resolution of the 2d navier stokes equations in velocity vorticity form by means of an influence matrix technique abstract an influence matrix technique is proposed to enforce both the continuity equation and the definition of the vorticity in the treatment of the 2d incompressible navier stokes equations it is shown and supported by numerical experiments that at each time step the divergence is actually equal to zero within machine accuracy the same result is obtained for the definition of the vorticity

constructing spectral schemes of the immersed interface method via a global description of discontinuous functions a global description of discontinuous functions is introduced in this paper by expressing a discontinuous function as the sum of a smooth function and a correction term determined by jump conditions we turn the unknown function from a discontinuous one into a sufficiently smooth one when solving a differential equation spectral schemes are developed based on this concept with the intention of eliminating or reducing the gibbs oscillation finite difference schemes are also constructed as an alternative of the current immersed interface methods both spectral and finite difference schemes are tested on one and two dimensional cases

numerical study of pseudospectral methods in shock wave applications abstract in this paper we use shock capturing spectral methods to simulate compressible flows in the presence of shock waves three applications are considered the first is an interaction of a one dimensional shock with an entropy wave the second case deals with interactions between shock wave and an entropy wave in two space dimensions and the third case is two dimensional shock vortex interactions the first two applications are found in the study of turbulence in high speed flow the last application is a key element in understanding the acoustic dynamics in aeroacoustic and in design of supersonic jet in aerodynamics the purpose of this study is to show the feasibility of simulating shocked flow with spectral methods the numerical methods involved are the chebyshev and fourier collocation methods the euler equations of gas dynamics is discretized by pseudospectral collocation methods in space and a nonlinearly stable third order runge kutta methods in time the fluxes are evaluated pointwise directly and not by the cell averaging technique a significant reduction in cpu time and storage usage are achieved by incorporating several well established numerical techniques such as grid transformation and filtering into the spectral algorithm the results of this study indicate that spectral method is well suited not only for smooth problems but also for those with discontinuity

a spectral solver for the navier stokes equations in the velocity vorticity formulation for flows with two nonperiodic directions a novel pseudospectral solution procedure for the navier stokes equations in the velocity vorticity formulation suitable to simulate flows with two nonperiodic directions is proposed an influence matrix method including a tau correction procedure has been employed to elicit an algorithmic substitute for thea priorilacking boundary conditions for the vorticity following o daube j comput phys 103 402 1992 the influence matrix is built by enforcing either the definition of the vorticity or the continuity equation at the boundary of the domain the influence matrix is nonsingular in both cases the order of the influence matrix is twice larger than one would expect from analogous solution methods based on finite differences or finite elements the spatial discretization is based on a 2d chebyshev expansion on anonstaggeredgrid of collocation points and the boundary conditions are imposed via the lanczos tau procedure the time marching scheme is adams bashforth for the advection term and crank nicolson for the viscous term the proposed scheme yields machine accurate divergence free flow fields and the definition of the vorticity is satisfied within machine accuracy

on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function it is well known that the fourier series of an analytic and periodic function truncated after 2n 1 terms converges exponentially with n even in the maximum norm it is also known that if the function is not periodic the rate of convergence deteriorates in particular there is no convergence in the maximum norm although the function is still analytic this is known as the gibbs phenomenon in this paper we show that the first 2n 1 fourier coefficients contain enough information about the function so that an exponentially convergent approximation in the maximum norm can be constructed the proof is a constructive one and makes use of the gegenbauer polynomials c n x it consists of two steps in the first step we show that the first m coefficients of the gegenbauer expansion based on c n x for 0 n m of any l2 function can be obtained within exponential accuracy provided that both and m are proportional to but smaller than n in the second step we construct the gegenbauer expansion based on c n 0 n m from the coefficients found in the first step we show that this series converges exponentially with n provided that the original function is analytic though nonperiodic thus we prove that the gibbs phenomenon can be completely overcome

a dynamic programming algorithm for simultaneous phase estimation and data decoding on random phase channels the problem of simultaneously estimating phase and decoding data symbols from baseband data is posed the phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally likely symbols transmitted over a perfectly equalized channel a dynamic programming algorithm viterbi algorithm is derived for decoding a maximum em a posteriori map phase symbol sequence on a finite dimensional phase symbol trellis a new and interesting principle of optimality for simultaneously estimating phase and decoding phase amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase symbol sequences simulation results for binary 8 ary phase shift keyed psk and 16 quadrature amplitude shift keyed qask symbol sets transmitted over random walk and sinusoidal jitter channels are presented and compared with results one may obtain with a decision directed algorithm or with the binary viterbi algorithm introduced by ungerboeck when phase fluctuations are severe and when occasional large phase fluctuations exist map phase symbol sequence decoding on circles is superior to ungerboeck s technique which in turn is superior to decision directed techniques

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

penalization modeling of a limiter in the tokamak edge plasma an original penalization method is applied to model the interaction of magnetically confined plasma with limiter in the frame of a minimal transport model for ionic density and parallel momentum the limiter is considered as a pure particle sink for the plasma and consequently the density and the momentum are enforced to be zero inside comparisons of the numerical results with one dimensional analytical solutions show a very good agreement in particular the penalization scheme followed in this paper tends to ensure an almost sonic plasma condition at the plasma obstacle interface bohm like criterion with relatively weak dependence on the target mach number profile within the obstacle the new system being solved in a periodic obstacle free domain an efficient pseudo spectral algorithm based on a fast fourier transform is also proposed and associated with an exponential filtering of the unphysical oscillations due to gibbs phenomenon finally the efficiency of the method is illustrated by investigating the flow spreading from the plasma core to the scrape off layer at the wall in a two dimensional system with one then two neighboring limiters

a viterbi type algorithm for efficient estimation of m psk sequences over the gaussian channel with unknown carrier phase a viterbi type algorithm for the efficient estimation of a convolutionally trellis coded or uncoded m psk sequence over the gaussian channel with unknown carrier phase is presented it performs coherent detection of m psk sequences with no explicit recovery of coherent references the metric computations involve only linear operations theoretical and simulated performance results are presented for various carrier phase processes the algorithm is called the suboptimum ml estimator smle its ber in the presence of a time invariant carrier phase is obtained analytically the simulation results for the ber with time invariant as well as time varying carrier phase processes allow a comparison of the performance of the smle with other sequence estimation algorithms and enable the applicability of the smle to burst mode tdma communications to be ascertained

maximum likelihood digital data sequence estimation over the gaussian channel with unknown carrier phase we consider the problem of simultaneous ml estimation of data and carrier phase from a linear suppressed carrier modulated signal received in the presence of additive white gaussian noise the ml detector of the data sequence is derived and its error probability performance is analyzed the result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length a suboptimum decision aided subsequence by subsequence detector whose complexity does not increase exponentially with sequence length is proposed and its performance is analyzed

a sampling expansion for nonbandlimited signals in chromatic derivatives in this paper we construct infinite band filterbanks for perfect reconstruction pr using hermite polynomials and hermite functions the analysis filters are linear combinations of derivative operators based on these polynomials the so called chromatic derivative filters together with the synthesis filterbanks they give pr for a large class of signals that may have infinite bandwidth several other related filterbanks are discussed as well the error in reconstruction for finite channel chromatic derivative filterbanks is calculated examples are given to demonstrate the use of these chromatic filterbanks

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

binary orthogonal signaling over the gaussian channel with unknown phase fading new results and interpretations the problem of binary orthogonal signaling over a gaussian noise channel with unknown phase fading is considered by viewing the problem in a rotated coordinate system the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement for data detection the optimum matched filter envelope detector is shown to be identical to a novel detector estimator receiver in which the detector performs partially coherent detection using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot tone component of the orthogonal signal structure this detector estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver it also leads to the development of new approaches for analyzing the error probability of the receiver an exponential chernoff upper bound is obtained for the rician channel

generalizations of chromatic derivatives and series expansions chromatic series expansions of bandlimited functions provide an alternative representation to the whittaker shannon kotel nikov sampling series chromatic series share similar properties with taylor series insofar as the coefficients of the expansions which are called chromatic derivatives are based on the ordinary derivatives of the function chromatic derivatives are linear combinations of ordinary derivatives in which the coefficients of the combinations are related to a system of orthonormal polynomials but unlike taylor series chromatic series have more useful applications in signal processing because they represent bandlimited functions more efficiently than taylor series the goal of this article is to generalize the notion of chromatic derivatives and then extend chromatic series expansions to a larger class of signals than the class of bandlimited signals in particular we extend chromatic series to signals given by integral transforms other than the fourier transform such as the laplace and hankel transforms

analysis of optimum detector of trellis coded mpsk in phase noise channels this paper presents a novel analytical expression which approximates the bit error rate ber of the joint phase and symbol maximum a posteriori jmap sequence estimator for trellis code modulation tcm with m ary phase shift keying mpsk modulation any arbitrary phase noise model i e not limited to the wiener process and either a matched or mismatched decoder first we derived convenient closed form expressions for approximating the pairwise error probability of two code sequences for both matched and mismatched decoders since the expressions are formulated either in the time or in the frequency domain it is possible to indicate the contribution of every frequency in the phase noise spectrum we then applied the union bound on the code sequence pairwise errors the analytical expression was tight usually 1db for mpsk constellations with m 4 and code rates 0 5 once developed the expressions will assist designers to consider the influence on receiver performance of the code characteristics decoder implementation and rf synthesizer phase noise it further enables joint optimization of the rf synthesizer the code and the decoder for achieving the lowest error rate or other design targets

vortex methods with spatially varying cores the accuracy of vortex methods employing smooth vortex particles blobs is determined by the blob size which can be viewed as a mollifier of the vorticity field for computational efficiency this core size needs to be spatially variable as particles are used to discretize different parts of the flow field such as the boundary layer and the wake in bluff body flows we derive here a consistent approximation for the viscous navier stokes equations using variable size vortex particles this derivation is based on the implementation of mappings that allow the consistent formulation of the diffusion and convection operators of the navier stokes equations in the context of vortex methods several local mappings can be combined giving the capability of mesh embedding to vortex methods it is shown that the proposed variable method offers a significant improvement on the computational efficiency of constant core size methods while maintaining the adaptive character of the method the method is ideally suited to flows such as wakes and shear layers and the validity of the approach is illustrated by showing results from cylinder flows and wall vortex interactions using this scheme previously unattainable simulations of cylinders undergoing rotary oscillations at high reynolds numbers reveal an interesting mechanism for drastic drag reduction

error probability analysis and applications of amplitude coherent detection in flat rayleigh fading channels this paper presents the detector design and symbol error rate ser analysis of m ary amplitude shift keying over multipath fading channels using amplitude coherent detection acd the optimum detector is derived using the maximum likelihood criterion and then it is used to derive two efficient low complexity suboptimal detectors the probability distribution function of the decision variables and the ser of the two suboptimal detectors are expressed using simple closed form analytical formulas when single receiving antenna is used the ser with receiver diversity is obtained using monte carlo simulation the obtained analytical and simulation results reveal that acd can provide reliable ser as compared with noncoherent detection moreover we present an efficient blind channel estimation algorithm using acd and hybrid modulation frame structures

fourier spectral and wavelet solvers for the incompressible navier stokes equations with volume penalization convergence of a dipole wall collision in this study we use volume penalization to mimic the presence of obstacles in a flow or a domain with no slip boundaries this allows in principle the use of fast fourier spectral methods and coherent vortex simulation techniques based on wavelet decomposition of the flow variables to compute turbulent wall bounded flow or flows around solid obstacles by simply adding one term in the equation convergence checks are reported using a recently revived and unexpectedly difficult dipole wall collision as a benchmark computation several quantities like the vorticity isolines truncation error kinetic energy and enstrophy are inspected for a collision of a dipole with a no slip wall and compared with available benchmark data obtained with a standard chebyshev pseudospectral method we quantify the possible deteriorating effects of the gibbs phenomenon present in the fourier based schemes due to continuity restrictions of the penalized navier stokes equations on the wall it is found that gibbs oscillations have a negligible effect on the flow evolution allowing higher order recovery of the accuracy on a fourier basis by means of postprocessing an advantage of coherent vortex simulations on the other hand is that the degrees of freedom of the flow computation can strongly be reduced in this study we quantify the possible reduction of degrees of freedom while keeping the accuracy for an optimal convergence scenario the penalization parameter has to scale with the number of fourier and wavelet modes in addition an implicit treatment of the darcy drag term in the penalized navier stokes equations is beneficial since this allows one to set the time step independent from the penalization parameter without additional computational or memory requirements

efficient estimation of continuous phase modulation with unknown carrier phase an efficient algorithm is presented for the estimation of continuous phase modulation cpm sequences over the gaussian channel with unknown carrier phase it operates on the excess phase trellis like the viterbi algorithm except that it is not a maximum likelihood ml estimator its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ml estimation in the limit as the carrier phase remains constant over a long interval so that the observation interval for forming the metric can be made large it is shown for the case of minimum shift keying msk that the bit error probability bep of perfectly coherent ml estimation is attained

generalization of the inverse polynomial reconstruction method in the resolution of the gibbs phenomenon the finite fourier representation of a function f x exhibits oscillations where the function or its derivatives are nonsmooth this is known as the gibbs phenomenon a robust and accurate reconstruction method that resolves the gibbs oscillations was proposed in a previous paper j comput appl math 161 2003 41 based on the inversion of the transformation matrix which represents the projection of a set of basis functions onto the fourier space if the function is a polynomial this inverse polynomial reconstruction method iprm is exact in this paper we develop the iprm by requiring that the proper error be orthogonal to the fourier or polynomial space the iprm is generalized to any set of basis functions the primitive basis polynomials nonclassical orthogonal polynomials and the gegenbauer polynomials are used to illustrate the wide validity of the iprm it is shown that the iprm yields a unique reconstruction irrespective of the basis set for any analytic function and yields spectral convergence the ill posedness of the transformation matrix due to the exponential growth of the condition number of the matrix is also discussed

an adaptive wavelet vaguelette algorithm for the solution of pdes the paper first describes a fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function this approach permits to compute the decomposition of a function into a lacunary wavelet basis i e a basis constituted of a subset of all basis functions up to a certain scale without modification the construction is then extended to operator adapted biorthogonal wavelets this is relevant for the solution of certain nonlinear evolutionary pdes where a priori information about the significant coefficients is available we pursue the approach described in j frohlich and k schneider europ j mech b fluids13 439 1994 which is based on the explicit computation of the scalewise contributions of the approximated function to the values at points of hierarchical grids here we present an improved construction employing the cardinal function of the multiresolution the new method is applied to the helmholtz equation and illustrated by comparative numerical results it is then extended for the solution of a nonlinear parabolic pde with semi implicit discretization in time and self adaptive wavelet discretization in space results with full adaptivity of the spatial wavelet discretization are presented for a one dimensional flame front as well as for a two dimensional problem

structure function scaling of bounded two dimensional turbulence statistical properties of forced two dimensional turbulence generated in two different flow domains are investigated by numerical simulations the considered geometries are the square domain and the periodic channel domain both bounded by lateral no slip sidewalls the focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no slip boundaries the scaling exponents of the velocity and the vorticity structure functions are compared to the classical kraichnan batchelor leith kbl theory which assumes isotropy homogeneity and self similarity for turbulence scales between the forcing and dissipation scale our investigation reveals that in the interior of the flow domain turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range but it is weakly intermittent however the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the kbl theory predicts near the walls the turbulence is strongly anisotropic at all flow scales

chromatic derivatives and local approximations we present a detailed motivation for the notions of chromatic derivatives and chromatic expansions chromatic derivatives are special numerically robust linear differential operators chromatic expansions are the associated local expansions which possess the best features of both the taylor and the nyquist expansions we give a simplified treatment of some of the basic properties of chromatic derivatives and chromatic expansions which are relevant for applications we also consider some signal spaces with a scalar product defined by a cesaro type sum of products of chromatic derivatives as well as an approximation of such a scalar product which is relevant for signal processing we also introduce a new kind of local approximations based on trigonometric functions

time step restrictions using semi explicit methods for the incompressible navier stokes equations time step restrictions using semi explicit methods for the incompressible navier stokes equations