interpolation operators in orlicz sobolev spaces we study classical interpolation operators for finite elements like the scott zhang operator in the context of orlicz sobolev spaces furthermore we show estimates for these operators with respect to quasi norms which appear in the study of systems of p laplace type

the boundary condition at an impedance wall in a non uniform duct with potential mean flow the boundary condition at an impedance wall in a duct with a steady mean flow requiring the specification of the normal component of acoustic particle velocity is examined it is found that when implemented in the weak formulation of the finite element method it can be considerably simplified the boundary condition would appear to require data which includes the tangential derivative of the tangential mean flow velocity the normal derivative of the normal component of mean flow velocity and the derivatives of the mean flow density and the boundary admittance along the boundary it is shown that with suitable rearrangement the normal and tangential velocity derivatives can be eliminated as can the derivatives of the mean flow density and admittance the boundary condition becomes only slightly more complicated than the corresponding boundary condition when mean flow is absent and is no more difficult to implement requiring only local values of tangential mean flow velocity density and admittance which are already required as data for the weak formulation of the field equation

on the finite element approximation of p stokes systems in this paper we study the finite element approximation of systems of p stokes type for p in 1 infty we derive in some cases optimal error estimates for finite element approximation of the velocity and for the pressure in a suitable functional setting the results are supported by numerical experiments

a three dimensional boundary element scheme for acoustic radiation in low mach number flows a boundary element scheme is proposed for acoustical radiation in moving flows the scheme relies upon a transformation valid at low mach numbers which permits the case with flow to be restated as an equivalent problem in the absence of flow but with modified boundary conditions this restatement of the original problem is then amenable to boundary integral representation and boundary element solution results obtained by using this approach are presented for the test case of a pulsating or juddering sphere of finite dimensions in a uniform low mach number flow a fully three dimensional boundary element model is used the validity of the results is established by comparison with an analytic perturbation solution where applicable and by comparison with results from an alternative axisymmetric numerical scheme

on the acoustics of low mach number bulged throated and baffled nozzles abstract the acoustic wave equation for quasi one dimensional propagation along a duct of varying cross section containing a low mach number mean flow is obtained section 2 by using as variables either the potential or the velocity section 2 1 the ray approximation that holds only for wavelengths which are short compared with the length scales of the variation of the cross section and mean flow velocity is used as a factor to reduce the wave equation to a schrodinger form section 2 2 it is shown that the latter reduced form for the potential is the most convenient for studying the acoustics of catenoidal section 2 3 and sinusoidal section 3 1 nozzles it is found that these inherit respectively the filtering properties of catenoidal horns and transparency properties of sinusoidal horns this approach also applies to the exponential nozzle section 3 3 whereas for the gaussian nozzle the sound field can be expressed in terms of hermite functions by using a semi reduced form section 3 2 of the wave equations the exact solutions of the nozzle wave equation section 3 for the four families of ducts are plotted section 4 as amplitude and phase versus distance for several combinations of frequency and low mach number the nozzle families considered include the catenoidal in figures 1 2 6 9 in section 4 1 the sinusoidal figures 3 10 11 and exponential figures 5 12 13 in section 4 2 and the first six eigenfunctions of gaussian nozzles figures 4 14 17 in section 4 3 the various cases presented here are applications of a technique which derives the acoustics of low mach number nozzles from that of the corresponding horns i e ducts of the same cross section but without mean flow

quasi newton minimization for the p x laplacian problem we propose a quasi newton minimization approach for the solution of the p x laplacian elliptic problem x r m this method outperforms those existing for the p x variable case which are based on general purpose minimizers such as bfgs moreover when compared to ad hoc techniques available in literature for the p constant case and usually referred to as mesh independent the present method turns out to be generally superior thanks to better descent directions given by the quadratic model

accuracy and stability of finite element schemes for the duct transmission problem a one dimensional numerical model is used to investigate the characteristics of finite element computational schemes for linearized acoustical transmission in ducts with flow primitive variables and coupled first order equations are used the relative performances of lagrangian and hermitian elements with galerkin and residual least squares formulations are assessed results of the numerical study are shown to correlate with the characteristics of analytic solutions for the equivalent regular grid difference equations galerkin solutions are shown to introduce spurious nonphysical modes which must be eliminated by careful attention to the local resolution requirements of the finite element mesh residual least squares formulations do not introduce spurious numerical modes but result in significant numerical damping this is particularly severe if lagrangian elements are used

computation of acoustic propagation in two dimensional sheared ducted flows most aeroacoustic noise prediction methods rely on an acoustic analogy featuring a propagation equation associated with source terms these models were mainly applied to computation of acoustic far fields radiated by simple free flows like jets the assumption is made in many formulations that the radiated acoustic field is not perturbed by the shear flow giving rise to the noise sources these acoustic analogies thus do not provide a full description of acoustic flow interactions the lilley equation was introduced to account to a certain extent for mean shear effects on propagation more recently this problem has been treated by making use of the linearized euler equations which are more flexible and more adequate for numerical simulations as several types of modes are supported by the euler equations problems linked to their coupling have to be considered it is then necessary to investigate acoustic field computations in complex flows our aim in the present article is to validate the wave operator associated with linearized euler equations numerical tests deal with propagation in two dimensional sheared ducted flows results are compared with other solutions deduced from analytical developments and direct numerical simulations this study shows that the linearized euler operator may be used to account for mean effects on wave propagation in the presence of sheared ducted flows processes that are specifically considered are 1 convection effects on axial disturbances 2 refraction effects on oblique wave generation and 3 source radiation effects on propagation in sheared flows

an efficient method for sound transmission in non uniform circular ducts an efficient method is presented in this paper for predicting the reflection and transmission coefficients of acoustic waves in ducts at the location of a continuous variation in cross sectional area conventional numerical methods yield high dimensionality in the resulting numerical problem due to segmentation of the non uniform section into a number of subsections this paper shows that an ingenious application of spherical coordinates according to the geometry of the non uniform section enables us to determine analytically the system of characteristic functions for various profiles of the non uniform portion this system of characteristic functions can be used as a complete set to express the solution over the non uniform region so that the numerical problem to be solved is of a much lower dimension than that yielded by conventional numerical methods a technique to render the characteristic functions independent of the frequency is also explained to keep the computation time short the present method is applicable to non plane wave modes of propagation by virtue of the use of standard three dimensional curvilinear co ordinates

convergence analysis for a finite element approximation of a steady model for electrorheological fluids in this paper we study the finite element approximation of systems of p cdot p stokes type where p cdot p is a non constant given function of the space variables we derive in some cases optimal error estimates for finite element approximation of the velocity and of the pressure in a suitable functional setting

finite element method to study harmonic aeroacoustics problems the analysis of aeroacoustics propagation is required to solve many practical problems as an alternative to euler s linearized equations an equation was established by galbrun in 1931 it assumes the flow verifies euler s equations and the perturbation is small and adiabatic it is a linear second order vectorial equation based on the displacement galbrun s equation derives from a lagrangian density and provides conservative expressions of the aeroacoustics intensity and energy density a caa method dealing with the numerical resolution of galbrun s equation using the finite element method fem is presented the exact solution for the propagation of acoustic modes inside an axisymmetric straight lined duct in the presence of a shear flow is known and compared with the fem solution comparisons are found to be in good agreement and validate a first step in the development of a caa method based on the fem and galbrun s equation the fem is then applied to an axisymmetric duct including a varying cross

on a coefficient conjecture of brannan soit 1 xz 1 z 1 n 1 a n x z n ou x 1 et 0 1 alors a 5 x a 5 1 et l egalite n est vraie que si et seulement si x 1

theoretical investigation of hydrodynamic surface mode in a lined duct with sheared flow and comparison with experiment abstract a spectral collocation method is used to solve the linearized euler equations in a duct with shear flow and lined walls in order to identify a possible hydrodynamic instability observed in published experiments this method is first checked against a reference test case in a cylindrical duct then a theoretical test case in a plane bi dimensional duct with no slip flow is considered the briggs bers stability criterion is proved to be valid and it shows that the hydrodynamic instability does correspond to a right running amplified wave eigenmode analyses are then performed on the experimental configuration an unstable hydrodynamic surface mode is found with an axial wavenumber and velocity eigenfunctions which are in good agreement with the experimental ones acoustic energy calculations show that the hydrodynamic instability paradoxically carries noticeable levels of acoustic energy in the upstream direction finally the influence of mach number and frequency is investigated

an integral formulation for wave propagation on weakly non uniform potential flows abstract an integral formulation for acoustic radiation in moving flows is presented it is based on a potential formulation for acoustic radiation on weakly non uniform subsonic mean flows this work is motivated by the absence of suitable kernels for wave propagation on non uniform flow the integral solution is formulated using a green s function obtained by combining the taylor and lorentz transformations although most conventional approaches based on either transform solve the helmholtz problem in a transformed domain the current green s function and associated integral equation are derived in the physical space a dimensional error analysis is developed to identify the limitations of the current formulation numerical applications are performed to assess the accuracy of the integral solution it is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field and as a means of solving scattering problems by rigid surfaces in non uniform flows the results show that the error associated with the physical model deteriorates with increasing frequency and mean flow mach number however the error is generated only in the domain where mean flow non uniformities are significant and is constant in regions where the flow is uniform

on linear and non linear wave equations for the acoustics of high speed potential flows the wave equation is derived for the acoustic potential in the following cases a linear non linear sound waves respectively of small large amplitude b medium at rest or steady potential flow the latter either of low mach number or high speed c three dimensional propagation in free space or quasi one dimensional acoustics of ducts of varying cross section thus there are 2 3 2 12 cases for which 34 distinct forms of the wave equations are derived table 1 of these 16 forms of the wave equation in 10 cases appear explicitly in the references given the wave equations are derived from a variational principle for linear sound part 1 and checked by elimination among the equations of potential unsteady flow for non linear acoustics part ii it is shown that the non linear wave equations partly new can be written in a form similar to the linear acoustics ones mostly known by taking into account the self convection of sound by sound this implies replacing the linear local and material derivatives byself convected and non linear extensions of these table 2 which also affect the sound speed

wave propagation and attenuation in herschel venturi tubes wave propagation and attenuation in a classical flow metering device the herschel venturi tube is investigated analytically and experimentally the analytical results are shown to compare well with the experimental observations for anechoically terminated herschel venturi tubes in the absence of flow the taylor series approximations to the governing differential equations and the stepwise expansion and contraction method are shown to be identical the effect of mean flow on the wave attenuation performance of herschel venturi tubes is also studied in terms of a solution obtained by the runge kutta method and the applicability of the stepwise expansion and contraction method is discussed with the mean flow through the duct

on the c1 γ ω w2 2 ω regularity for a class of electro rheological fluids abstract we are concerned with a system of nonlinear partial differential equations with p x structure 1 p p x p 0 and no slip boundary conditions we prove the existence and uniqueness of a c 1 w 2 2 solution corresponding to small data without further restrictions on the bounds p p 0 in particular this result is applicable to the steady motion of shear dependent electro rheological fluids

stability and accuracy of finite element methods for flow acoustics i general theory and application to one dimensional propagation the dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar helmholtz equation and on the galbrun equation are examined the current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions a general two dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh and results are presented for the particular case of one dimensional acoustic propagation in which the wave direction is aligned with the mean flow the magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes quadratic helmholtz elements in particular are shown to be much less effective for downstream as opposed to upstream propagation even when the effect of wave shortening or elongation due to the mean flow is taken into account these trends are also observed in solutions obtained for simple test problems on finite meshes a similar analysis of two dimensional propagation is presented in an accompanying article

extension of the eulerian lagrangian description to nonlinear perturbations in an arbitrary inviscid flow abstract a new theoretical formulation is proposed to describe the propagation of large amplitude perturbations in an arbitrary flow of inviscid fluid this formulation relies on the mixed eulerian lagrangian description for which exact nonlinear equations are derived using properties of hamiltonian formalism generalized expressions are found for the acoustic pseudo energy density and flux they verify a conservative energy balance all these expressions only depend on the reference flow variables and the displacement vector of the fluid particles due to the perturbation when the small perturbation assumption is added the linear expressions from the literature are retrieved

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

on applications of hypergeometric functions abstract this is a survey article on the author s involvement over the years with hypergeometric functions we discuss our counter example to one of m robertson s conjectures our results on the omitted values problems brannan s conjecture on the coefficients of a certain power series generalizations of ramanujan s asymptotic formulas for complete elliptic integrals and muir s 1883 approximation to the arc length of an ellipse involving an inequality for some 3f2 s

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

the element free galerkin method for the nonlinear p laplacian equation abstract the element free galerkin efg method is developed in this paper for solving the nonlinear p laplacian equation the moving least squares approximation is used to generate meshless shape functions the penalty approach is adopted to enforce the dirichlet boundary condition the galerkin weak form is employed to obtain the system of discrete equations and two iterative procedures are developed to deal with the strong nonlinearity then the computational formulas of the efg method for the p laplacian equation are established numerical results are finally given to verify the convergence and high computational precision of the method

on the positivity of certain trigonometric sums and their applications in this paper we find conditions on the coefficients b k k 1 n such that the corresponding trigonometric cosine and sine sums given respectively by k 1nb email protected 0 and k 1nb email protected 0 for all email protected n are positive using these results we find that the functions f that are in the class of analytic functions a are starlike of certain order in the unit disc d by means of conditions on the taylor coefficients of f as an application we also find conditions such that the cesaro means of order b of f z are close to convex and starlike in d

acoustic transmission in non uniform ducts with mean flow part i the method of weighted residuals 3n this and a companion paper the problem of transmission of sound through non uniform ducts carrying a high speed subsonic compressible flow is approached using the method of weighted residuals mwr in the form of a modified galerkin method and the finite element method fem the intent of the investigation is to carry out a careful evaluation of these methods in this computationally difficult problem to this end both mwr and fem have been limited to in core computer implementations to generate useful results with relatively modest computational requirements this paper part i details the mwr formulation and presents numerical results establishing the degree of accuracy of mwr as compared to exact eigenvalue calculations and approximate one dimensional transmission calculations the comparison of mwr and fem results is carried out in the companion paper part ii

finite element approximation of the p laplacian in this paper we consider the continuous piecewise linear finite el ement approximation of the following problem given p 1 oo and g find u such that v vu 2vu f iniicr2 u g on a the finite element approximation is defined over i2 a union of regular tri angles yielding a polygonal approximation to q for sufficiently regular so lutions u achievable for a subclass of data g and i2 we prove optimal error bounds for this approximation in the norm wlq q 1 q p for p 2 under the additional assumption that qh c 2 numerical results demonstrating these bounds are also presented

on the acoustic modes in a duct containing a parabolic shear flow abstract the exact solution of the acoustic wave equation in an unidirectional shear flow with a parabolic velocity profile is obtained representing sound propagation in a plane parallel walled duct with two boundary layers over rigid or impedance walls it is shown that there are four cases depending on the critical level s where the doppler shifted frequency vanishes i for propagation upstream the critical levels are outside the duct case ii ii for propagation downstream there may be two case iv one case i or no case iii critical level inside the duct the acoustic wave equation is transformed in each of the four cases to particular forms of the extended hypergeometric equation which has power series solutions some involving logarithmic singularities in the cases where critical levels occur at real or imaginary distance matching of two or three pairs of solutions valid over regions each overlapping the next is needed the particular case of the parabolic velocity profile is used to address general properties of sound in unidirectional shear flows for example it is shown that for ducted shear flows there exist a pair of even and odd eigenfunctions in the absence of critical levels it is also proved in more than one instance that there is no single set of eigenvalues and eigenfunctions valid across one or two shear layers this leads to the general conjecture considering the acoustics of shear flows in ducts that critical levels separate regions with distinct sets of eigenvalues and eigenfunctions

acoustic transmission in non uniform ducts with mean flow part ii the finite element method this second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non uniform duct carrying a high speed subsonic compressible flow a finite element scheme based on both the galerkin method and the residual least squares method and with eight noded isoparametric elements is described multi modal propagation is investigated by coupling of the solution in the duct non uniform section to modal expansions in uniform sections the accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified galerkin method as introduced in part i of this pair of papers the results of calculations show that modal interactions particularly in transmitted modes become increasingly important with increasing duct flow mach number power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking

interior penalty discontinuous galerkin fem for the p x laplacian in this paper we construct an interior penalty discontinuous galerkin method to approximate the minimizer of a variational problem related to the p x laplacian the function p omega to p 1 p 2 is log holder continuous and 1 p 1 leq p 2 infty we prove that the minimizers of the discrete functional converge to the solution we also make some numerical experiments in dimension one to compare this method with the conforming galerkin method in the case where p 1 is close to one this example is motivated by its applications to image processing

numerical experiments on acoustic reciprocity in compressible potential flows in ducts a reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with acoustically hard walls or with acoustically absorbing walls has been given in a companion publication it was found that for a source at a specified end of the duct suitably scaled reflection matrices in direct and reverse flow have a reciprocal relationship scaled transmission matrices obtained for direct flow and reversed flow with simultaneous switching of source location from one end to the other also have a reciprocal relationship a reverse flow theorem for the equivalent one dimensional propagation model which is a good approximation to the three dimensional model at low frequencies was also obtained in this case using reciprocity and acoustic power conservation arguments it is additionally found that the acoustic power transmission coefficient is the same for a source at either end of the duct for a given flow direction this result leads to an invariance theorem which relates acoustic power propagated due to sources of equal pressure amplitude at the two ends of the duct a numerical verification of these reciprocal relationships is given here for propagation in axially symmetric circular and annular ducts with multi modal propagation and at low frequencies when a one dimensional model is appropriate

comparison of a finite element model with a multiple scales solution for sound propagation in varying ducts with swirling flows a multiple scales ms solution is proposed to study sound propagation in slowly varying ducts with mean swirling flows instead of the standard linearized euler equations the ms method is applied to the so called galbrun s equation this equation is based on an eulerian lagrangian description and corresponds to a wave equation written only in terms of the lagrangian perturbation of the displacement this yields simpler differential equations to solve for the ms model as well as simpler boundary conditions in this paper galbrun s equation is also solved by a mixed pressure displacement finite element method fem the proposed fem model has already been tested in authors previous papers this model is quite general and is extended here to arbitrary mean flows including compressibility and swirling flow effects some ms and fem solutions are then compared in order to validate both models

displacement pressure based mixed finite element formulations for acoustic fluid structure interaction problems summary we present reliable finite element discretizations based on displacement pressure interpolations for the analysis of acoustic fluid structure interaction problems the finite element interpolations are selected using the inf sup condition and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation we show that with our analysis procedure no spurious non zero frequencies are encountered as heretofore calculated with other displacement based discretizations 1997 by john wiley sons ltd

oscillation constants for euler type differential equations involving the p t laplacian abstract this paper deals with the oscillation problem for the nonlinear differential equation x p t 2 x t p t x p t 2 x 0 where is a positive parameter and p t 1 is a nondecreasing and smooth function some non oscillation criteria are given for this equation the obtained results are the best possible in a certain sense we use the riccati technique and the function sequence technique moreover we propose a conjecture concerning the oscillation problem for this equation in the case when p t tends to infinity as t

the time dependent finite difference procedure for propagation of sound in a non uniform lined duct a comparison with experiments abstract a time dependent finite difference procedure is developed for the calculation of acoustic fields which incorporate finite impedance and rigid wall boundaries a numerical mapping technique is evoked to transform the solution domain into a rectangular geometry and the procedure is used to solve for frequencies where cross modes can propagate in the straight sections of duct numerical results are corroborated with experiments

a mixed finite element method for acoustic wave propagation in moving fluids based on an eulerian lagrangian description a nonstandard wave equation established by galbrun in 1931 is used to study sound propagation in nonuniform flows galbrun s equation describes exactly the same physical phenomenon as the linearized euler s equations lee but is derived from an eulerian lagrangian description and written only in term of the lagrangian perturbation of the displacement this equation has interesting properties and may be a good alternative to the lee only acoustic displacement is involved even in nonhomentropic cases it provides exact expressions of acoustic intensity and energy and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly in this paper galbrun s equation is solved using a finite element method in the axisymmetric case with standard finite elements the direct displacement based variational formulation gives some corrupted results instead a mixed finite element satisfying the inf sup condition is proposed to avoid this problem a first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow obtained from pridmore brown s equation a second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple scale method which is an adaptation for the incompressible case of rienstra s recent work

on longitudinal acoustic propagation in convergent and divergent nozzle flows abstract the longitudinal propagation of sound in quasi one dimensional low mach number nozzle flow is considered in section 1 the solution in the ray approximation section 2 1 is used to transform the wave equation into a schrodinger form which is studied for the family of power law ducts including as a particular case the conical nozzle it is shown that the coincidence of flow sources sinks with sound sources can lead to appearance of essential singularities section 2 2 which can be removed by using a riccati transformation section 2 4 the exact solutions of the acoustic equations for the parabolic figure 1 and hyperbolic figure 2 nozzles are obtained in terms of bessel functions section 2 3 respectively of complex order and argument the general formulas together with limiting forms in the compactness ray and asymptotic approximations section 3 1 are used to establish properties of the acoustic velocity and pressure section 3 2 kinetic and compression energies and energy flux and wave action section 3 3 for example it is shown that the equipartition of energies for moderate variations in cross section gives way table 2 to a predominance of kinetic compression energies respectively near blockages openings the effects of non uniform mean flow table 1 are discussed by comparing horns with nozzles section 3 4 e g it is shown that the duality principle in three alternative forms does not extend from horn to nozzles and the acoustic equations have no elementary solutions for the latter in contrast with the former

phase shift and attenuation characteristics of acoustic waves in a flowing gas confined by cylindrical walls abstract wave propagation in flowing ideal gases confined by cylindrical waveguides is described in the low frequency range using an iterative frobenius series expansion method the primary concern is to present a mathematical model enabling any radial dependent flow profile to be analyzed in contrast to previous analytical results the present model is applicable in the general case where cubic and higher order terms in the axial acoustic velocity become important and to examine the influence of a non vanishing radial velocity term as a numerical test case it is found that a gas flow velocity w r for simplifying reasons assumed to be a linear combination of a flat flow profile and a parabolic flow profile corresponding to a mean flow equal to w is well approximated by a flat flow profile of the same mean flow value w at low shear wavenumbers and at higher shear wavenumbers calculations were done for shear wavenumbers up to 8 in actual fact the error introduced by making this mean flow approximation is smaller than the error introduced by neglecting the radial velocity term

finite element computation of three dimensional elastoacoustic vibrations abstract in this paper the interior elastoacoustic problem in a 3d domain is solved displacement variables are used for both the fluid and the solid to avoid the typical spurious modes of this formulation a non standard discretization is used consisting of classical linear tetrahedral finite element for the solid and raviart thomas elements of lowest order for the fluid a new unknown is introduced on the interface between solid and fluid to impose the transmission conditions

a comparison of measured and computed sound pressure levels in a non uniform acoustically lined duct a comparison of measured and numerically calculated acoustical fields is presented for a non uniform lined duct in the absence of appreciable mean flow the frequency range investigated includes the cut on frequencies of several transverse modes in certain portions of the duct measured pressure fields are compared to those predicted by one and two dimensional numerical models the validity of the one dimensional model is confirmed for frequencies below cut on of the first transverse mode for higher frequencies the one dimensional model is clearly unsatisfactory as might be expected the two dimensional model gives reasonable results for frequencies below and above cut on of the transverse modes although it indicates a very strong sensitivity of acoustical fields to small variations in local wall impedance data

a boundary element scheme for evaluation of four pole parameters of ducts and mufflers with low mach number non uniform flow a boundary element scheme is proposed for evaluation of the four pole parameters of ducts and mufflers in the presence of a low mach number non uniform flow a transformation of variable is used such that the governing sound propagation equation reduces to the helmholtz equation in the transformed variable which has a known fundamental solution and is therefore amenable to bem analysis the validity of the results is confirmed by comparison with those of existing one dimensional models of the flow the boundary element scheme has been developed as it enables one to determine effectively the four pole parameters when the flow is non uniform and also high order mode behavior in ducts and mufflers of any given geometry

singular solutions of nonlinear differential equations with p t laplacian abstract this paper deals with the singular solutions of the nonlinear differential equation a t x p t 2 x b t x q t 2 x involving p t laplacian sufficient conditions are given for the existence and the nonexistence of singular solutions of the first second kind in addition we study the existence of proper solutions and the coexistence of proper solutions and singular solutions of the second kind finally some examples are given to illustrate our results

numerical study of acoustic modes in ducted shear flow the propagation of small amplitude modes in an inviscid but sheared mean flow inside a duct is studied numerically for isentropic flow in a circula r duct with zero swirl and constant mean flow density the pressure modes are described in te rms of the eigenvalue problem for the pridmore brownequation since for sufficiently high helmholtz and wavenum bers which are of great interest for the applications the fi eld equation is inherently stiff special care is taken to insure the stability of the numerica l algorithm designed to tackle this problem the accuracy of the method is checked against the well known analytical solution for the uniform flow the numerical method is shown t o be consistent with the analytical predictions at least for the helmholtz numbers up to 100 and the circumferential wavenumber as large as 50 typical mach numbers being up to 0 65 in order to gain further insight into the possible structure of the modal solutions and to get an independent verification of the robustness of the nu merical scheme comparison to the asymptotic solution of the problem based on the wkb method is performed the asymptotic solution is also used as a benchmark for computations with high helmholtz numbers where numerical solutions of other authors are not available the bulk of the analysis concentrates on the influence of the w all lining the proposed numerical procedure is adapted in order to include ingard myers boundary conditions in parallel with this the wkb solution is used to check the numerical predictions of the typical behaviour of the axial wavenumber in the complex plane when the wall impedance varies in the complex plane numerical analysis of the problem with zero mean flow at the wa ll and acoustic lining shows that the use of ingard myers condition in combination with an appropriate slipstream approximation instead of the actual no slip mean flow profile gives valid results in the limit of vanishing boundary layer thickness although the boundary layer must be very thin in some cases

plane wave analysis of conical and exponential pipes with incompressible mean flow the general equation for one dimensional wave propagation at low flow mach numbers m less than or equals slant0 2 is derived and is solved analytically for conical and exponential shapes the transfer matrices are derived and shown to be self consistent comparison is also made with the relevant data available in the literature the transmission loss behaviour of conical and exponential pipes and mufflers involving these shapes are studied analytical expressions of the same are given for the case of a stationary medium the mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers of similar dimensions at higher frequencies from the point of view of noise abatement as was observed earlier experimentally

a multigrid algorithm for the p laplacian we introduce a full approximation storage fas multigrid algorithm to find the finite element solution for a class of nonlinear monotone elliptic problems since the solution of the problem is equivalent to minimize a strictly convex functional we use a polak ribiere conjugate gradient method as the nonlinear smoother in our algorithm the advantage in so doing is that we do not have to calculate derivatives of operators we prove local convergence of our algorithm and illustrate its performance by solving benchmark problems

a low mach number model for time harmonic acoustics in arbitrary flows this paper concerns the finite element simulation of the diffraction of a time harmonic acoustic wave in the presence of an arbitrary mean flow considering the equation for the perturbation of displacement due to galbrun we derive a low mach number formulation of the problem which is proved to be of fredholm type and is therefore well suited for discretization by classical lagrange finite elements numerical experiments are done in the case of a potential flow for which an exact approach is available and a good agreement is observed

on sound propagation in a nozzle with non uniform swirl abstract the propagation of sound is considered in an axisymmetric mean flow with uniform axial velocity and non uniform swirl with angular velocity proportional to the radius two simplifications are made i that the maximum tangential velocity of the mean flow is small compared to the sound speed ii that the doppler shift due to rotation is much smaller than the wave frequency including doppler shift by the uniform axial flow divided by the maximum angular velocity of swirl it is shown that these conditions are not too restrictive for practical swirling flows in exhaust nozzles and that they allow the solution of the wave equation in terms of confluent hypergeometric functions instead of bessel functions in the case of rigid body rotation this type of radial dependence allows for propagating waves with decaying amplitude in the case of slow swirl and for evanescent and unstable modes in the case of fast swirl the borderline between slow and fast swirl is given by a rotation parameter related to the second approximation ii above and defined as the ratio of the doppler shift due to rotation to the product of the frequency by the radial compactness

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

finite element approximation of some degenerate monotone quasilinear elliptic systems in this paper we examine the continuous piecewise linear finite element approximation of the following system given bf f equiv f j and bf g equiv g j find bf u equiv u j j 1 to r with r 1 or 2 such that nabla cdot k z nabla bf u z nabla bf u z bf f z quad z in omega subset r 2 quad bf u partial omega bf g partial omega where nabla bf u equiv partial u j partial z i 1 leq i leq 2 1 leq j leq r and k is a given matrix on omega times r 2 times r we characterize a class of matrices k for which we prove error bounds for this discretization for sufficiently regular solutions bf u achievable at least for some model problems our bounds improve on existing results in the literature it is shown that for a notable subclass of k for which only suboptimal error bounds have been previously derived the piecewise linear finite element approximation of this problem will converge

finite element approximation of the p cdot laplacian we study a priori estimates for the p cdot laplace dirichlet problem mathrm div vert nabla mathbf v vert p cdot 2 nabla mathbf v mathbf f we show that the gradients of the finite element approximation with zero boundary data converge with rate o h alpha if the exponent p is alpha holder continuous the error of the gradients is measured in the so called quasi norm i e we measure the l 2 error of vert nabla mathbf v vert frac p 2 2 nabla mathbf v

precise estimates for differences of the gaussian hypergeometric function abstract by showing certain combinations of the gaussian hypergeometric functions f a b a b 1 x c and f a b a b 1 x d to be monotone on 0 1 for given a b c d 0 a b and c d the authors study the problem of comparing these two functions they find sup 0 a f a b a b 1 x c f a b a b 1 x d for x 0 1 thus solving an open problem and a recent conjecture

inequalities for compound mean iterations with logarithmic asymptotes abstract we consider the compound means arising as limits from the arithmetic geometric mean iteration and related iterations each of these iterations possesses a logarithmic asymptote we show that these limit means satisfy very precise inequalities these can be deduced in a quite uniform fashion from a comparison lemma for compound means

aerodynamics and interaction noise of streamlined bodies in nonuniform flows abstract the unsteady aerodynamics and interaction noise of streamlined bodies are modeled in terms of the euler equations linearized about a nonuniform flow the validity of the inviscid approach is supported by recent les simulations of an airfoil in a gust indicating that for not too small impinging excitations the interaction process is dominated by inertia forces results in the present paper are focused on the aerodynamics and interaction noise of a turbofan modeled as an annular cascade the model accounts for the inflow fan duct coupling and the high frequency of the interaction process two high order numerical algorithms are developed with body fitted coordinate system one algorithm uses a primitive variable formulation the other uses an efficient velocity splitting algorithm and is suitable for broadband computations analytical and numerical analysis of disturbances in rotational flows is developed and exact inflow outflow boundary conditions are derived yielding directly the radiated acoustics the upstream disturbances evolve in rotational flows and as a result the aerodynamic aeroacoustic response of the annular cascade depends on the initial conditions location computational results show that the three dimensional geometry of the annular cascade the mean flow swirl and the blade geometry have strong influence on the blade sectional lift and the radiated sound these results also show the inadequacy of using the popular linear cascade model particularly for realistic fan geometry and inflow conditions

the influence of a liquid flow on sound fields confined by conical walls abstract sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co ordinate r only a general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the green function method in the second part of this paper flow measurement properties are discussed the designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide instead the so called pseudo guide wave number and pseudo phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively it is shown that changes due to a background flow in pseudo guide wave number pseudo phase speed and zero point crossing times all exhibit an oscillatory behavior as a function of the r co ordinate this is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter the oscillatory behavior in the changes in zero point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is in principle that a one to one correspondence between measured output changes in zero point crossing times and actual flow determined by v 0 at a specific receiver location exists it is shown that this requirement is fulfilled as changes in zero point crossing times depend linearly on the flow coefficient v 0 at a given r co ordinate there are however certain discrete r co ordinate values where this is not the case namely those where changes in zero point crossing times become zero for any value of v 0 in other words if the receiver is positioned near r co ordinates where zero point crossing times are at a maximum or a minimum for a given value of v 0 the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero point crossing times induced by a background flow

convergence analysis for incompressible generalized newtonian fluid flows with nonstandard anisotropic growth conditions we study equations to describe incompressible generalized newtonian fluids where the extra stress tensor satisfies a nonstandard anisotropic asymptotic growth condition an implicit finite element discretization and a simple fully practical fixed point scheme with proper thresholding criterion are proposed and convergence toward weak solutions of the limiting problem is shown computational experiments are included which motivate nontrivial fluid flow behavior

inequalities for zero balanced hypergeometric functions the authors study certain monotoneity and convexity properties of the gaussian hypergeometric function and those of the euler gamma function

quasi norm error bounds for the finite element approximation of a non newtonian flow we consider the finite element approximation of a non newtonian flow where the viscosity obeys a general law including the carreau or power law for sufficiently regular solutions we prove energy type error bounds for the velocity and pressure these bounds improve on existing results in the literature a key step in the analysis is to prove abstract error bounds initially in a quasi norm which naturally arises in degenerate problems of this type

a reverse flow theorem and acoustic reciprocity in compressible potential flows in ducts a reverse flow theorem for acoustic propagation in compressible potential flow has been obtained directly from the field equations without recourse to energy conservation arguments a reciprocity theorem for the scattering matrix for the propagation of acoustic modes in a duct with either acoustically rigid walls or acoustically absorbing walls follows it is found that for a source at a specific end of the duct suitably scaled reflection matrices in direct and reverse flow have a reciprocal relationship scaled transmission matrices obtained for direct flow and reversed flow with simultaneous switching of source location from one end to the other also have a reciprocal relationship a related reverse flow theorem specialized to one dimensional acoustic propagation has also been obtained reciprocity relationships for the scattering coefficients for propagation are derived and are found to be similar though much simpler than in the case of multi mode propagation in one dimensional flow reciprocal relations and power conservation arguments are used to show that scaled power reflection and transmission coefficients are invariant to flow reversal and switching of source location from one end of the duct to the other numerical verification of the reciprocal relationships is given in a companion paper

acoustic vorticity waves in swirling flows the propagation of small disturbances in an annular duct with a mean vortical swirling flow is studied the disturbance velocity is split into a nearly convected part and a nearly sonic part obeying weakly coupled equations a normal mode analysis shows that the eigenvalues are segregated into a finite number of propagating pressure dominated nearly sonic waves and a cluster of infinite number of vorticity dominated nearly convected modes a generalized gust can then be identified with the vorticity dominated nearly convected eigensolutions the nearly convected eigenvalues form two branches on either side of a critical layer which corresponds to purely convected modes an asymptotic analysis is used to investigate the stability of the nearly convected eigensolutions in the vicinity of the critical layer