on the depth of the tangent cone and the growth of the hilbert function for a d dimensional cohen macaulay local ring r mn we study the depth of the associated graded ring of r with respect to an rm primary ideal i in terms of the vallabrega valla conditions and the length of it jit where j is a j minimal reduction of i and t 1 as a corollary we generalize sally s conjecture on the depth of the associated graded ring with respect to a maximal ideal to rm primary ideals we also study the growth of the hilbert function

finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a kam theory for conformally symplectic systems efficient algorithms and their validation abstract we present a kam theory for some dissipative systems geometrically these are conformally symplectic systems i e systems that transform a symplectic form into a multiple of itself for systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with a fixed n dimensional diophantine frequency by adjusting the parameters we do not assume that the system is close to integrable but we present the results in an a posteriori format our unknowns are a parameterization of the quasi periodic solution and some parameters in the system we formulate an invariance equation that expresses that the system with the parameters leaves invariant the solution given by the embedding we show that if there is a sufficiently approximate solution of the invariance equation which also satisfies some non degeneracy conditions then there is a true solution nearby the smallness assumptions above can be understood either in sobolev or in analytic norms the a posteriori format has several consequences a smooth dependence on the parameters including the singular limit of zero dissipation b estimates on the measure of parameters covered by quasi periodic solutions c convergence of perturbative expansions in dissipative analytic systems d bootstrap of regularity i e that all tori which are smooth enough are analytic if the map is analytic e a numerically efficient criterion for the breakdown of the quasi periodic solutions the proof is based on an iterative quadratically convergent method the iterative step takes advantage of some geometric identities these identities also lead to an efficient algorithm if we discretize the parameterization with n terms a modified newton step requires o n storage and o n log n operations the a posteriori theorems allow one to be confident on the numerical results even very close to breakdown the algorithm does not require that the system is close to integrable so that a continuation algorithm is guaranteed to continue the tori till the breakdown in practice only limitation being the total memory and the precision the algorithms have been implemented and run in other papers

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

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

frequency domain linearized euler model for turbomachinery noise radiation through engine exhaust a numerical model for the exhaust noise radiation problem is presented in the model it is assumed that an incoming wave is propagating through the exhaust nozzle or the fan duct and radiating outside the near field propagation is based on the solution of the linearized euler equations in the frequency domain for each wave number a linearized euler problem is solved using a finite element method on unstructured grids for arbitrarily shaped axisymmetric geometries the frequency domain approach enables the suppression of the kelvin helmholtz instability waves moreover each single calculation limited to a single frequency is well suited to the exhaust noise radiation problem in which the incoming wave can be treated as a superposition of elementary duct modes to reduce the memory requirements a continuous galerkin formulation with linear triangular and quadrangular elements is employed and the global matrix inversion is performed with a direct solver based on a parallel memory distributed multifrontal algorithm for sparse matrices the acoustic near field is then radiated in the far field using the formulation of ffowcs williams and hawkings numerical calculations for a validation test case the munt problem and two turbomachinery configurations are compared with analytical solutions and experimental data

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

use of finite element methods in frequency domain aeroacoustics the linearized euler equations are used widely in many aerodynamic noise prediction schemes the linearized euler equations also support instability waves which can obscure the acoustic solution an approach to suppress the instability waves is to solve the linearized euler equations in the frequency domain also the frequency domain approach is far less expensive compared to the time domain approach in terms of the computational time though only a single frequency can be computed at one time the application and comparison of two unstructured grid methods for the solution of aeroacoustic problems in the frequency domain are presented algorithms are developed using the discontinuous galerkin and the streamline upwind petrov galerkin finite element methods in two spatial dimensions on conforming triangular meshes using nodal polynomial basis sets unlike other existing frequency domain solvers no assumption is made regarding the nature of the mean flow the application of the two methods to a two dimensional benchmark problem involving the suppression of instability waves is presented the two methods are compared in terms of the computational cost it is concluded that the discontinuous galerkin method is prohibitively more expensive compared to the streamline upwind petrov galerkin method for aeroacoustic applications in the frequency domain using conforming meshes and nodal polynomials

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

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

quadrature free implementation of discontinuous galerkin method for hyperbolic equations a discontinuous galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions this approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent in the discontinuous galerkin method test problems include the linear and nonlinear one dimensional scalar advection of smooth initial value problems that are discretized by using unstructured grids with varying degrees of smoothness and regularity and two dimensional linear euler solutions on unstructured grids

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

reliable reduced order models for time dependent linearized euler equations development of optimal reduced order models for linearized euler equations is investigated recent methods based on proper orthogonal decomposition pod applicable for high order systems are presented and compared particular attention is paid to the link between the choice of the projection and the efficiency of the reduced model a stabilizing projection is introduced to induce a stable reduced order model at finite time even if the energy of the physical model is growing the proposed method is particularly well adapted for time dependent hyperbolic systems and intrinsically skew symmetric models this paper also provides a common methodology to reliably reduce very large nonsymmetric physical problems

a high resolution petrov galerkin method for the 1d convection diffusion reaction problem abstract we present the design of a high resolution petrov galerkin hrpg method using linear finite elements for the problem defined by the residual r t u x k 2 x 2 s f where k s 0 the structure of the method in 1d is identical to the consistent approximate upwind petrov galerkin cau pg method a c galeao e g dutra do carmo a consistent approximate upwind petrov galerkin method for the convection dominated problems comput methods appl mech engrg 68 1988 83 95 except for the definitions of the stabilization parameters such a structure may also be attained via the finite calculus fic procedure e onate derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems comput methods appl mech engrg 151 1998 233 265 e onate j miquel g hauke stabilized formulation for the advection diffusion absorption equation using finite calculus and linear finite elements comput methods appl mech engrg 195 2006 3926 3946 by an appropriate definition of the characteristic length the prefix high resolution is used here in the sense popularized by harten i e second order accuracy for smooth regular regimes and good shock capturing in nonregular regimes the design procedure embarks on the problem of circumventing the gibbs phenomenon observed in l 2 projections next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term a conjuncture of the two results is made to deal with the problem at hand that is usually plagued by gibbs global and dispersive oscillations in the numerical solution it is shown that the method indeed reproduces stabilized high resolution numerical solutions for a wide range of values of u k s and f finally some remarks are made on the extension of the hrpg method to multidimensions

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

a posteriori kam theory with optimal estimates for partially integrable systems abstract in this paper we present a posteriori kam results for existence of d dimensional isotropic invariant tori for n dof hamiltonian systems with additional n d independent first integrals in involution we carry out a covariant formulation that does not require the use of action angle variables nor symplectic reduction techniques the main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates which may cause difficulties and underperformance when quantifying the hypotheses of the kam theorem in such reduced coordinates the results include ordinary and generalized iso energetic kam theorems the approach is suitable to perform numerical computations and computer assisted proofs

finite element stabilization parameters computed from element matrices and vectors abstract we propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline upwind petrov galerkin supg and pressure stabilizing petrov galerkin pspg formulations the parameters are computed based on the element level matrices and vectors which automatically take into account the local length scales advection field and the reynolds number we describe how we compute these parameters in the context of first a time dependent advection diffusion equation and then the navier stokes equations of unsteady incompressible flows

a frequency domain linearized navier stokes equations approach to acoustic propagation in flow ducts with sharp edges acoustic wave propagation in flow ducts is commonly modeled with time domain non linear navier stokes equation methodologies to reduce computational effort investigations of a linearized approach in frequency domain are carried out calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present results of transmission and reflections at the orifice are presented on a two port scattering matrix form and are compared to measurements with good agreement the wave propagation is modeled with a frequency domain linearized navier stokes equation methodology this methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field i e when whistling does not occur

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

approaches for adjoint based a posteriori analysis of stabilized finite element methods this study derives a posteriori error estimates for linear functionals of the solution of systems of partial differential equations discretized using stabilized continuous galerkin methods we investigate a convection diffusion equation the stokes equations and incompressible low reynolds number flow governed by the navier stokes equations we consider three well known stabilization methods and show that only one of the three is adjoint consistent and that even this case is contingent upon a proper treatment of the adjoint data a standard approach for a posteriori error analysis uses the adjoint of the stabilized formulation which inherits the difficulties induced by the lack of adjoint consistency we introduce and analyze two alternative approaches the first is based on the addition of stabilization terms to the adjoint data while the second is based on a stabilized formulation of the formal adjoint problem we show that any of the three approaches can be used to derive a fully computable error r

multiscale stabilized solutions to one dimensional systems of conservation laws abstract we present a variational multiscale formulation for the numerical solution of one dimensional systems of conservation laws the key idea of the proposed formulation originally presented by hughes comput methods appl mech engrg 127 1995 387 401 is a multiple scale decomposition into resolved grid scales and unresolved subgrid scales incorporating the effect of the subgrid scales onto the coarse scale problem results in a finite element method with enhanced stability properties capable of accurately representing the sharp features of the solution in the formulation developed herein the multiscale split is invoked prior to any linearization of the equations special attention is given to the choice of the matrix of stabilizing coefficients and the discontinuity capturing diffusion the methodology is applied to the one dimensional simulation of three phase flow in porous media and the shallow water equations these numerical simulations clearly show the potential and applicability of the formulation for solving highly nonlinear nearly hyperbolic systems on very coarse grids application of the numerical formulation to multidimensional problems is presented in a forthcoming paper

on the last hilbert samuel coefficient of isolated singularities abstract j lipman proved that the last hilbert samuel coefficient of normal ideals of a 2 dimensional complete local ring r are bounded by the geometric genus of x spec r in this paper we extend this result to ideals i of a d dimensional cohen macaulay local ring r such that the associated graded ring of r with respect to i n is cohen macaulay for n 0 we study the ideals such that their last hilbert samuel coefficients equal the geometric genus

a finite element method for fluid structure interaction with surface waves using a finite calculus formulation abstract a stabilized semi implicit fractional step finite element method fem for solving coupled fluid structure interaction problems involving free surface waves is presented the stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus fic procedure a mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described examples of the efficiency of the stabilized semi implicit algorithm for the analysis of fluid structure interaction problems in totally or partially submerged bodies is presented

an algebraic subgrid scale finite element method for the convected helmholtz equation in two dimensions with applications in aeroacoustics abstract an algebraic subgrid scale finite element method formally equivalent to the galerkin least squares method is presented to improve the accuracy of the galerkin finite element solution to the two dimensional convected helmholtz equation a stabilizing term has been added to the discrete weak formulation containing a stabilization parameter whose value turns to be the key for the good performance of the method an appropriate value for this parameter has been obtained by means of a dispersion analysis as an application we have considered the case of aerodynamic sound radiated by incompressible flow past a two dimensional cylinder following lighthill s acoustic analogy we have used the time fourier transform of the double divergence of the reynolds stress tensor as a source term for the helmholtz and convected helmholtz equations and showed the benefits of using the subgrid scale stabilization

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

a stabilized finite element method for the two field and three field stokes eigenvalue problems in this paper the stabilized finite element approximation of the stokes eigenvalue problems is considered for both the two field displacement pressure and the three field stress displacement pressure formulations the method presented is based on a subgrid scale concept and depends on the approximation of the unresolvable scales of the continuous solution in general subgrid scale techniques consist in the addition of a residual based term to the basic galerkin formulation the application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient as a distinguished feature of the present study we take the space of the unresolved subscales orthogonal to the finite element space which promises a remedy to the above mentioned complication in essence we put forward that only if the orthogonal projection is used the residual is simplified and the use of term by term stabilization is allowed thus we do not need to put the whole residual in the formulation and the linear eigenproblem form is recovered properly we prove that the method applied is convergent and present the error estimates for the eigenvalues and the eigenfunctions we report several numerical tests in order to illustrate that the theoretical results are validated

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

accurate strategies for small divisor problems many interesting problems in mechanics are close to systems that can be solved exactly in such systems it is natural to consider perturbative expansions about the known system frequently it is possible to compute all of the terms in the expansion recursively which can lead to expressions involving denominators that become arbitrarily small

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

construction of analytic kam surfaces and effective stability bounds a class of analytic possibly time dependent hamiltonian systems withd degrees of freedom and the corresponding class of area preserving twist diffeomorphisms of the plane are considered implementing a recent scheme due to moser salamon and zehnder we provide a method that allows us to construct explicitly kam surfaces and hence to give lower bounds on their breakdown thresholds we then apply this method to the hamiltonianh y2 2 e cosx cos x t and to the map y x y e sinx x y e sinx obtaining with the aid of computer assisted estimations explicit approximations within an error of 10 5 of the golden mean kam surfaces for complex values of e with e less or equal than respectively 0 015 and 0 65 the experimental numerical values at which such surfaces are expected to disappear are about respectively 0 027 and 0 97 a possible connection between break down thresholds and singularities in the complex e plane is pointed out

on finite element methods for 3d time dependent convection diffusion reaction equations with small diffusion the paper studies finite element methods for the simulation of time dependent convection diffusion reaction equations with small diffusion the supg method a sold method and two types of fem fct methods the methods are assessed in particular with respect to the size of the spurious oscillations in the computed solutions at a 3d example with nonhomogeneous dirichlet boundary conditions and homogeneous neumann boundary conditions

space time finite element computation of compressible flows involving moving boundaries and interfaces abstract the deformable spatial domain stabilized space time dsd sst formulation introduced by tezduyar et al is applied to computation of viscous compressible flows involving moving boundaries and interfaces the stabilization technique employed is a streamline upwind petrov galerkin supg method with a modified supg stabilization matrix the stabilized finite element formulation of the governing equations is written over the space time domain of the problem and therefore the deformation of the spatial domain with respect to time is taken into account automatically the frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations the implicit equation systems arising from the space time finite element discretizations are solved iteratively it is demonstrated that the combination of the supg stabilization and the space time approach gives the capability of handling complicated compressible flow problems including those with moving surfaces and shock boundary layer interactions

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

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

accounting for convective effects in zero mach number thermoacoustic models this paper presents a methodology to account for some mean flow effects on thermo acoustic instabilities when using the zero mach number assumption it is shown that when a computational domain is represented under the m 0 assumption a nonzero mach number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer not computed flow domain a model that accounts for the coupling between acoustic and entropy waves is presented it relies on a delayed entropy coupled boundary condition decbc for the helmholtz equation satisfied by the acoustic pressure the model proves able to capture low frequency entropic modes even without mean flow terms in the fluctuating pressure equation

approximation of the thermally coupled mhd problem using a stabilized finite element method a numerical formulation to solve the mhd problem with thermal coupling is presented in full detail the distinctive feature of the method is the design of the stabilization terms which serve several purposes first convective dominated flows in the navier stokes and the heat equation can be dealt with second there is no restriction in the choice of the interpolation spaces of all the variables and finally flows highly coupled with the magnetic field can be accounted for different aspects related to the design of the final fully discrete and linearized algorithm are also discussed

on the numerical treatment of a small divisor problem quasiperiodic solutions of perturbed integrable hamiltonian equations such as weakly coupled harmonic oscillators can be found by constructing an appropriate coordinate transformation which leads to a small divisor problem however the numerical difficulties are not merely caused by the small divisors but rather by the appearence of ghost solutions which appear in any reasonable discretization of the problem our numerical treatment based on a newton type iteration guarantees an approximation of the relevant solution of the nonlinear problem numerical solutions are found up to a critical value of the coupling constant which is much larger than the coupling constants allowed by the existence theory available so far

a fast high resolution algorithm for linear convection problems particle transport method the paper is devoted to a novel explicit technique the particle transport method ptm for solving linear convection problems while being a lagrangian characteristic based method ptm has the advantage of eulerian methods to represent the solution on a fixed mesh the proposed approach belongs to the class of monotone high resolution numerical schemes possesses the property of unconditional stability and works with structured and unstructured meshes it is also demonstrated that the method has a linear computational complexity the performance of the presented algorithm is tested on one and two dimensional benchmark problems the numerical results confirm that the method has the 2nd order spatial accuracy and can be significantly faster than the grid based methods of the same order copyright 2006 john wiley sons ltd

breakup of invariant tori for the four dimensional semi standard map abstract we compute the domain of existence of two dimensional invariant tori with fixed frequency vectors for a four dimensional complex symplectic map the map is a generalization of the semi standard map studied by greene and percival it has three parameters a 1 and a 2 representing the strength of the kicks in each degree of freedom and the coupling the domain of existence of a torus in a 1 a 2 is shown to be complete and log convex for fixed k a 1 a 2 explicit bounds on the domain for fixed k are obtained numerical results show that quadratic irrationals can be more robust than the cubic irrational the spiral mean

an exhaustive criterion for the non existence of invariant circles for area preserving twist maps we present a necessary and sufficient condition for the non existence of rotational invariant circles for area preserving twist maps of the cyclinder or annulus based on the cone crossing and killends criteria of mackay and percival 1985 given a number of technical restrictions on the implementation of these criteria this condition leads to a proof of mackay and percival s finite computation conjecture

accurate fic fem formulation for the multidimensional steady state advection diffusion absorption equation abstract in this paper we present an accurate stabilized fic fem formulation for the multidimensional steady state advection diffusion absorption equation the stabilized formulation is based on the galerkin fem solution of the governing differential equations derived via the finite increment calculus fic method using two stabilization parameters the value of the two stabilization parameters ensuring an accurate nodal fem solution using uniform meshes of linear elements is obtained from the optimal values for the 1d problem the accuracy of the new fic fem formulation is demonstrated in the solution of 2d steady state advection diffusion absorption problems for a range of physical parameters and boundary conditions

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

time accurate consistently stabilized mesh free methods for convection dominated problems this is the pre peer reviewed version of the following article huerta a fernandez s time accurate consistently stabilized mesh free methods for convection dominated problems international journal for numerical methods in engineering gener 2003 vol 56 num 9 p 1225 1242 which has been published in final form at http www3 interscience wiley com journal 102522343 abstract

converse kam theory and practice we unify extend reinterpret and apply criteria of birkhoff 1 herman 9 mather 2 3 aubry et al 4 5 and newman and percival 6 for the nonexistence of invariant circles for area preserving twist maps the criteria enable one to establish regions of phase space through which no rotational invariant circles pass for families of maps the same can be done for regions of the combined space of phase points and parameters the criteria can be implemented rigorously on a computer and give a practical method of proving quite strong results as an example we present a computer program which proved that the standard map has no rotational invariant circles for any parameter value k 63 64

an efficient two dimensional implementation of the ffowcs williams and hawkings equation abstract this paper describes a two dimensional formulation of the ffowcs williams and hawkings equation in the frequency domain by assuming subsonic rectilinear motion of all acoustic sources an efficient and easily implemented form of the equation is developed this method is capable of predicting the farfield noise from non linear nearfield flow quantities the ability to use non linear input data is a clear advantage over kirchhoff methods that are only valid in regions where the linear wave equation accurately describes the flow several example problems are used to demonstrate that the new method performs well for problems with a mean flow tonal and broadband noise signatures and non linear near fields in most practical acoustic problems three dimensionality is important and should not be neglected for these real world applications two dimensional solutions can be used to guide and augment full three dimensional calculations but not replace them

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

extension of kirchhoff s formula to radiation from moving surfaces kirchhoff s formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers because the closed surface on which the boundary data are prescribed in these cases is in motion an extension of kirchhoff s formula to this condition is required in this paper such a formula obtained originally by morgans for the interior problem is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory it is shown that the usual kirchhoff formula is a special case of the main result of the paper the general result applieds to a deformable surface however the special form it assumes for a rigid surface in motion is also noted some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

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

proper orthogonal decomposition with supg stabilized isogeometric analysis for reduced order modelling of unsteady convection dominated convection diffusion reaction problems abstract we consider reduced order modelling of unsteady convection dominated convection diffusion reaction problems with proper orthogonal decomposition pod in combination with isogeometric analysis isogeometric analysis has potential advantages in exact geometry representations efficient mesh generation different h p and k refinements and smooth bspline nurbs basis functions in order to compensate the oscillations caused by the convection dominated effect the streamline upwind petrov galerkin supg stabilization method is used both in generation of snapshots and pod galerkin method based on the recent novel and promising discretization method isogeometric analysis we propose a new fully discrete supg stabilized scheme the associated numerical error features three components due to spatial discretization by isogeometric analysis with supg stabilization time discretization with the crank nicolson scheme and modes truncation by pod we show a priori error estimates of the fully discrete scheme and give suitable stabilization parameters numerically a variety of two and three dimensional benchmark tests and numerical examples are provided to show the effectiveness accuracy and efficiency of the reduced order modelling methods by virtue of potential advantages of isogeometric analysis

improving stability and accuracy of reissner mindlin plate finite elements via algebraic subgrid scale stabilization abstract stabilized finite element methods for the solution of reissner mindlin type plate problems are presented the formulations are based on previously described mixed formulations like the assumed natural strain ans or mitc concept or the discrete shear gap dsg method in particular the algebraic subgrid scale asgs formulation is used for the stabilization term the essential idea is to obtain stable elements and improve coarse mesh accuracy at the same time it is shown how this can be achieved by a proper choice of stabilization parameters on the basis of physical insight into the mechanical behavior of shear deformable plates in this context there is a strong relationship to concepts that have been developed long before stabilization techniques appeared in finite element technology particularly the residual bending flexibility or deflection matching technique