result generalizes some of the results obtained by lax and phillips in comm pure appl math 22 1969 737 787

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

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

inverse scattering problem for the wave equation with time dependent potential abstract consider the equation u q t x u 0 x r 3 with a time dependent potential q t x compactly supported in x let u s c r s lloc2 r s 2 be the asymptotic wave profiles of a suitably chosen one parameter family of solutions if q1 q2 and the profiles ui related to qi i 1 2 coincide we prove that q1 q2

property c and an inverse problem for a hyperbolic equation let utt u q x t u 0 in d 0 t where d r3 is a bounded domain with a smooth boundary d t d d diam d q x t c 0 t l d suppose that for every u d f x t c1 d 0 t the value un d h s t is known where n is the outer normal to d u solves and and satisfies the initial conditions u ut 0 at t 0 then q x t is uniquely determined by the data f h f c1 d 0 t in the subset s of d 0 t consisting of the lines which make 45 with the t axis and which meet the planes t 0 and t t outside d 0 t provided that q x t is known outside s here d is the closure of d

time dependent wave envelope finite difference analysis of sound propagation a transient finite difference wave envelope formulation is presented for sound propagation without steady flow before the finite difference equations are formulated the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction this transformation reduces the required number of grid points by an order of magnitude physically the transformed pressure represents the amplitude of the conventional sound wave the derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements to illustrate the method example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct the numerical results are in good agreement with exact analytical results

adaptation of the solution of the two dimensional tidal equations using the method of characteristics to wind induced currents and storm surges abstract the method of characteristics previously employed to predict two dimensional tidal flows is extended to examine wind driven currents and storm surges after the shallow water equations used to model flow in coastal regions are given modifications are made in two of the forcing functions to incorporate wind contributions two hypothetical storms are constructed and results are presented in a series of figures which show sea level heights and velocity fields at various times as the storm progresses

scattering properties of wave equations with time dependent potentials we consider finite energy solutions of the perturbed wave equation with impurities which depend upon space and time u q x t u 0 with x rn t r in the case n odd 3 we prove that under suitable assumptions on the potential q x t the scattering operator exist and we analyse some of its properties finally we present a uniqueness result on an inverse scattering problem associated to the above equation in the case n 3

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

exponential growth for the wave equation with compact time periodic positive potential we prove the existence of smooth positive potentials v t x periodic in time and with compact support in x for which the cauchy problem for the wave equation u tt xu cv t x ud 0 has solutions with exponentially growing global and local energy moreover we show that there are resonances 2 c

an operator splitting algorithm for two dimensional convection dispersion reaction problems an operator splitting algorithm for the two dimensional convection dispersion reaction equation is developed the flow domain is discretized into triangular elements which are fixed in time the governing equation is split into three successive initial value problems a pure convection problem a pure dispersion problem and a pure reaction problem for the pure convection problem solutions are found by the method of characteristics the solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point a cubic polynomial is used to interpolate the concentration and its derivatives on an element for the pure dispersion problem an explicit finite element algorithm is employed analytical solutions are obtained for the pure reaction problem the treatment of the boundary conditions is also discussed several numerical examples are presented numerical results agree well with analytical solutions because cubic polynomials are used in the interpolation very little numerical damping and oscillation are introduced even for the pure convection problem

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

stable determination outside a cloaking region of two time dependent coefficients in an hyperbolic equation from dirichlet to neumann map abstract in this paper we treat the inverse problem of determining two time dependent coefficients appearing in a dissipative wave equation from measured neumann boundary observations we establish in dimension n 2 stability estimates with respect to the dirichlet to neumann map of these coefficients provided that they are known outside cloaking regions moreover we prove that they can be stably recovered in larger subsets of the domain by enlarging the set of data

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