growth of rounding errors and repetitivity of large eddy simulations this paper studies the propagation of rounding errors in large eddy simulation and shows that instantaneous flowfields produced by large eddy simulation are partially controlled by these rounding errors and depend on multiple parameters number of processors used for parallel simulation even in an explicit code changes in initial conditions even of the order of machine accuracy machine precision simple double or quadruple etc using a laminar poiseuille pipe flow a fully developed turbulent channel flow and a complex burner geometry as test cases results show that only turbulent flows exhibit a high sensitivity to these parameters these results confirm that large eddy simulation reflects the true nature of turbulence insofar as it may exponentially amplify infinitely small perturbations on initial conditions in time however they highlight an often overlooked limitation of large eddy simulation in terms of validation and prediction of unsteady phenomena

development of high order taylor galerkin schemes for les in this paper we describe the implementation and development of a new taylor galerkin finite element scheme within an unstructured hybrid parallel solver the scheme has been specifically conceived for unsteady les it is third order in space and time and has a low dissipative error minimal additional cpu costs are achieved by using a new approximation of the finite element integrals and a simple iterative method for the approximate inversion of the modified mass matrix basic convective tests are carried out in 2 and 3 dimensions for arbitrary elements numerical estimates of the order of convergence are presented on regular and perturbed grids finally test cases that are relevant to les are carried out and these clearly demonstrate the important improvements that our new scheme offers relative to a selection of existing methods

direct noise simulation of a canonical high lift device and comparison with an analytical model the noise of a canonical main element flap high lift device hld is computed directly using compressible wall resolved large eddy simulation an experimental database for the chosen configuration allows us to successfully validate the chosen numerical approach both the noise sources and the far field acoustic pressure are shown to be well predicted although the two elements trailing edge noise can be observed in the near field the flap remains as the dominant source in the far field the simplicity of the studied configuration enables the comparison of the validated numerical results with a recently developed analytical model that takes into account the diffraction of the flap noise by the main element a two dimensional 2d with and without kutta condition and a three dimensional without kutta correction analytical formulations are compared with the numerical results all formulations compare favorably with the numerical reference in terms of noise levels and directivities however the 2d formulation with a kutta correction provides the best quantitative agreement as expected from the narrow span of the numerical domain the recently developed analytical model is therefore a good predictive tool for hld showing that it can properly account for the diffraction effect of the main element on the flap main noise source

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

coloring non gaussian sequences we propose a novel method for generating random sequences matching both a target non gaussian distribution and a target autocorrelation in the proposed scheme samples matching the target distribution are drawn independently and then suitably rearranged to match the target autocorrelation our method overcomes the difficulties of the standard method in generating sequences with unknown inverse distribution many examples are included

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

compatibility of characteristic boundary conditions with radial equilibrium in turbomachinery simulations setting up outlet boundary conditions in configurations that have a strong rotating motion is a crucial issue for turbomachinery simulations this is usually done using the so called radial equilibrium assumption which is used before the simulation and provides an approximate expression for the pressure profile to impose in the outlet plane this paper shows that recent methods developed for compressible flows based on characteristic methods including the effects of transverse terms can capture the radial equilibrium naturally without having to impose a precomputed pressure profile in addition these methods are also designed to control acoustic reflections on boundaries and the present work suggests that they could replace classical radial equilibrium assumption approximations when nonreflecting boundary conditions are required at the outlet of a turbomachine simulation for example in large eddy simulation this is demonstrated in two cases 1 a simple annulus flow with a swirl imposed at the inlet and 2 a transonic turbine vane

evaluation of numerical strategies for large eddy simulation of particulate two phase recirculating flows predicting particle dispersion in recirculating two phase flows is a key issue for reacting flows and a potential application of large eddy simulation les methods in this study euler euler and euler lagrange les approaches are compared in the bluff body configuration from boree et al j boree t ishima i flour the effect of mass loading and inter particle collisions on the development of the polydispersed two phase flow downstream of a confined bluff body j fluid mech 443 2001 129 165 where glass beads are injected into a complex recirculating flow these tests are performed for non reacting non evaporating sprays but are mandatory validations before computing realistic combustion chambers two different codes one explicit and compressible and the other implicit and incompressible are also tested on the same configuration results show that the gas flow is well predicted by both codes the dispersed phase is also well predicted by both codes but the lagrangian approach predicts root mean square values more accurately than the eulerian approach the effects of mesh solvers and numerical schemes are discussed for each method

comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids this paper describes extensions and tests of characteristic methods for outlet boundary conditions in compressible solvers three methods based on the specification of incoming waves using one and multidimensional approximations are extended to unstructured grids they are first compared for weak to strong vortices propagating on low to high speed mean flows through outlet sections a major issue is to determine the mach number to be used in the specification of the transverse terms that must be taken into account in the incoming wave amplitude specifications for the vortex computations results show that the averaged mach number leads to better results than its local value the boundary conditions are then tested in a more complex case the flow around a turbine blade a reference solution using a long distance between the blade trailing edge and the outlet plane is first computed for this solution outlet boundary conditions have almost no effect on the flow around the blade the distance between the trailing edge and the outlet plane is then shortened and the various characteristic treatments are compared in which intense vortices cross the outlet plane results confirm the conclusions obtained on the simple vortex test case

an introduction to finite element methods for transient advection problems abstract an introduction is presented to time accurate finite element methods recently developed for solving unsteady problems governed by linear and nonlinear advection equations this includes methods making an explicit use of the characteristic curves methods based on the taylor series in time and least squares methods

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

accounting for acoustic damping in a helmholtz solver thermoacoustic helmholtz solvers provide a cheap and efficient way of predicting combustion instabilities however because they rely on the inviscid euler equations at zero mach number they cannot properly describe the regions where aerodynamics may interact with acoustic waves in the vicinity of dilution holes and injectors for example a methodology is presented to incorporate the effect of non purely acoustic mechanisms into a three dimensional thermoacoustic helmholtz solver the zones where these mechanisms are important are modeled as two port acoustic elements and the corresponding matrices which notably contain the dissipative effects due to acoustic hydrodynamic interactions are used as internal boundary conditions in the helmholtz solver the rest of the flow domain where dissipation is negligible is solved by the classical helmholtz equation with this method the changes in eigenfrequency and eigenmode structure introduced by the acoustic hydrodynamic effects are captured while keeping the simplicity and efficiency of the helmholtz solver the methodology is successfully applied on an academic configuration first with a simple diaphragm then with an industrial swirler with matrices measured from experiments and large eddy simulation

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

high order taylor galerkin and adaptive h p methods for second order hyperbolic systems application to elastodynamics a new family of high order taylor galerkin schemes is presented for the analysis of second order hyperbolic systems the use of such schemes within an adaptive h p finite element strategy for spatial approximation in two dimensional problems is described numerical results are presented to demonstrate performance of these methods

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

assessing goodness of fit of parametric regression models for lifetime data graphical methods graphical methods are often used to check goodness of fit of models to data it is common to plot residuals against a reference distribution so that when the model fits the data the configuration should be close to a straight line since the resemblance to a straight line is often unclear it has been suggested to add simulated envelopes within which the configuration is expected to lie the implementation of this method for survival data analysis is not straightforward in this paper we point out the difficulties which arise in constructing envelopes on residual plots for randomly censored data methods are suggested to deal with the problems and evaluated they are illustrated by simulated data and on a follow up study of myeloma

graphical generalized residuals in fitting distributions applications to epidemiological follow up data three kinds of generalized residuals based on probability integral transformation are defined and their roles in graphical goodness of fit testing are discussed although they are useful in fitting parametric distributions their value is questionable however in fitting cox s proportional hazard rate phr models they almost always appear to give a good fit because of a almost non parametric nature of the phr models b heavy right hand censoring in epidemiological data and c scale adjustment in graphical presentation thus the apparent overall fit has little inferential meaning but the residuals are useful in exploratory analysis a simple method based on non parametric stratified residual plots for selection of risk factors is discussed it is in fact equivalent to comparison of several empirical survival functions one for each set of values stratum of a covariable under consideration it is also suggested that for the preliminary phr model the continuous variables should be discretized and indicator variables used in the model to check analytically the graphical perception of the possible functional form of the contribution of each covariable to the phr model

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

on the second order statistics of nakagami fading simulators we derive important second order statistics joint distribution of the envelope and its time derivative second order distribution autocorrelation level crossing rate and average fade duration of an existing nakagami fading simulator and show that these statistics but the autocorrelation differ considerably from the well established statistics of the classical simulator

propagation and stability of wavelike solutions of finite difference equations with variable coefficients abstract an asymptotic approach is used to analyze the propagation and dissipation of wavelike solutions to finite difference equations it is shown that to first order the amplitude of a wave is convected at the local group velocity and varies in magnitude if the coefficients of the finite difference equation vary asymptotic boundary conditions coupling the amplitudes of different wave solutions are also derived equations are derived for the motion of wavepackets and their interaction at boundaries comparison with numerical experiments demonstrates the success and limitations of the asymptotic approach finally a global stability analysis is developed

comparative study of coupling coefficients in dirichlet robin procedure for fluid structure aerothermal simulations this paper tests the performance of coupling coefficients of a dirichlet robin transmission procedure in the context of steady conjugate heat transfer cht particular emphasis is put on the optimal coefficients highlighted recently in a theoretical study based on a normal mode stability analysis this work can be seen as the logical continuation of that study in order to assess the relevance of the coefficients provided by the model problem in a realistic aerothermal computation first the numerical and physical cht modeling methodologies are presented then the optimal procedure applied to a dirichlet robin algorithm one coefficient method is briefly described in order to gauge the ability of this model to predict the stability and convergence properties of a realistic case it is compared on a heated cylinder in a flowfield test case a series of five coupling coefficients and three fourier numbers are considered these parameters are introduced into the model problem as data to compute the amplification factor and the stability limits the stability and convergence properties predicted by the model problem are then compared to those obtained in the cht computation this comparison shows an excellent overall agreement moreover for all the fourier numbers considered the numerical solution is stable and oscillation free when the optimal coefficient of the model problem is used this would suggest that the one dimensional normal mode analysis can provide relevant coefficients directly applicable to real cht problems

high order taylor galerkin methods for linear hyperbolic systems a new family of high order taylor galerkin schemes is presented for the analysis of first order linear hyperbolic systems the schemes are unconditionally stable which makes them very attractive to use in conjunction with adaptive hp finite element methods for spatial approximation