a family of dynamic finite difference schemes for large eddy simulation a family of dynamic low dispersive finite difference schemes for large eddy simulation is developed the dynamic schemes are constructed by combining taylor series expansions on two different grid resolutions the schemes are optimized dynamically during the simulation according to the flow physics and dispersion errors are minimized through the real time adaption of the dynamic coefficient in case of dns resolution the dynamic schemes reduce to the standard taylor based finite difference schemes with formal asymptotic order of accuracy when going to les resolution the schemes seamlessly adapt to dispersion relation preserving schemes the schemes are tested for large eddy simulation of burgers equation and numerical errors are investigated as well as their interaction with the subgrid model very good results are obtained

a representation of bounded viscous flow based on hodge decomposition of wall impulse a lagrangian representation of bounded incompressible flow is introduced in which viscous boundary conditions are given kinematic expression by the generation of impulse at the wall the relationship between such a process and the boundary conditions is deduced from two complementary hodge decompositions the orientation of the created impulse vector may be chosen to be parallel at the wall this being equivalent to a thin vortex doublet sheet or normal at the wall this being a thin monopole vortex sheet although the representation is developed here for two dimensions it can be generalized in a natural way to three dimensions the case of tangentially oriented wall impulse is applied to flow over a semi infinite plate the case of normally oriented wall impulse is applied to flow past a circular cylinder

pseudo time stepping methods for space time discontinuous galerkin discretizations of the compressible navier stokes equations the space time discontinuous galerkin discretization of the compressible navier stokes equations results in a non linear system of algebraic equations which we solve with pseudo time stepping methods we show that explicit runge kutta methods developed for the euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality to evaluate its effectiveness we compare with an implicit explicit runge kutta method which does not suffer from the viscous stability constraint we analyze the stability of the methods and illustrate their performance by computing the flow around a 2d airfoil and a 3d delta wing at low and moderate reynolds numbers

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

estimating a changepoint boundary or frontier in the presence of observation error a range of problems in economics and statistics involve calculation of the boundary or frontier of the support of a distribution several practical and attractive solutions exist if the sampled distribution has a sharp discontinuity at the frontier but accuracy can be greatly diminished if the data are observed with error indeed if the error is additive and has variance 2 then inaccuracies are usually of order for small in this article we suggest an elementary method for reducing the effect of error to o 2 and show that refinements can improve accuracy still further to o 3 or less the problem is inherently ill posed however to such an extent that the frontier is generally not even identifiable unless the error distribution is known the latter assumption is unreasonable in most practical settings not in the least because the error is often asymmetrically distributed for example in the context of productivity analysis the error distribution tends to have a longer tail in the directi

testing and estimating shape constrained nonparametric density and regression in the presence of measurement error in many applications we can expect that or are interested to know if a density function or a regression curve satisfies some specific shape constraints for example when the explanatory variable x represents the value taken by a treatment or dosage the conditional mean of the response y is often anticipated to be a monotone function of x indeed if this regression mean is not monotone in the appropriate direction then the medical or commercial value of the treatment is likely to be significantly curtailed at least for values of x that lie beyond the point at which monotonicity fails in the case of a density common shape constraints include log concavity and unimodality if we can correctly guess the shape of a curve then nonparametric estimators can be improved by taking this information into account addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint and if the conclusion of the test is positive a technique for e

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

a multi scale formulation for compressible turbulent flows suitable for general variational discretization techniques based on the recently introduced variational multi scale vms approach to large eddy simulation les as introduced in t j r hughes l mazzei k e jansen large eddy simulation and the variational multiscale method comput visual sci 3 2001 47 59 s s collis monitoring unresolved scales in multiscale turbulence modeling phys fluids 13 6 2001 1800 1806 we present a vms formulation which can be used in the simulation of compressible flows special attention is given to obtain a vms formulation which is suitable for complex flow domains and general variational discretization techniques a generalization of the favre averaging procedure is introduced such that the formulation resembles the favre filtered navier stokes equations traditionally used in les of compressible flow and no explicit subgrid terms arise in the continuity equation also we show that with the use of discretization methods other than fourier spectral methods the vms projection no longer commutes with differentiation this results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to les

analysis of numerical errors in large eddy simulation using statistical closure theory this paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large eddy simulation the analysis is based on edqnm closure theory and is applied to the les of decaying isotropic turbulence first the effects of finite differencing truncation error aliasing error and the dynamic smagorinsky model are independently considered the time evolution of kinetic energy and spectra predicted by the analysis are compared to actual les using the navier stokes equations and good agreement is obtained the analysis is then extended to simultaneously consider all sources of error in a second order discretely energy conserving central difference les solver good agreement between the analysis and actual les is obtained the analysis is used to compare the contribution of the subgrid model to that of numerical errors and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors the proposed one dimensional edqnm les model shows potential as a more general tool for the analysis of numerical error and sgs model in simulations of turbulent flow

semiparametric density estimation by local l2 fitting this article examines density estimation by combining a parametric approach with a nonparametric factor the plug in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor the nonparametric factor is derived by a criterion called local l 2 fitting a class of estimators that have multiplicative adjustment is provided including estimators proposed by several authors as special cases and the asymptotic theories are developed theoretical comparison reveals that the estimators in this class are better than or at least competitive with the traditional kernel estimator in a broad class of densities the asymptotically best estimator in this class can be obtained from the elegant feature of the bias function

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

turbulence control simulation using the variational multiscale method the capabilities of the variational multiscale vms method are explored in the context of turbulence control by applying vms to the simulation of a simple opposition control strategy for turbulent channel flow with the results compared to prior direct numerical simulations and large eddy simulations based on the dynamic subgrid scale model in all cases the vms method is found to be more efficient and more accurate than the dynamic model and the simplicity accuracy and generality of vms makes it particularly attractive for turbulence control investigations

a fourier approach to nonparametric deconvolution of a density estimate we consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f when a represents the convolution of h and f our approach is based on truncated fourier inversion in which the truncation point plays the role of a smoothing parameter we derive the asymptotic mean integrated squared error of the estimate and use this formula to suggest a simple practical method for choosing the truncation point from the data strikingly when the smoothing parameter is chosen in this way then in many circumstances the estimator behaves to first order as though the true f were known

a semiparametric approach to density estimation abstract one method of fitting a parametric density function f x is first to estimate by maximum likelihood say and then to estimate f x by on the other hand when the parametric model does not hold the true density f x may be estimated nonparametrically as in the case of a kernel estimate the key idea proposed is to fit a combination of the parametric and nonparametric estimates namely where 0 1 is unknown the parameter is estimated from the data and its estimate is then used in as the proposed density estimate the main point is that we expect to be close to unity when the parametric model prevails and close to zero when it does not hold we show that under certain conditions converges to the parametric density when the parametric model holds and approaches the true f x when the parametric model does not hold the procedure was applied to a number of actual data sets in each case the maximum likelihood estimate was readily obtained and the semiparametric density es

an eulerian lagrangian approach to the navier stokes equations we present a formulation of the incompressible viscous navier stokes equation based on a generalization of the inviscid weber formula in terms of a diffusive back to labels map and a virtual velocity we derive a generalization of the inviscid cauchy formula and obtain certain bounds for the objects introduced

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

a random vortex simulation of falkner skan boundary layer flow chorin j comput phys 27 428 1978 applied a random vortex sheet method to the problem of incompressible boundary layer flow with a uniform external velocity u x u0 the application of the method is here extended to the case of an external flow field of the form u x u0xm where m is a real number the method generates time dependent solutions to the prandtl equations and these non similar solutions in their temporal mean are compared to the corresponding similar solutions of the falkner skan equation a visualisation of the spatial structure of the velocity field in the boundary layer is obtained numerically for various values of m

generation of vorticity near the boundary in planar navier stokes flows we construct the solutions of the planar navier stokes flow for a viscous incompressible fluid in the half plane by means of a boundary layer equation describing the production of vorticity on the boundary regularity properties are also discussed

an eulerian lagrangian approach for incompressible fluids local theory we study a formulation of the incompressible euler equations in terms of the inverse lagrangian map in this formulation the equations become a first order advective nonlinear system of partial differential equations

the use of explicit filters in large eddy simulation abstract explicit filtering is considered as a means of controlling the numerical errors that result when finite difference methods are used in large eddy simulation les the notion that the finite difference expressions themselves act as an effective filter is shown to be false for three dimensional simulations performed on nonuniform meshes for consistency the nonlinear terms in the navier stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost explicit filtering is shown to improve the computed results but this improvement comes at a rather high computational cost the explicitly filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution

a dynamically optimized finite difference scheme for large eddy simulation a low dispersive dynamic finite difference scheme for large eddy simulation is developed the dynamic scheme is constructed by combining taylor series expansions on two different grid resolutions the scheme is optimized dynamically through the real time adaption of a dynamic coefficient according to the spectral content of the flow such that the global dispersion error is minimal in the case of dns resolution the dynamic scheme reduces to the standard taylor based finite difference scheme with formal asymptotic order of accuracy when going to les resolution the dynamic scheme seamlessly adapts to a dispersion relation preserving scheme the scheme is tested for large eddy simulation of burgers equation very good results are obtained

adaptively local one dimensional subproblems with application to a deconvolution problem in this paper a method for finding global minimax lower bounds is introduced the idea is to adjust automatically the direction of a local one dimensional subproblem at each location to the nearly hardest one and to use locally the difficulty of the one dimensional subproblem this method has the advantages of being easily implemented and understood the lower bound is then applied to nonparametric deconvolution to obtain the optimal rates of convergence for estimating a whole function other applications are also addressed

a class of local likelihood methods and near parametric asymptotics observations in the neighbourhood of t the paper studies the sense in which f t t is closer to the true distribution g t than the usual estimate f t is asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the sample size tends to1 i n this setting the relative entropy risk of the local method is better than that of maximum likelihood the form of optimum weights for the local likelihood is obtained and illustrated for the normal distribution

a variational multiscale stabilized finite element method for the solution of the euler equations of nonhydrostatic stratified flows we present a compressible version of the variational multiscale stabilization vms method applied to the finite element fe solution of the euler equations for nonhydrostatic stratified flows this paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics this effort is justified by the previously observed good performance of vms and by the advantages that a compact galerkin formulation offers on massively parallel architectures a paradigm for both computational fluid dynamics cfd and numerical weather prediction nwp practitioners we also propose a simple technique to construct a well balanced approximation of the dominant hydrostatics that if not properly discretized may cause unacceptable vertical oscillations this is a relevant problem in nwp especially in the proximity of steep topography to evaluate the performance of the method for stratified environments six standard 2d and two 3d test cases are selected of these two admit a semi analytic solution while the remaining six are non steady and non linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability

a study of differentiation errors in large eddy simulations based on the edqnm theory this paper is concerned with the investigation of numerical errors in large eddy simulations by means of two point turbulence modeling based on the eddy damped quasi normal markovian edqnm theory a stochastic model is developed in order to predict the time evolution of the kinetic energy spectrum obtained by a large eddy simulation les including the effects of the numerics using this framework the influence of the accuracy of the approximate space differencing schemes on les quality is studied for decaying homogeneous isotropic incompressible turbulence with reynolds numbers rek based on the transverse taylor scale equal to 780 2500 and 8000 the results show that the discretization of the filtered navier stokes equations leads to differentiation and aliasing errors error spectra are also presented and indicate that the numerical errors are mainly originating from the approximate differentiation in addition increasing the order of accuracy of the differencing schemes or using algorithms optimized in the fourier space is found to widen the range of well resolved scales unfortunately for all the schemes the smaller scales with wavenumbers close to the grid cut off wavenumber are badly calculated and generate differentiation errors over the whole energy spectrum the eventual use of explicit filtering to remove spurious motions with short wavelength is finally shown to significantly improve les accuracy

an unconstrained hamiltonian formulation for incompressible fluid flow the equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical hamiltonian system the incompressibility of the flow is consequent upon certain first integrals of the motion the variable conjugate to the configuration field is not the usual linear momentum but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure the definition of the hamiltonian involves a minimization with respect to this auxiliary field the method of derivation may be generally applied to obtain unconstrained hamiltonian descriptions of lagrangian field equations subject to pointwise constraints

filtered viscous fluid equations abstract we analyze an eulerian lagrangian description of filtered incompressible fluid equations a viscous cauchy formula is derived for such equations the models discussed are related to vortex methods and to filtered kuzmin oseledets equations

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

mathematical and physical constraints on large eddy simulation of turbulence recent progress in the theoretical foundations of large eddy simulation is reviewed most of the work reported is motivated by conceptual difficulties encountered in applying the large eddy simulation method to inhomogeneous complex geometry flows among the topics covered are the problem of the lack of commutation between filtering and derivative operators for inhomogeneous flows the issues of enforcing symmetry and realizability conditions in subgrid modeling and the problem of unacceptably high numerical errors in large eddy simulation implementations with finite difference methods

space time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows i general formulation a new space time discontinuous galerkin finite element method for the solution of the euler equations of gas dynamics in time dependent flow domains is presented the discontinuous galerkin discretization results in an efficient elementwise conservative upwind finite element method which is particularly well suited for local mesh refinement the upwind scheme uses a formulation of the hllc flux applicable to moving meshes and several formulations for the stabilization operator to ensure that monotone solutions around discontinuities are investigated the non linear equations of the space time discretization are solved using a multigrid accelerated pseudo time integration technique with an optimized runge kutta method the linear stability of the pseudo time integration method is investigated for the linear advection equation the numerical scheme is demonstrated with simulations of the flow field in a shock tube a channel with a bump and an oscillating naca 0012 airfoil these simulations show that using the data at the superconvergence points the accuracy of the numerical discretization is o h5 2 in space for smooth subsonic flows both on structured and on locally refined meshes and that the space time adaptation can significantly improve the accuracy and efficiency of the numerical method

statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows abstract numerical simulations have proved that variational multiscale methods vmm perform well as pure numerical large eddy simulation les models in this paper we focus on the orthogonal subgrid scale oss finite element method and make an analysis of the statistical behavior of its stabilization terms in the quasi static approximation this is done by resorting to results from classical statistical fluid mechanics concerning two point velocity pressure and combined correlation functions of various orders given a fine enough mesh with characteristic element size h in the inertial subrange of a turbulent flow it is shown that the rate of transfer of subgrid kinetic energy provided by the oss stabilization terms does not depend on h and that it equals the molecular physical dissipation rate up to a dimensionless constant that only depends on the finite element shapes for a proper redesign of the standard parameters of the formulation this is a noteworthy fact taking into account that the subgrid stabilization terms do not arise from physical considerations but from the mathematical necessity to allow equal interpolation for the pressure and velocity fields as well as to control convection therefore the obtained results contribute somehow to the line of reasoning supporting that pure numerical approaches i e without introducing additional physical models could probably suffice in the les simulation of turbulent flows

hamiltonian dynamics of an elastica and the stability of solitary waves a method is presented for deriving unconstrained hamiltonian systems of partial differential equations equivalent to given constrained lagrangian systems the method is applied to the theory of planar finite amplitude motions of inextensible and unshearable elastic rods the constraints of inextensibility and unshearability become integrals of motion in the hamiltonian formulation

a variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes application to vortex shedding the variational multiscale formulation of large eddy simulations developed by hughes and his co workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows next a finite volume element discretization on tetrahedral meshes of this method is proposed this discretization features an economical procedure based on agglomeration for separating a priori the scales a corresponding projector for eliminating the small scales from the system of equations and an effective control of the numerical dissipation induced by upwinding the resulting les method is validated with the three dimensional numerical simulation of a low speed flow past a square cylinder at m 0 1 and re 22 000 and various comparisons with experimental data

artificial neural network approach to large eddy simulation of compressible isotropic turbulence a subgrid scale sgs model for large eddy simulation les of compressible isotropic turbulence is constructed by using a data driven framework an artificial neural network ann based on local stencil geometry is employed to predict the unclosed sgs terms the input features are based on the first order and second order derivatives of filtered velocity and temperature which appear in the second order taylor approximation of the sgs stress and heat flux it is shown that the proposed ann 7 model performs better than the gradient model in the a priori test the correlation coefficient is larger and the relative error is smaller for ann 7 model as compared to those of the gradient model in the a priori test in an a posteriori analysis the performance of ann 7 model shows advantage over the dynamic smagorinsky model and dynamic mixed model in the prediction of spectra and structure functions of velocity and temperature and instantaneous flow structures artificial neural network is a promising tool for understanding the physical fundamentals of sgs unclosed terms with further improvement

nonparametric density estimation with a parametric start the traditional kernel density estimator of an unknown density is by construction completely nonparametric in the sense that it has no preferences and will work reasonably well for all shapes the present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities for example the normal while not losing much in precision when the true density is far from the parametric class the idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor this works well in cases where the correction factor function is less rough than the original density itself extensive comparisons with the kernel estimator are carried out including exact analysis for the class of all normal mixtures the new method with a normal start wins quite often even in many cases where the true density is far from normal procedures for choosing the smoothing parameter of the estimator are also discussed the new estimator should be particularly useful in higher dimensions where the usual nonparametric methods have problems the idea is also spelled out for nonparametric regression

using simex for smoothing parameter choice in errors in variables problems simex methods are attractive for solving curve estimation problems in errors in variables regression using parametric or semiparametric techniques however nonparametric approaches are generally of quite a different type being based on for example kernels local linear modeling ridging orthogonal series or splines all of these techniques involve the challenging and not well studied issue of empirical smoothing parameter choice we show that simex can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors in variable regression in particular we suggest an approach based on multiple error inflated or remeasured data sets and extrapolation

the basic equations for the large eddy simulation of turbulent flows in complex geometry abstract the equations for large eddy simulation les of turbulent flows are derived by applying a filtering operation to the navier stokes equations les of inhomogeneous turbulent flows requires the use of filters with variable filter width the use of such filters invalidates the standard derivation of the basic equations for the filtered fields since the filtering operation in general does not commute with the operation of differentiation in this paper an alternate definition of the filtering operation based on the mapping function of the nonuniform grid is introduced it is shown that with this modified definition the filtering and differentiation operations commute up to an error which is second order in the filter width it is also shown that the commutation error can be expressed in terms of the filtered field and its derivatives as an asymptotic series in the square of the filter width these results are then applied to the navier stokes equations to derive the basic equations satisfied by the filtered fields

underlying mechanism of numerical instability in large eddy simulation of turbulent flows this paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation m ida and n taniguchi phys rev e 68 036705 2003 in our previous paper it was shown based on a simple assumption regarding the instantaneous streamwise velocity that the application of the gaussian filter to the incompressible navier stokes equations can result in the appearance of a numerically unstable term that can be decomposed into positive and negative viscosities that result raises the question as to whether an accurate solution can be achieved by a numerically stable subgrid scale model in the present paper based on assumptions regarding the statistically averaged velocity we present similar theoretical investigations to show that in several situations the shears appearing in the statistically averaged velocity field numerically destabilize the fluctuation components because of the derivation of a numerically unstable term that represents negative diffusion in a fixed direction this finding can explain the problematic numerical instability that has been encountered in large eddy simulations of wall bounded flows the present result suggests that this numerical problem is universal in large eddy simulations and that if there is no failure in modeling the resulting subgrid scale model can still have unstable characteristics that is the known instability problems of several existing subgrid scale models are not something that one may remove simply by an artificial technique but must be taken seriously so as to treat them accurately

stability theory for dissipatively perturbed hamiltonian systems it is shown that for an appropriate class of dissipatively perturbed hamiltonian systems the number of unstable modes of the dynamics linearized at a nondegenerate equilibrium is determined solely by the index of the equilibrium regarded as a critical point of the hamiltonian in addition the movement of the associated eigenvalues in the limit of vanishing dissipation is analyzed 1995 john wiley sons inc

implicit large eddy simulation of non wall bounded turbulent flows based on the multiscale properties of a high order finite volume method in this paper it is presented the application of a higher order finite volume method based on moving least squares approximations fv mls to the resolution of non wall bounded compressible turbulent flows our approach is based on the monotonically implicit large eddy simulation miles the main idea of miles methodology is the absence of any explicit subgrid scale sgs model in the numerical algorithm to solve turbulent flows in the case of the fv mls method we take advantage of the multiresolution properties of moving least squares approximations and we show that they can be used as an implicit sgs model the numerical results are encouraging the third order fv mls method is able to reproduce the inertial subrange and it obtains better results than other usual numerical schemes in les computations such as the muscl scheme we note that in the present state of this research the numerical method is not yet suited for wall bounded flows this paper is the first step in the application of the fv mls method to general turbulent flows

computational error analysis of a discontinuous galerkin discretization applied to large eddy simulation of homogeneous turbulence a computational error assessment of large eddy simulation les in combination with a discontinuous galerkin finite element method is presented for homogeneous isotropic decaying turbulence the error landscape database approach is used to quantify the total simulation error that arises from the use of the smagorinsky eddy viscosity model in combination with the galerkin discretization we adopt a modified hllc flux allowing an explicit control over the dissipative component of the numerical flux the optimal dependence of the smagorinsky parameter on the spatial resolution is determined for second and third order accurate galerkin methods in particular the role of the numerical dissipation relative to the contribution from the smagorinsky dissipation is investigated we observed an exchange of dissipation principle in the sense that an increased numerical dissipation implied a reduction in the optimal smagorinsky parameter the predictions based on galerkin discretization with fully stabilized hllc flux were found to be less accurate than when a central discretization with mainly smagorinsky dissipation was used this was observed for both the second and third order galerkin discretization suggesting to emphasize central discretization of the convective nonlinearity and stabilization that mimics eddy viscosity as sub filter dissipation

local quasi likelihood with a parametric guide generalized linear models and the quasi likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves however nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in fan heckman and wand j amer statist assoc 90 1995 141 150 in this work we propose a unified family of parametrically guided nonparametric estimation schemes this combines the merits of both parametric and nonparametric approaches and enables us to incorporate prior knowledge asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart

numerical integration of constrained hamiltonian systems using dirac brackets we study the numerical properties of the equations of motion of constrained systems derived with dirac brackets this formulation is compared with one based on the extended hamiltonian as concrete examples a pendulum in cartesian coordinates and a chain molecule are treated

a dynamic variational multiscale method for large eddy simulations on unstructured meshes abstract a dynamic version of the variational multiscale vms method for large eddy simulation les on unstructured meshes of turbulent compressible flows is presented its key features include two variational analogues of germano s algebraic identity and a computationally efficient agglomeration based numerical procedure agglomeration is used both for separating a priori the scales and computing dynamically a smagorinsky parameter and the turbulent prandtl number on unstructured finite volume or finite element meshes numerical predictions of low speed 20 angle of attack turbulent flows past a 6 1 prolate spheroid and a forward swept scaled wing are presented they are contrasted with counterpart results obtained using similar implementations on unstructured meshes of the vms les traditional les and traditional dynamic les methods they are also compared to experimental data when available

interactions of breaking waves with a current over cut cells by design of the external and internal wave current generators the objective of this paper is to extend our efficient navier stokes solver t li p troch j de rouck wave overtopping over a sea dike j comput phys 198 2004 686 726 for modelling of interactions between breaking waves and a current over a cut cell grid based on a dynamic subgrid scale sgs model this solver is constructed by a novel vof finite volume approach coupled with surface tension when studying waves following a positive current our external generator creates the combined inflow motions of waves and a current which is viewed as one type of wavy inflow conditions for cases of waves against strong currents our internal generator describes the opposing current by incorporating the source function to the continuity and momentum equations as a net driving force acting on the fluid elements lying within the finite thickness source region the outgoing waves downstream are dissipated with a breaking type wave absorber placed in the tank extremity five test cases recommended are of distinctly different applications of interest characterized by overtopping of following waves over sloping and vertical structures under the grid refinement effects the results in 2d and 3d are in close agreement with the experimental data available in terms of the surface wave additionally the performance of convergence in computations is also investigated including full discussion for waves on beaches between 2d and 3d by visualization of the motions that describe the physics of turbulence it has been shown that our solver can capture most of the significant features in wave current interactions varying with three different current speeds positive zero negative

locally parametric nonparametric density estimation this paper develops a nonparametric density estimator with parametric overtones suppose f x is some family of densities indexed by a vector of parameters we define a local kernel smoothed likelihood function which for each x can be used to estimate the best local parametric approximant to the true density this leads to a new density estimator of the form f x o x thus inserting the best local parameter estimate for each new value of x when the bandwidth used is large this amounts to ordinary full likelihood parametric density estimation while for moderate and small bandwidths the method is essentially nonparametric using only local properties of data and the model alternative ways more general than via the local likelihood are also described the methods can be seen as ways of nonparametrically smoothing the parameter within a parametric class properties of this new semiparametric estimator are investigated our preferred version has approximately the same variance as the ordinary kernel method but potentially a smaller bias the new method is seen to perform better than the traditional kernel method in a broad nonparametric vicinity of the parametric model employed while at the same time being capable of not losing much in precision to full likelihood methods when the model is correct other versions of the method are approximately equivalent to using particular higher order kernels in a semiparametric framework the methodology we develop can be seen as the density estimation parallel to local likelihood and local weighted least squares theory in nonparametric regression

a simple bias reduction method for density estimation a new method for bias reduction in nonparametric density estimation is proposed the method is a simple two stage multiplicative bias correction its theoretical properties are investigated and simulations indicate its practical potential the method is easy to compute and to analyse and extends simply to multivariate and other estimation problems

space time discontinuous galerkin method for the compressible navier stokes equations a space time discontinuous galerkin finite element method for the compressible navier stokes equations is presented we explain the space time setting derive the weak formulation and discuss our choices for the numerical fluxes the resulting numerical method allows local grid adaptation as well as moving and deforming boundaries which we illustrate by computing the flow around a 3d delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2d airfoil in rapid pitch up maneuver

parametrically assisted nonparametric estimation of a density in the deconvolution problem nonparametric estimation of a density from contaminated data is a difficult problem for which convergence rates are notoriously slow we introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density without degrading much the quality of purely nonparametric estimators in other cases we establish optimal convergence rates for our problem and discuss estimators that attain these rates the very good numerical properties of the methods are illustrated via a simulation study supplementary materials for this article are available online

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

enhancement of an industrial finite volume code for large eddy type simulation of incompressible high reynolds number flow using near wall modelling abstract we present a validation strategy for enhancement of an unstructured industrial finite volume solver designed for steady rans problems for large eddy type simulation with near wall modelling of incompressible high reynolds number flow different parts of the projection based discretisation are investigated to ensure les capability of the numerical method turbulence model parameters are calibrated by using a minimisation of least squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow then the method is applied to the flow over a backward facing step at reh 37 500 of special interest is the role of the spatial and temporal discretisation error for low order schemes for wall bounded flows present results confirm existing best practice guidelines for mesh design for free shear layers a sensor to quantify the resolution quality of the les based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at reh 37 500

local polynomial regression and simulation extrapolation summary the paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error we address the measurement error with cook and stefanski s simulation extrapolation simex algorithm our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses simex s particular estimation method and considers higher degree local polynomial estimators we illustrate the accuracy of our asymptotic expressions with a monte carlo study compare our method with other estimators with a second set of monte carlo simulations and apply our method to a data set from nutritional epidemiology simex was originally developed for parametric models although simex is in principle applicable to nonparametric models a serious problem arises with simex in nonparametric situations the problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing we believe that this is the first paper to address this difficulty

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

estimation of integrated squared density derivatives from a contaminated sample we propose a kernel estimator of integrated squared density derivatives from a sample that has been contaminated by random noise we derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term this coincides with results that are available for non contaminated observations we then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives based on contaminated data we propose a data driven bandwidth selection procedure of the plug in type and investigate its finite sample performance via a simulation study

convergence of gauge method for incompressible flow a new formulation a gauge formulation of the incompressible navier stokes equations in terms of an auxiliary field a and a gauge variable u a was proposed recently by e and liu this paper provides a theoretical analysis of their formulation and verifies the computational advantages we discuss the implicit gauge method which uses backward euler or crank nicolson in time discretization however the boundary conditions for the auxiliary field a are implemented explicitly vertical extrapolation the resulting momentum equation is decoupled from the kinematic equation and the computational cost is reduced to solving a standard heat and poisson equation moreover such explicit boundary conditions for the auxiliary field a will be shown to be unconditionally stable for stokes equations for the full nonlinear navier stokes equations the time stepping constraint is reduced to the standard cfl constraint t x c we also prove first order convergence of the gauge method when we use mac grids as our spatial discretization the optimal error estimate for the velocity field is also obtained

density estimation in the presence of heteroscedastic measurement error we consider density estimation when the variable of interest is subject to heteroscedastic measurement error the density is assumed to have a smooth but unknown functional form that we model with a penalized mixture of b splines we treat the situation in which multiple mismeasured observations of each variable of interest are observed for at least some of the subjects and the measurement error is assumed to be additive and normal the measurement error variance function is modeled with a second penalized mixture of b splines the article s main contributions are to address the effects of heteroscedastic measurement error effectively explain the biases caused by ignoring heteroscedasticity and present an equivalent kernel for a spline based density estimator derivation of the equivalent kernel may be of independent interest we use small sigma asymptotics to approximate the biases incurred by assuming that the measurement error is homoscedastic when it actually is heteroscedastic the biases incurred

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

on the accuracy of impulse methods for fluid flow a lagrangian numerical method based on impulse variables is analyzed the relation between discrete impulse vectors and vortex dipoles with a prescribed dipole moment is presented and used to adapt the high accuracy cutoff functions of vortex methods for use in impulse based methods the long time implementation of the impulse method is shown to contain a source of error whose growth in time leads to a severe loss of accuracy in interior flows applications for which impulse methods are well suited are identified

an ergodic sampling scheme for constrained hamiltonian systems with applications to molecular dynamics this article addresses the problem of computing the gibbs distribu tion of a hamiltonian system that is subject to holonomic constraints in doing so we extend recent ideas of cances et al m2an vol 41 no 2 pp 351 389 2007 who could prove a law of large numbers for unconstrained molecular systems with a separable hamiltonian em ploying a discrete version of hamilton s principle studying ergodicity for constrained hamiltonian systems we specifically focus on the numerical discretization error even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization the discretization error is taken care of by means of a hybrid monte carlo al gorithm that allows for sampling bias free expectation values with respect to the gibbs measure independently of the stable step size we give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide

a computational error assessment of central finite volume discretizations in large eddy simulation using a smagorinsky model we present a framework for the computational assessment and comparison of large eddy simulation methods we apply this to large eddy simulation of homogeneous isotropic decaying turbulence using a smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions we compare four different central finite volume methods these discretization methods arise from the four possible combinations that can be made with a second order and a fourth order central scheme for either the convective and the viscous fluxes by systematically varying the simulation resolution and the smagorinsky coefficient we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error we include both physics based and mathematics based error definitions leading to different error measures designed to emphasize either errors in large or in small scale flow properties it is shown that the evaluation of simulations based on a single physics based error may lead to inaccurate perceptions on quality we demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy both for physics based and mathematics based errors parameter regions where all considered errors are simultaneously near optimal are referred to as multi objective optimal parameter regions the effects of discretization errors are particularly important at marginal spatial resolution such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations under these circumstances the asymptotic error behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors we find that the level of overall simulation errors for a second order central discretization of both the convective and viscous fluxes the 2 2 method and the fully fourth order 4 4 method is equivalent in their respective multi objective optimal regions mixed order methods i e the 2 4 and 4 2 combinations yield errors which are considerably higher

hamilton based numerical methods for a fluid membrane interaction in two and three dimensions the hamiltonian formulation of incompressible inviscid fluid dynamics is recalled numerical methods based on this formulation have several conservation properties that make them attractive this formulation is applied to study the interaction of a fluid with a membrane in two and three dimensions linear analysis is performed in two and three dimensions for axisymmetric flow the result in two dimensions agrees with linear analysis obtained by the vorticity formulation numerical schemes based on this formulation are derived and applied to the evolution of membranes in two and three dimensions the numerical results are in agreement with linear analysis

explicit filtering and exact reconstruction of the sub filter stresses in large eddy simulation explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation les we use a differential filter namely the inverse helmholtz operator which is readily applied to unstructured meshes the filter is invertible which allows the sub filter scale sfs stresses to be exactly reconstructed in terms of the filtered solution unlike eddy viscosity models the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime the sub grid scale sgs stresses are not recoverable by reconstruction but the second order finite element method used here is an adequate source of numerical dissipation in lieu of an sgs model results for incompressible turbulent channel flow at re 180 are presented which show that explicit filtering and exact sfs reconstruction is a significant improvement over the standard les approach of implicit filtering and eddy viscosity sgs modelling

the dynamic procedure for accuracy improvement of numerical discretizations in fluid mechanics in cfd computations discretization or truncation errors should be small providing an acceptable level of accuracy in this paper an extension is made of the recently proposed les formalism based on sampling operators it is shown that the sampling based dynamic procedure in combination with an appropriate truncation error model can be used as a technique to increase the numerical accuracy of a discretization the technique is resemblant to the well known richardson extrapolation the procedure is tested on a 1d convection diffusion equation and a 2d lid driven cavity at re 400 using a finite difference method promising results are found

a further study of numerical errors in large eddy simulations numerical errors in large eddy simulations les arise from aliasing and discretization errors and errors in the subfilter scale sfs turbulence model using a direct numerical simulation dns dataset of stably stratified shear flow to perform a priori tests we compare the numerical error from several finite difference schemes to the magnitude of the sfs force this is an extension of ghosal s analysis j comput phys 125 1996 187 to realistic flow fields by evaluating different grid resolutions as well as different filter grid ratios we provide guidelines for les for a second order finite difference scheme a filter grid ratio of at least four is desired for a sixth order pade scheme a filter grid ratio of two is sufficient