globally hyperbolic regularization of grad s moment system in this paper we propose a globally hyperbolic regularization to the general grad s moment system in multidimensional spaces systems with moments up to an arbitrary order are studied the characteristic speeds of the regularized moment system can be analytically given and depend only on the macroscopic velocity and the temperature the structure of the eigenvalues and eigenvectors of the coefficient matrix is fully clarified the regularization together with the properties of the resulting moment systems is consistent with the simple one dimensional case discussed in 1 in addition all characteristic waves are proven to be genuinely nonlinear or linearly degenerate and the studies on the properties of rarefaction waves contact discontinuities and shock waves are included 2014 wiley periodicals inc

the fine structure of the recovering auditory detection threshold detection thresholds were gathered for a 2 khz gaussian shaped probe standard deviation 0 5 ms centered at intervals of as little as half a millisecond over 0 30 ms following a 200 ms 97 db spl 2 khz tone surprisingly there were small sudden rises and falls superimposed on each subject s generally smooth recovery even more obvious were nonmonotonicities in the standard deviation of the cumulative normal fitted to each threshold s psychometric function

effects of masker duration in pure tone forward masking the masking of one tone by a preceding tone forward masking was studied as a function of the duration of the masker in general it was found that forward masking increased with increasing masker duration for the range of durations used 35 to 500 msec the functions relating masked probe threshold in decibels to the logarithm of masker duration were well described by straight lines the rate of growth of forward masking as a function of masker duration was greatest for relatively high masker levels and frequencies

effects of peripheral nonlinearity on psychometric functions for forward masked tones psychometric functions pfs for forward masked tones were obtained for conditions in which signal level was varied to estimate threshold at several masker levels variable signal condition and in which masker level was varied to estimate threshold at several signal levels variable masker condition the changes in pf slope across combinations of masker frequency masker level and signal delay were explored in three experiments in experiment 1 a 2 khz 10 ms tone was masked by a 50 70 or 90 db spl 20 ms on frequency forward masker with signal delays of 2 20 or 40 ms in a variable signal condition pf slopes decreased in conditions where signal threshold was high in experiments 2 and 3 the signal was a 4 khz 10 ms tone and the masker was either a 4 or 2 4 khz 200 ms tone in experiment 2 on frequency maskers were presented at 30 to 90 db spl in 10 db steps and off frequency maskers were presented at 60 to 90 db spl in 10 db steps with signal delays of 0 10 or 30 ms in a variable signal condition pf slopes decreased as signal level increased and this trend was similar for on and off frequency maskers in experiment 3 variable masker conditions with on and off frequency maskers and 0 ms signal delay were presented in general the results were consistent with the hypothesis that peripheral nonlinearity is reflected in the pf slopes the data also indicate that masker level plays a role independent of signal level an effect that could be accounted for by assuming greater internal noise at higher stimulus levels

streamwise upwind algorithm for computing unsteady transonic flows past oscillating wings a streamwise upwind algorithm has been extended to compute unsteady flows with a moving grid system and applied to compute flows over oscillating wings at transonic mach numbers comparisons have been made between results obtained from this upwind algorithm using both temporally nonconservative and conservativeimplicit methods with the results obtained from a central difference method and also with experimental data the efficiency and practicality of the temporally nonconservative implicit solver are illustrated results to show the robustness and accuracy of the upwind method for unsteady computations compared to the central difference method are presented

flux difference split algorithm for unsteady thin layer navier stokes solutions an efficient flux difference split scheme for calculating steady and unsteady thin layer navier stokes solutions for airfoils and wings is presented steady solutions for a flat plate laminar boundary layer profile are correctly modeled with only three grid cells internal to the boundary layer the flux difference split algorithm was used to evaluate the scheme for unsteady viscous calculations the diffusive terms are time lagged in the solution process the scheme is second order accurate in space and first order accurate in time due to the explicit treatment or the diffusive terms

dependence of post masking on masker duration and its relation to temporal effects in loudness temporal masking of tones by noise was investigated using a post forward masking paradigm the masker level and duration were varied for every masker level employed the rate of decay of masking was found to depend on the duration of the masker specific loudness values were computed from the forward masking functions and an electronic device which simulates these loudness functions is presented in the simulation a series of integrators or a single integration with one long time constant was utilized the effect of the proposed integrators on loudness meters is discussed

two dimensional unsteady navier stokes solution method with moving overset grids a simple numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across two dimensional structured overset grids is presented overset grids are allowed to move in time relative to each other intergrid boundary points are localized in a triangular stencil on the donor grid by a directional search algorithm the final parameters of the search algorithm give the interpolation weights at the intergrid boundary point numerical results are presented for steady and unsteady viscous flow solutions over an airfoil undergoing a sinusoidal flapping motion computed flowfields demonstrate the accuracy of the method and excellent agreement is obtained against the single grid solutions the method is independent of numerical solution algorithms and it may easily be implemented on any two dimensional single block flow solver to make it a multiblock zonal solver with arbitrarily overset overlapping computational grids

new implicit boundary procedures theory and applications analytical techniques for the application of implicit boundary conditions for inviscid flows to shock and body boundary layer conditions involving the euler equations are presented the theory of characteristics is used to update boundary points with spatial second order accuracy the method is useful for implicit schemes which feature approximate factorization and as such is incorporated into an existing pns code examples are provided in terms of flows over a cone over a maneuverable reentry vehicle and over a finned vehicle improvements in the convergence rate are demonstrated for the conical flow solutions

nr xx simulation of microflows with shakhov model in this paper we propose a method to simulate the microflows with shakhov model using the nr xx method developed in z cai and r li siam j sci comput 32 2010 pp 2875 2907 z cai r li and y wang commun comput phys 11 2012 pp 1415 1438 z cai r li and y wang j sci comput to appear the equation under consideration is the boltzmann equation with force terms and the shakhov model is adopted to achieve the correct prandtl number as the focus of this paper we derive a uniform framework for different order moment systems on the wall boundary conditions which is a major difficulty in the moment methods numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments

fast p multigrid discontinuous galerkin method for compressible flows at all speeds ap multigrid wherep is the polynomial degree discontinuous galerkin method is presented for the solution of the compressible euler equations on unstructured grids the method operates on a sequence of solution approximations of different polynomial orders a distinct feature ofthisp multigrid method is the application of an explicit smoother on the higher level approximations p 0 and an implicit smoother on the lowest level approximation p 0 resulting in a fast and low storage method that can be efficiently used to accelerate the convergence to a steady state solution furthermore this p multigrid method can be naturally applied to compute the flows with discontinuities in which a monotonic limiting procedure is usually required for discontinuous galerkin methods an accurate representation of the boundary normals based on the definition of the geometries is used for imposing slip boundary conditions for curved geometries krivodonova l and berger m high order implementation of solid wall boundary conditions in curved geometries journal of computational physics vol 211 no 2 2006 pp 492 512 and luo h baum j d and lohner r on the computation of steady state compressible flows using a discontinuous galerkin method international journal for numerical methods in engineering vol 73 no 5 2008 pp 597 623 a variety of compressible flow problems for a wide range of flow conditions from low mach number to supersonic in both two dimensional and three dimensional configurations are computed to demonstrate the performance ofthisp multigrid method the numerical results obtained strongly indicate the order independent property of this p multigrid method and demonstrate that this method is orders of magnitude faster than its explicit counterpart the performance comparison with a finite volume method shows that using this p multigrid method the discontinuous galerkin method provides a viable attractive competitive and probably even superior alternative to the finite volume method for computing compressible flows at all speeds

solving discontinuous galerkin formulations of poisson s equation using geometric and p multigrid methods for solving discontinuous galerkin formulations of the poisson equation by coupling p multigrid to geometric multigrid are investigated the simple approach of performing iterative relaxation on solution approximations of decreasing polynomial degree p down to p 0 and then applying geometric multigrid is ineffective the transition from p 1 top 0 causes the performance of the entire iteration to degrade because the long wavelength eigenfunctions of the p 1 discontinuous system are not represented well in thep 0 space a new approach is proposed that coarsens from thep 1 discontinuous space to thep 1 continuous space this approach eliminates the problems caused by the p 1 to p 0 transition furthermore the p 1 continuous space is a standard finite element space for which geometric multigrid is well defined in addition when the discontinuous galerkin equations are restricted to a continuous space one recovers the galerkin formulation of continuous finite elements thus applying geometric multigrid to this system is straightforward and effective numerical tests agree well with the analysis and confirm that the new approach gives rapid convergence rates that are grid independent and only weakly sensitive to the polynomial order

a new multigrid approach to convection problems abstract a new multigrid method for convection problems is presented it is designed to overcome the problem of alignment the flow being aligned with the grid the technique employs semi coarsening in several directions simultaneously and gives rise to multiple coarser grids with the same total number of points per grid level but with different sizes in each co ordinate direction the amount of work per multigrid cycle is still o n as an example the method is applied to the nonlinear upwind differenced euler equations of gas dynamics in two dimensions convergence rates are estimated by two level fourier analysis for the linearised equations numerical experiments on the nonlinear equations confirm these estimates

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

a framework on moment model reduction for kinetic equation through a deep investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for the boltzmann equation in z cai y fan and r li commun math sci 11 2013 pp 547 571 we propose a uniform framework for the derivation of reduced models from general kinetic equations the resulting model appears as a symmetric hyperbolic moment system this reveals the underlying reason why some models in the literature are hyperbolic while others are not this framework provides a simple flow chart following which a number of existing models can be derived in a new way the framework is also helpful in discovering new models we apply this to grad s 13 moment distribution function and obtain a new 13 moment model with global hyperbolicity

improvements to a dual time stepping method for computing unsteady flows the nonlinear problem to be solved within an implicit time marching method has several differences from a typical steady state problem the initial guess is usually quite good and the degree of convergence required is quite small perhaps a few orders of magnitude reduction in residual therefore algorithms developed for steady problems may not be optimal for use in a dual time context we present some modifications to the diagonal approximately factored algorithm that lead to savings in a dual time stepping context

age related changes in within and between channel gap detection using sinusoidal stimuli pure tone gap stimuli with identical within channel or dissimilar between channel marker frequencies of 1 and 2 khz were presented to young and old listeners in a two interval forced choice gap detection task to estimate the influence of extraneous duration cues on gap detection thresholds in the between channel conditions were obtained for two different sets of reference stimuli reference stimuli that were matched to the overall duration of the gap stimulus i e two markers plus the gap and reference stimuli that were fixed at the combined duration of the two markers excluding the gap results from within channel conditions were consistent with previous studies i e there were small but highly reliable age differences smaller gap thresholds at longer marker durations and an interaction between the two variables in between channel conditions however age differences were not as clear cut rather the effect of age varied as a function of duration cue and was more pronounced when stimuli were matched for overall duration than when the duration of the reference tone was fixed

an efficient steady state solver for microflows with high order moment model in z hu r li and z qiao acceleration for microflow simulations of high order moment models by using lower order model correction j comput phys 327 225 244 2016 it has been successfully demonstrated that using lower order moment model correction is a promising idea to accelerate the steady state computation of high order moment models of the boltzmann equation to develop the existing solver the following aspects are studied in this paper first the finite volume method with linear reconstruction is employed for high resolution spatial discretization of the resulting equations second by introducing an appropriate parameter in the correction step it is found that the performance of the solver can be improved significantly i e more levels would be involved in the solver which further accelerates the convergence of the method third heun s method is employed as the smoother in each level to enhance the robustness of the solver numerical experiments in microflows are carried out to demonstrate the efficiency and to investigate the behavior of the new solver in addition several order reduction strategies for the choice of the order sequence of the solver are tested and the strategy ml 1 ml 2 is found to be most efficient

numerical regularized moment method of arbitrary order for boltzmann bgk equation we introduce a numerical method for solving grad s moment equations or regularized moment equations for an arbitrary order of moments in our algorithm we do not explicitly need the moment equations instead we directly start from the boltzmann equation and perform grad s moment method h grad commun pure appl math 2 1949 pp 331 407 and the regularization technique h struchtrup and m torrilhon phys fluids 15 2003 pp 2668 2680 numerically we define a conservative projection operator and propose a fast implementation which makes it convenient to add up two distributions and provides more efficient flux calculations compared with the classic method using explicit expressions of flux functions for the collision term the bgk model is adopted so that the production step can be done trivially based on the hermite expansion extensive numerical examples for one and two dimensional problems are presented convergence in moments can be validated by the numerical results for different numbers of moments

modification of the osher upwind scheme for use in three dimensions the pertinent formulas are given by eq 24 for the variation of c kleb with the modified clauser pressure gradient parameter by eq 14 for the variation of ccp with ckleb and by eq 26 for the variation of the clauser factor k with low reynolds number as presented here the relations for the baldwin lomax factors have an indirect experimental validity by being derived from the experimentally confirmed velocity similarity laws finally it should be apparent that for boundary layers in pressure gradients constant values for the baldwin lomax factors are unsatisfactory in satisfying the velocity similarity laws to approach the same accuracy as the parent cebeci smith method the baldwinlomax factors should be varied as indicated

an implicit form for the osher upwind scheme conservative upwind schemes for the euler equations such as the osher scheme accurately resolve flow discontinuities and correctly model the physics of the problem however these schemes require many more arithmetic operations per integration step than simple central difference schemes and hence result in large computing times an implicit version of the first order and second order accurate osher schemes in two spatial dimensions and generalized coordinates is developed in this study because implicit schemes permit the use of large integration steps in many cases they require fewer integration steps to reach steady state especially in calculations on grids with widely varying mesh cell sizes the implicit scheme developed in this study accelerated convergence speeds by almost an order of magnitude in the problems considered test cases include quasi one dimensional nozzle flow and supersonic flow past a cylinder

the role of stimulus complexity spectral overlap and pitch for gap detection thresholds in young and old listeners thresholds for detecting a gap between two complex tones were determined for young listeners with normal hearing and old listeners with mild age related hearing loss the leading tonal marker was always a 20 ms 250 hz complex tone with energy at 250 500 750 and 1000 hz the lagging marker also tonal could differ from the leading marker with respect to fundamental frequency f0 the presence versus absence of energy at f0 and the degree to which it overlapped spectrally with the leading marker all stimuli were presented with steeper 1 ms and less steep 4 ms envelope rise and fall times f0 differences decreases in the degree of spectral overlap between the markers and shallower envelope shape all contributed to increases in gap detection thresholds age differences for gap detection of complex sounds were generally small and constant when gap detection thresholds were measured on a log scale when comparing the results for complex sounds to thresholds obtained for pure tones in a previous study by heinrich and schneider 2006 j acoust soc am 119 2316 2326 thresholds increased in an orderly fashion from markers with identical within channel pure tones to different between channel pure tones to complex sounds this pattern of results was true for listeners of both ages although younger listeners had smaller thresholds overall

a high resolution euler solver based on multigrid semi coarsening and defective correction abstract in an earlier paper an o n method for the computation of stationary solutions to the euler equations of inviscid compressible gas dynamics has been described the method is a variant of the multigrid technique and employs semi coarsening in all co ordinate directions simultaneously it provides good convergence rates for first order upwind discretisations even in the case of alignment the flow being aligned with the grid here we discuss the application of this scheme to higher order discretisations two grid analysis for the linear constant coefficient case shows that it is difficult to obtain uniformly good convergence rates for a higher order scheme because of waves perpendicular to stream lines the defect correction technique suffers from the same problem however convergence to a point where the residual of the total error the sum of the iteration error and the discretisation error is of the order of the truncation error can be obtained in about seven defect correction cycles according to estimates for the linear constant coefficient equations this result is explored for the nonlinear case by some illustrative numerical experiments

gap detection and the precedence effect in young and old adults thresholds for detecting a gap between two gaussian enveloped standard deviation 0 5 ms 2 khz tones were determined in young and old listeners the gap detection thresholds of old adults were more variable and about twice as large as those obtained from young adults moreover gap detection thresholds were not correlated with audiometric thresholds in either group estimates of the width of the temporal window of young subjects based on the detection of a gap between two tone pips were smaller than those typically obtained when a relatively long duration pure tone is interrupted moore et al j acoust soc am 85 1266 1275 1989 because the amount of time it takes to recover from an adapting stimulus is likely to affect gap detection thresholds glasberg et al j acoust soc am 81 1546 1556 1987 smaller estimates of temporal window size would be expected in this paradigm if the amount of adaptation produced by the first tone pip was negligible the larger gap detection thresholds of o

acceleration for microflow simulations of high order moment models by using lower order model correction we study the acceleration of steady state computation for microflow which is modeled by the high order moment models derived recently from the steady state boltzmann equation with bgk type collision term by using the lower order model correction a novel nonlinear multi level moment solver is developed numerical examples verify that the resulting solver improves the convergence significantly thus is able to accelerate the steady state computation greatly the behavior of the solver is also numerically investigated it is shown that the convergence rate increases indicating the solver would be more efficient as the total levels increases three order reduction strategies of the solver are considered numerical results show that the most efficient order reduction strategy would be ml1 ml 2

forward masking by sinusoidal and noise maskers a 2 khz sinusoid and a narrow band noise centered at 2 khz with the same total power served as maskers for a 2 khz sinusoidal signal we compare the forward masking produced by these two maskers 1 as a function of offset offset time for 5 and 35 ms signals 2 as a function of signal duration for a fixed offset onset time and 3 as a function of signal duration for a fixed offset offset time in all these comparisons we find that the noise and sinusoid not only produce different amounts of masking for the same experimental condition but they also show different trends for the same manipulation the important relations in these results are demonstrated in an additional set of conditions with a 1 khz signal in order to account for the differences observed in both experiments we argue that forward masking is determined by at least two factors we suggest signal energy as one factor and the presence or absence of differences in quality between masker and signal as another

coupling p multigrid to geometric multigrid for discontinuous galerkin formulations of the convection diffusion equation an improved p multigrid algorithm for discontinuous galerkin dg discretizations of convection diffusion problems is presented the general p multigrid algorithm for dg discretizations involves a restriction from the p 1 to p 0 discontinuous polynomial solution spaces this restriction is problematic and has limited the efficiency of the p multigrid method for purely diffusive problems helenbrook and atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p 1 it is shown that this method is not directly applicable to the convection diffusion cd equation because it results in a central difference discretization for the convective term to remedy this ideas from the streamwise upwind petrov galerkin supg formulation are used to devise a transition from the discontinuous to continuous space at p 1 that yields an upwind discretization the results show that the new method converges rapidly for all peclet numbers

euler equations implicit schemes and boundary conditions implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady euler equations this new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations along with the theoretical background the practical application of the method to several types of boundaries is also explained using several examples the specific boundary conditions covered include subsonic inflow and outflow surface tangency and shock waves the example problems include one dimensional laval nozzle flow dual throat rocket engine nozzle flow and supersonic flow past a sphere the implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions at least an order of magnitude increase in computational speed is demonstrated in the examples shown background t he growing popularity of solutions to the euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions the potential of implicit schemes in this direction has not been fully exploited for want of correct implicit application of boundary conditions the predominant use of implicit algorithms for the navier stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the euler equations thus there is a need for correct and stable procedures for the easy implicit application of boundary conditions such methods will serve the two purposes of 1 reaching time asymptotic steady state faster and 2 permitting a time step for truly unsteady flow that is not necessarily restricted by the cfl stability criterion but is based upon the magnitude of the transients for clues and information on how to construct such boundary condition procedures one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations the unsteady euler equations belong to this category the theory for hyperbolic systems is rich with information on signal propagation directions the characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution boundary condition procedures based on this theory have been known and applied for several years by kentzer 1 porter and coakley 2 de neef 3 and others in earlier work by this author 4 5 easily understood and implementable methods for boundary point treatment were presented however all of the above techniques were developed for explicit finite difference schemes it seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes and indeed it is simple enough the rest of this paper describes such implicit boundary condition procedures the given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme

comparison of kinetic theory and hydrodynamics for poiseuille flow comparison of particle dsmc simulation with the numerical solution of the navier stokes ns equations for pressure driven plane poiseuille flow is presented and contrasted with that of the acceleration driven poiseuille flow although for the acceleration driven case dsmc measurements are qualitatively different from the ns solution at relatively low knudsen number the two are in somewhat better agreement for pressure driven flow