new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

a robust method for generating inflow conditions for direct simulations of spatially developing turbulent boundary layers a method for generating inflow conditions for direct numerical simulations dns of spatially developing turbulent boundary layers is presented the method is a modification of that of lund et al j comput phys 140 1998 233 the approach of lund et al is based on having an auxiliary simulation code a in a three dimensional domain similar to that of the main simulation code b the instantaneous velocity field on a selected plane in code a is used as the instantaneous inflow conditions for code b the inflow conditions for code a are generated through a sequence of operations in which the velocity field at a downstream station is rescaled and re introduced at the inlet plane our present method modifies the operations in code a by introducing a set of additional steps preceding the rescaling process this set involves imposing at the inlet plane an appropriate spectrum e k for the turbulence kinetic energy tke and a condition for insuring that the statistical correlation u 1 u 3 between the streamwise and vertical velocity fluctuations retain a non vanishing magnitude this modification is essential for sustaining the production rate of tke near the wall throughout the domain our dns results obtained with the new modification are in excellent agreement with the experimental data of degraaff and eaton j fluid mech 422 2000 319 for re 0 1430

further development of the k enstrophy turbulence closure model the k model is extended to the study of two dimensional and three dimensional separated external e ows where morkovin s hypothesis is expected to hold the resulting model is free of damping and wall functions and is coordinate independent further all modeled correlations are tensorially consistent and galilean invariant applications include a variety of separated e ows over airfoils and a cylinder offset e are juncture comparisons are made with other turbulence models and experiment in general good agreement with experiment is indicated the results demonstrate that it is possible to develop a two equation turbulence model that is capable of predicting separated e ows without sacrie cing performance for free shear layers

discrete series representations for mathfrak sl 2 1 meixner polynomials and oscillator models we explore a model for a one dimensional quantum oscillator based on the lie superalgebra for this purpose a class of discrete series representations of is constructed each representation characterized by a real number 0 in this model the position and momentum operators of the oscillator are odd elements of and their expressions involve an arbitrary parameter in each representation the spectrum of the hamiltonian is the same as that of a canonical oscillator the spectrum of a position operator can be continuous or infinite discrete depending on the value of we determine the position wavefunctions both in the continuous and the discrete case and discuss their properties in the discrete case these wavefunctions are given in terms of meixner polynomials from the embedding it can be seen why the case 1 corresponds to a paraboson oscillator consequently taking the values 1 2 1 in the model yields a canonical oscillator

reconstruction of turbulent fluctuations using a hybrid rans les approach a hybrid rans les approach is presented and assessed considering several flows which can be interpreted as the most general case of the nlde approach as defined by morris et al p j morris l n long a bangalore and a wang j comput phys 133 56 1997 a decomposition into three parts of the exact solution of the navier stokes equations is considered mean flow resolved fluctuations and unresolved subgrid fluctuations the mean flow is computed using a classical rans method while resolved fluctuations are derived from a les method this approach is succesfully assessed on the stationary and the pulsed plane channel flow configurations the case of the flow around a low pressure turbine blade is discussed in a second step the hybrid method is also demonstrated to be robust with respect to several sources of error and provides good results in the case of a coarsened grid simulation a reduced computational domain simulation and nonconsistent mean flow fields

comparison between simultaneous and sequential updating in 2n 1 1 cellular automata properties of cellular automata with packard wolfram code 2n 1 1 have been studied without and with noise on square n 4 and triangular n 6 lattices the outer totalistic rule used assign a central spin opposite to the majority spin of its neighbourhood and flips it in the case of equality starting from random configurations with a variable proportion r of up spins different relaxation behaviours and equilibrium structures are obtained a ferromagnetic f structure and an antiferromagnetic af structure for simultaneous and sequential updatings respectively on a square lattice when the spins are processed simultaneously in the presence of noise a first order transition f af is observed for a square lattice and a second order transition for a triangular lattice the results show similarities with ising models domains but also strong differences magnetization as a function of r

numerical computations of supersonic base flow with special emphasis on turbulence modeling abstract a zonal implicit time marching navier stokes computational technique has been used to compute the turbulent supersonic base flow over cylindrical afterbodies a critical element of calculating such flows is the turbulence model various eddy viscosity turbulence models have been used in the base region flow computations these models include two algebraic turbulence models and a two equation k epsilon model the k epsilon equations are developed in a general coordinate system and solved using an implicit algorithm calculations with the k epsilon model are extended up to the wall flow field computations have been performed for a cylindrical afterbody at m 2 46 and at angle of attack alpha 0 the results are compared to the experimental data for the same conditions and the same configuration details of the mean flow field as well as the turbulence quantifies have been presented in addition the computed base pressure distribution has been compared with the experiment in general the k epsilon turbulence model performs better in the near wake than the algebraic models and predicts the base pressure much better base flow base pressure turbulence models wake supersonic flow

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

reynolds averaged navier stokes large eddy simulations of supersonic base flow several zonal and nonzonal hybrid reynolds averaged navier stokes large eddy simulation approaches have been assessed to handle a high reynolds number supersonic base flow the results obtained on 5 and 13 5 x 10 6 points grids are compared to the available experimental data herrin j l and dutton j c supersonic base flow experiments in the near wake of a cylindrical afterbody aiaa journal vol 32 no 77 1994 and the capabilities of these different methodologies to predict supersonic flows are discussed the highly compressible separated shear layer proved to be a challenging issue for hybrid methods due to an alteration in the instability process as compared to the incompressible case leading to three dimensional coherent structures numerous numerical parameters relevant to hybrid methods have been assessed the incoming boundary layer thickness needs to be properly set while a weak influence of the subgrid scale model is observed when small scale structures in the separating mixing layer are resolved another finding of the present study is the dramatic influence displayed by the numerical dissipation on the flowfield sensitivity to the c des model constant is observed even with the finest grid leading to a delay in the generation of instabilities in the shear layer

hybrid reynolds averaged navier stokes large eddy simulations of supersonic turbulent mixing aturbulentmixinglayerformedfromtwosupersonicstreamsinitially separatedbyasplitterplateisinvestigated withahybridcomputationalmethodusingareynolds averagednavier stokes rans approachforwall bounded regions and a large eddy simulation les approach for the turbulent mixing region simulations of the mixing layer predict a vortex shedding originating from the splitter base and then a rapid transition to turbulence which is in agreement with experimental observations as a result the potential of the hybrid method is demonstrated for e ows in which a geometric feature such as the blunt splitter plate considered here provides the dominant unsteady feature leading to turbulence without imposing additional ine ow disturbances parametric studies of les subgrid modeling settings variations in the spanwise computational domain and wall temperature settings in the rans region were conducted the subgrid model cases using a baseline computational grid with small spanwise computational domain overpredicted the mixing layer turbulencelevels but only showed small variation in the mixing layer predictions with large changes in the model parameters the cases examining wider spanwise domains enabled more turbulent energy to be released in the spanwise direction which in turn reduced axial and vertical turbulence levels finally prescribing the wall temperatures in the rans regions instead of using the more traditional adiabatic wall boundary conditions further reduced turbulence levels and enabled reasonable agreement with experimental data

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

universality two dimensional kauffman model for parallel and sequential updating kauffman s random boolean nets are studied on the square lattice by computer simulation comparing parallel and sequential updating of the automata at the phase transition the fractal dimensions of time and actual damage are found to be independent of the updating method

time quantization and q deformations we extend to quantum mechanics the technique of stochastic subordination by means of which one can express any semi martingale as a time changed brownian motion as examples we considered two versions of the q deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules

oblique shock wave boundary layer interaction using near wall reynolds stress models a synthesis is presented of the predictive capability of a family of near wall wall normal free reynolds stress models which are completely independent of wall topology i e of the distance fromthe wall and the normal to thewall orientation for oblique shock wave turbulent boundary layer interactions for the purpose of comparison results are also presented using a standard low turbulence reynolds number k e closure and a reynolds stress model that uses geometric wall normals and wall distances studied shock wave mach numbers are in the range msw 2 85 2 9 and incoming boundary layer thickness reynolds numbers are in the range re 0 1 2 106 computations were carefully checked for grid convergence comparison with measurements shows satisfactory agreement improving on results obtained using a k e model and highlights the relative importance of redistribution and diffusion closures indicating directions for future modeling work

a unified rans les model large eddy simulation les is computationally extremely expensive for the investigation of wall bounded turbulent flows at high reynolds numbers a way to reduce the computational cost of les by orders of magnitude is to combine les equations with reynolds averaged navier stokes rans equations used in the near wall region a large variety of such hybrid rans les methods are currently in use such that there is the question of which hybrid rans les method represents the optimal approach the properties of an optimal hybrid rans les model are formulated here by taking reference to fundamental properties of fluid flow equations it is shown that unified rans les models derived from an underlying stochastic turbulence model have the properties of optimal hybrid rans les models the rest of the paper is organized in two parts first a priori and a posteriori analyses of channel flow data are used to find the optimal computational formulation of the theoretically derived unified rans les model and to show that this computational model which is referred to as linear unified model lum does also have all the properties of an optimal hybrid rans les model second a posteriori analyses of channel flow data are used to study the accuracy and cost features of the lum the following conclusions are obtained i compared to rans which require evidence for their predictions the lum has the significant advantage that the quality of predictions is relatively independent of the rans model applied ii compared to les the significant advantage of the lum is a cost reduction of high reynolds number simulations by a factor of 0 07 re 0 46 for coarse grids the lum has a significant accuracy advantage over corresponding les iii compared to other usually applied hybrid rans les models it is shown that the lum provides significantly improved predictions

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

k zeta enstrophy compressible turbulence model for mixing layers and wall bounded flows we extend the model of robinson et al to compressible turbulent flows the success of the in reproducing a variety of incompressible flows should provide a good basis for the current model as in the incompressible model the current model will be based on the exact compressible equations to ensure that the correct physics is incorporated

a connection between the percolation transition and the onset of chaos in the kauffman model it is demonstrated numerically that the percolation transition of the unstable sites and the onset of chaos in the kauffman model 1969 happens for the same value of the bias on the randomly chosen rules in the two dimensional triangular lattice and in the three and four dimensional hypercubic lattices the percolation thresholds for the stable sites are different for the three and presumably also four dimensional lattices on the triangular lattice the differences between the thresholds are too small to be resolved the fractal dimension of the damage is calculated and also the spreading time on the four dimensional hypercubic lattice

on position and momentum operators in the q oscillator the position and momentum operators of the q oscillator with the main relation aa qa a 1 are symmetric but not self adjoint if q 1 they have one parameter family of self adjoint extensions these extensions are given explicitly their spectra and eigenfunctions are derived spectra of different extensions do not intersect the results show that the creation and annihilation operators a and a of the q oscillator at q 1 cannot determine a physical system without further more precise definition in order to determine a physical system we have to choose appropriate self adjoint extensions of the position and momentum operators

the oscillator model for the lie superalgebra sh 2 2 and charlier polynomials we investigate an algebraic model for the quantum oscillator based upon the lie superalgebra sh 2 2 known as the heisenberg weyl superalgebra or the algebra of supersymmetric quantum mechanics and its fock representation the model offers some freedom in the choice of a position and a momentum operator leading to a free model parameter using the technique of jacobi matrices we determine the spectrum of the position operator and show that its wavefunctions are related to charlier polynomials cn with parameter 2 some properties of these wavefunctions are discussed as well as some other properties of the current oscillator model

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

the compressible hybrid rans les formulation using an additive operator in this work the compressible governing equations for the hybrid reynolds averaged large eddy simulations are formally derived by applying a hybrid filter to the navier stokes equations this filter is constructed by linearly combining the reynolds average rans and large eddy simulation les operators with a continuous blending function the derived hybrid equations include additional terms that represent the interactions between rans and les formulations the relevance of these terms is investigated in flat plate turbulent boundary layer simulations and indicate that these additional terms play a fundamental role in compensating for the turbulence that is neither modeled nor resolved in the transition region between rans and les results also show that when the additional terms are included the calculations are not very sensitive to the blending function implemented in the hybrid filter in the contrary when these terms are neglected and a step function is implemented in the hybrid filter nonphysical discontinuities are predicted in the flow statistics

a robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state this paper addresses issues in high fidelity numerical simulations of transcritical turbulent flows at supercritical pressure the proposed strategy builds on a tabulated look up table method based on refprop database for an accurate estimation of non linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions based on the look up table method we propose a numerical method that satisfies high order spatial accuracy spurious oscillation free property and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface the method introduces artificial mass diffusivity to the continuity and momentum equations in a physically consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious oscillation free property in the velocity field the pressure evolution equation is derived from the full compressible navier stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look up table method flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness accuracy and consistency of the proposed approach

compressible boundary layer predictions at high reynolds number using hybrid les rans methods simulations of compressible boundary layer flow at three different reynolds numbers re 5 59 10 4 1 78 10 5 and 1 58 x 10 6 are performed using a hybrid large eddy simulation reynolds averaged navier stokes method variations in the recycling rescaling method the higher order extension the choice of primitive variables the reynolds averaged navier stokes to large eddy simulation transition parameters and the mesh resolution are considered in order to assess the model the results indicate that the present model can provide good predictions of the mean flow properties second moment statistics and structural features of the boundary layers considered normalized turbulent statistics in the outer layer are found to be independent of reynolds number similar to incompressible turbulent boundary layers

large eddy reynolds averaged navier stokes simulation of a mach 5 compression corner interaction simulations of mach 5 turbulent flow over a 28 deg compression corner are performed using a hybrid large eddy reynolds averaged navier stokes method the model captures the mean flow structure of the interaction reasonably well with observed deficiencies relating to an underprediction of the displacement effects of the shock induced separation region the computational results provide some support for a recent theory concerning the underlying causes of low frequency shock wave oscillation in the simulations the sustained presence of a collection of streaks of fluid with lower higher momentum than the average induces a low frequency undulation of the separation front power spectra obtained at different streamwise stations are in good agreement with experimental results downstream of reattachment the simulations capture a three dimensional mean flow structure dominated by counter rotating vortices that produce wide variations in the surface skin friction predictions of the structure of the reattaching boundary layer agree well with experimental pitot pressure measurements in comparison with reynolds averaged model predictions the hybrid large eddy reynolds averaged navier stokes model predicts more amplification of the reynolds stresses and a broadening of the reynolds stress distribution within the boundary layer that is probably due to reattachment shock motion

on position and momentum operators in the q oscillator algebra the aim of this paper is to study the position and momentum operators in q deformed oscillator algebras the natural form of the position operator is xp qpn a a qpn where p is a real number this operator is an operator representable by a jacobi matrix using the theory of jacobi matrices the theory of classical moment problem and the theory of basic hypergeometric functions it is shown that depending on values of q and p xp can be unbounded symmetric operator which has the deficiency indices 1 1 and hence is not self adjoint but has self adjoint extensions bounded self adjoint operator with continuous simple spectrum or self adjoint operator of trace class therefore with discrete spectrum with zero as the point of accumulation of eigenvalues the connection of the q deformed heisenberg relation px qxp 1 for the position and momentum operators with a q deformation of the quantum harmonic oscillator is also considered

wall normal free reynolds stress model for rotating flows applied to turbomachinery a recently developed near wall wall normal free reynolds stress model is extended and applied to the computation of transonic three dimensional e ows in turbomachinery rotors with tip clearance the reynolds stress model used is completely independent of the distance from the wall and of the normal to the wall direction this is achieved by using a pseudonormal direction dee ned by the gradients of turbulence length scale and anisotropy tensor invariants in the pressure strain echo terms the effects of rotation are included through theexact coriolis termsin the reynolds stress transport equations and through the isotropization of absolute e ow production model used for the rapid pressure strain terms the model is initially validated by comparison with measurements in rotating fully developed plane channel e ows computational results obtained with the proposed reynolds stress model are compared with measurements and with k computations for various operating points of the nasa 37 rotor using a 3 10 6 multiblock computational grid with 41 radial stations within the tip clearance gap the proposed model substantially improves the agreement with measurements compared to existing algebraic and two equation models

analysis and prediction of thin airfoil stall phenomena with hybrid turbulence methodology analysis and prediction of thin airfoil stall phenomena of a naca 64a006 airfoil are numerically investigated using large eddy simulation les reynolds averaged navier stokes rans hybrid methodology with a high order compact differencing scheme subsonic flow of m 0 17 with the high reynolds number of re 5 8 x 10 6 is considered and the angle of attack is varied from 4 0 to 11 0 deg

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

large eddy simulation inflow conditions for coupling with reynolds averaged flow solvers hybrid approaches using a combination of reynolds averaged navier stokes rans approaches and large eddy simulations les have become increasingly popular one way to construct a hybrid approach is to apply separate flow solvers to components of a complex system and to exchange information at the interfaces of the domains for the les flow solver boundary conditions then have to be defined on the basis of the reynolds averaged flow statistics delivered by a rans flow solver this is a challenge which also arises for instance when defining les inflow conditions from experimental data the problem for the coupled rans les computations is further complicated by the fact that the mean flow statistics at the interface may vary in time and are not known a priori but only from the rans solution the present study defines a method to provide les inflow conditions through auxiliary a priori les computations where an les inflow database is generated the database is modified to account for the unsteadiness of the interface flow statistics

hybrid simulation approach for cavity flows blending algorithm and boundary treatment issues the maturation of high performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the reynolds averaged navier stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation the application of a new hybrid approach is discussed where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties as well as the local mesh spacing the utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set removing much of the burden from the grid generation process moreover the model framework allows for the combination of existing closure model equations avoiding the difficulty of formulating a single set of closure coefficients that perform well in both reynolds averaged and large eddy simulation modes simple modifications to common second order accurate reynolds averaged navier stokes algorithms are proposed to enhance the capturing of large eddy motions

zonal detached eddy simulation of the flow around a high lift configuration a zonal hybrid reynolds averaged navier stokes large eddy simulation rans les approach called zonal des used to handle a two dimensional high lift configuration with deployed slat and flap is presented this method allows to reduce significantly the cost of an accurate numerical prediction of the unsteady flow around wings compared to a complete les some issues concerning grid generation as well as the use of zonal detached eddy simulation for a multi element airfoil are discussed the basic planar grid has 250 000 points and the finest spanwise grid has 31 points with az c 0 002 the effort is geared toward detailed comparison of the numerical results with the europiv2 experimental particle image velocimetry data including both mean and fluctuating properties of the velocity field arnott and al

high speed turbulent separated flows consistency of mathematical models and flow physics a large fraction of the experimental database used for validation of computational fluid dynamics cfd predictions of shock induced turbulent separated flows consists of time averaged measurements if meaningful conclusions are to be drawn from comparisons of these time averaged data with computations it is important to understand how the data are generated physically this can be difficult and time consuming but is an essential element in the selection of an appropriate mathematical model for the computation for the separated compression ramp interaction which is widely used as a cfd test case global unsteadiness is a dominant phenomenon without modeling the unsteadiness accurate predictions of the time averaged wall pressure outgoing velocity profiles and other parameters will likely remain elusive irrespective of the turbulence model

large eddy simulation of a supersonic boundary layer using an unstructured grid a mach 3 adiabatic flat plate turbulent boundary layer is studied using large eddy simulation les the filtered compressible navier stokes equations are solved on a three dimensional unstructured grid of tetrahedral cells a compressible extension of the rescaling reintroducing process of lund et al is developed to generate the inflow conditions the effect of the subgrid scale motion is incorporated using two approaches namely monotone integrated les miles and the smagorinsky subgrid scale model a detailed grid refinement study is performed

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

damage spreading in a gradient we propose a new method of analyzing the frozen chaotic transition in a cellular automaton by propagating damage in a gradient we obtain estimations forpc and for the critical exponents for the kauffman model and the mixture of or and xor rules

high order fluxes for conservative skew symmetric like schemes in structured meshes developing high order non dissipative schemes is an important research task for both steady and unsteady flow computations we take as a starting point the built in de aliasing property of the discretized skew symmetric form for the non linear terms of the navier stokes equations recalled in kravchenko and moin 1 two families of high order locally conservative schemes matching this discretized skew symmetric form are considered and rewritten in terms of telescopic fluxes for both finite difference and finite volume approximations in the context of compressible flows the jameson s scheme 2 is shown to be the second order member of larger families of skew symmetric like centered schemes the fourth order finite volume and finite difference and the sixth order finite difference schemes which belong to this family are provided the proposed schemes are extended to shock capturing schemes either by modifying the jameson s artificial viscosity or by hybriding the centered flux with weno 3 fluxes an adapted interpolation is proposed to extend the use of the proposed schemes to non regular grids several tests are provided showing that the conjectured order is properly recovered even with irregular meshes and that the shock capturing properties allow us to improve the second order results for standard test cases the improvement due to fourth order is then confirmed for the estimation of the growth of two ts waves and three crow instability dimensional unstable modes for both confined and free shear flows the last application concerns the steady computation using the spalart allmaras model of a separated boundary layer it confirms that the use of a high order scheme improves the results even in this type of steady applications

blending functions in hybrid large eddy reynolds averaged navier stokes simulations several blending functions for use in hybrid large eddy simulation les reynolds averaged navier stokes rans simulations of shock separated flows are tested the blending functions shift the turbulence closure from a k turbulence model near solid surfaces to a k subgrid closure away from the wall three distinct forms for the blending function are developed one that depends on the ratio of the von karman length scale and the taylor microscale another that depends on the ratio of the rans eddy viscosity to the subgrid eddy viscosity and a third which replaces the von karman length scale in the first form with the distance to the nearest wall comparisons are made for two cases mach 2 79 flow over a 20 deg compression corner and mach 2 88 flow over a 25 deg compression expansion corner inflow boundary conditions for all calculations employ the rescaling reintroducing procedure developed by xiao et al xiao x edwards j r hassan h a and baurle r a inflow boundary conditions for hybrid large eddy reynolds averaged navier stokes simulations aiaa journal v ol 41 no 8 2003 pp 1481 1489 for hybrid les rans simulations of wall bounded flows in general the blending function based on the von karman length scale gives the best results when compared with measured data the skin friction predictions show the highest sensitivity to the various blending functions

inflow boundary conditions for hybrid large eddy reynolds averaged navier stokes simulations inflow boundary conditions are developed for hybrid large eddy simulation les reynolds averaged navier stokes approaches they are based on an extension of the rescaling reintroducing method developed for les to a hybrid scheme a blending function is used to shift the turbulence closure from a model near the wall to a subgrid scale model away from the wall the approach was tested for a flat plate and then applied to the study of a 25 deg compression expansion ramp for a mach number of 2 88 and a reynolds number of 3 24 10 7 m in general improvements over the model were noted in the recovery region the significance of this work is that it provides a way for les methods to address flows at a high reynolds number