a global meshless collocation particular solution method for solving the two dimensional navier stokes system of equations the two dimensional navier stokes system of equations for incompressible fluids is solved by the method of approximate particular solutions maps in its global formulation the fluid velocity and pressure fields are approximated by a linear superposition of particular solutions of a stokes non homogeneous system of equations with multiquadric mq radial basis function as the source term the nonlinear convective terms of the momentum equations are linearly approximated by using a guess value of the velocity field and the resulting linear system of equations is solved by a simple direct iterative scheme picard iteration with the velocity guess given by the solution at the previous iteration although the continuity equation is not explicitly imposed in the resulting formulation the scheme is mass conservative because the particular solutions exactly satisfy the mass conservation equation the proposed numerical scheme is validated by comparison of the obtained numerical results with the corresponding analytical solution of the kovasznay flow problem at different reynolds numbers re from this analysis it is observed that the maps results are stable and accurate for a wide range of shape parameter values in addition lid driven cavity flow problems in rectangular and triangular domains up to re 3200 and re 1000 respectively and the backward facing step at re 800 are solved and the results obtained are compared with corresponding benchmark numerical solutions showing excellent agreement

solution of the implicitly discretised reacting flow equations by operator splitting abstract a non iterative method for handling the coupling of the implicitly discretised time dependent fluid flow equations is described the method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations the main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step with the split sets of equations being amenable to solution by standard techniques at each time step the procedure yields solutions which approximate the exact solution of the difference equations the accuracy of this splitting procedure is assessed for a linearised form of the discretised equations and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time step size by virtue of this it is possible to dispense with iteration thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods this is verified in a companion paper which presents results of computations carried out using the method

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

bracket formulations and energy and helicity preserving numerical methods for the three dimensional vorticity equation abstract the vorticity equation for three dimensional viscous incompressible fluid flows is formulated within different bracket formalisms using the poisson or nambu bracket together with a dissipative bracket the budgets of kinetic energy helicity and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method in particular energy and helicity are conserved precisely in inviscid flow computations the energy and enstrophy dissipate properly owing to viscosity in viscous flow computations and the enstrophy is appropriately produced by the vortex stretching effect in both inviscid and viscous flow computations the relationships between the stream function velocity and vorticity as well as the solenoidal conditions on the velocity and vorticity fields are also inherited numerical experiments on a periodic array of rolls that permits analytical solutions have been done to examine the properties and usefulness of the proposed method

stochastic dominance on unidimensional grids special stochastic dominance relations for probability distributions on a finite grid of evenly spaced points are considered the relations depend solely on iterated partial sums of grid point probabilities and are very computer efficient their corresponding classes of utility functions for expected utility comparisons consist of functions defined on the grid that mimic in the large the traditional continuous functions whose derivatives alternate in sign the first degree and second degree relations are identical to their traditional counterparts defined from iterated integrals of cumulative distribution functions the higher degree relations differ from the traditional relations in interesting and sometimes subtle ways the paper explores aspects of the partial sums relations including effects of grid refinements and extensions and describes their relationships to the traditional relations

dominance relations among standardized variables this paper examines stochastic dominance relations among discrete random variables defined on a common integer domain while these restrictions are minimal they lead both to new theoretical results and to simpler proofs of existing one the new results obtained for dominance criteria of any degree generalize an ssd result of rothschild stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms if the variables are comparable under fsd the perturbations are downward shift terms while under ssd tsd all but two three of the perturbations are zero mean disturbance terms noise under ssd the remaining perturbations are shift terms and under tsd noise and shift terms however under either ssd or tsd these remaining terms are identically zero if the variables to be compared have equal means the paper also finds new proofs of well known results relating dominance criteria to preferences

understanding the qr algorithm the qr algorithm is currently the most popular method for finding all eigenvalues of a full matrix while qr is now well understood by specialists in eigenvalue computations this understanding is not being conveyed effectively to the mathematical public many accounts present wilkinson s 1965 convergence proof others establish some of the connections between the qr algorithm the power method and inverse iteration usually much emphasis is rightly placed on the refinements such as shifts of origin which are required to make the algorithm competitive but practically all accounts fail to explain the basic meaning of qr iterations as a consequence the qr algorithm is widely thought to be difficult to understand the purpose of this paper is to try to convince the reader that the opposite is true in fact the qr algorithm is neither more nor less than a clever implementation of simultaneous iteration which is itself a natural easily understood extension of the power method this point

the constrained newton method on a lie group and the symmetric eigenvalue problem the newton method for estimating a critical point of a real function is formulated in a coordinate free manner on an arbitrary lie group convergence proofs for the numerical method are given an application of the general approach to computing the eigenvalues of a symmetric matrix is given and the resultant algorithm is compared with the classical shifted qr algorithm properties of the method described suggest that it is of interest for certain computations in online and adaptive environments

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

generalized simple based pressure correction method for unstructured colocated grids this paper reports on the simple like solution algorithm that significantly improves velocity pressure coupling leading to the accelerated convergence the algorithm is applicable to both incompressible and compressible flows it is implemented within the framework of a cell centered finite volume method using colocated storage of flow variables on unstructured grids the convergence acceleration is an outcome of the novel treatment of the pressure correction equation that accounts for two commonly neglected terms appearing in a general pressure correction equation these terms namely the neighbor and nonorthogonal corrections represent velocity corrections from neighboring cells and the cell face pressure correction gradient associated with the grid nonorthogonality respectively reminiscent of the piso method both neighbor and nonorthogonal corrections are taken into account by performing two or more correction steps however the full inclusion of neighbor velocity corrections can prevent the sol

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

differential equations and the qr algorithm in this paper we consider a variety of isospectral flows on the set of n times n matrices these flows arise from lax pairs and can all be interpreted in terms of the qr decomposition for nonsingular matrices the asymptotics of these differential equations are considered in detail and for symmetric matrices these asymptotics provide a new method of solving the eigenvalue problem

a compressible finite volume formulation for large eddy simulation of turbulent pipe flows at low mach number in cartesian coordinates a finite volume formulation for large eddy simulation les of turbulent pipe flows based on the compressible time dependent three dimensional navier stokes equations in cartesian coordinates with non cartesian control volumes is presented the small scale motions are modeled by a dynamic subgrid scale sgs model a dual time stepping approach with time derivative preconditioning is employed to enable the simulations to run efficiently at low mach numbers the equations with primitive variables p u v w t are solved with an implicit lower upper symmetric gauss seidel lu sgs scheme an isothermal turbulent pipe flow at two reynolds numbers and a turbulent pipe flow with a low heat transfer are simulated to evaluate this compressible les finite volume formulation the results agree very well with the experimental data and dns results verifying the accuracy of the present scheme

outflow conditions for integrated large eddy simulation reynolds averaged navier stokes simulations the numerical flow prediction of highly complex flow systems such as the aerothermal flow through an entire aircraftgasturbineengine requirestheapplicationofmultiplespecializedflowsolvers whichhavetorunsimultaneously in order to capture unsteady multicomponent effects the different mathematical approaches of different flow solvers especially large eddy simulation les and reynolds averaged navier stokes rans flow solvers pose challenges in the definition of boundary conditions at the interfaces here a method based on a virtual body force is proposed to impose reynolds averaged velocity fields near the outlet of an les flow domain in order to take downstream flow effects computed by a rans flow solver into account this method shows good results in the test case of a swirl flow where the influence of a flow contraction downstream of the les domain is represented entirely by the reynolds averaged velocity field at the outlet of the les domain i motivation n umericalsimulationsofcomplexlarge scaleflowsystems must capture a variety of physical phenomena in order to predicttheflowaccurately currently manyflowsolversarespecialized to simulate one part of a flow system effectively but are either inadequate or too expensive to be applied to a generic problem asanexample theaerothermalflowthroughagasturbineengine can be considered in the compressor and the turbine section the flow solver has to be able to handle the moving blades model the wall turbulence and predict the pressure and density distributions properly this can be done efficiently by a flow solver based on the reynolds averaged navier stokes rans approach on the other hand the flow in the combustion chamber is governed by largescale turbulence complex mixing processes chemical reactions and the presence of fuel spray experience shows that these phenomena require an unsteady approach 1 hence the use of a large

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

stochastic orderings of convex concave type on an arbitrary grid several new classes of discrete stochastic orderings are introduced for comparing discrete random variables that are valued in an arbitrary ordered finite grid of nonnegative points these order relations correspond to particular cases of integral stochastic orderings which are generated by different classes of functions of convex concave type defined on the grid they are natural extensions from equidistant to arbitrary grids of various orderings familiar in the literature the main question addressed in the paper is how an extension of the grid of points can affect such stochastic orderings it will be shown that a crucial factor is the location of the additional point that is inserted in the grid

the computation of compressible and incompressible recirculating flows by a non iterative implicit scheme abstract the piso algorithm which is presented in a companion paper is a non iterative method for solving the implicity discretised time dependent fluid flow equations the algorithm is here applied in conjunction with a finite volume technique employing a backward temporal difference scheme to the computation of compressible and incompressible flow cases the results of calculations are compared with similar ones obtained with an existing iterative method it is shown that for time evolving flows the splitting error of piso is negligibly small at the level of time step required to eliminate the temporal truncation error while the avoidance of iteration results in a substantial reduction in computing effort over that required by iterative methods it is also demonstrated that piso is stable for fairly large time steps which renders it useful for steady state calculations as well

on the continuous realization of iterative processes many important mathematical problems are solved by iterative methods many of these iterative schemes may be regarded as the discrete realization of certain continuous dynamical systems this paper summarizes some of the recent developments in the continuous realization of several popular basic iterative methods

a cbs type stabilizing algorithm for the consolidation of saturated porous media the presented method stems from the works by zienkiewicz and co workers for coupled fluid thermal problems starting from the early 1990s they propose algorithms to overcome the difficulties connected to the application of the fem to the area of fluid mechanics which include the problems of singular behaviour in incompressibility and the problems connected to convective terms the major step forward was to introduce the concept of characteristic lines the particle paths in a simple convection situation for a class of problems with a single scalar variable the equations in the characteristic co ordinates regain self adjointness the procedure is called characteristic based split algorithm cbs we use here a cbs type procedure for a saturated deformable elastic porous medium in which the fluid velocity is governed by darcy s equation which comes directly from navier stokes ones the physical mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains the power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual u p problem into a u v p one where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid respectively attention is focused on the expression of darcy s velocity which is considered as the starting point of the algorithm the accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u p solutions a good fitting among different results has been obtained it is further shown that the procedure eliminates the oscillations at the onset of consolidation typical for many schemes the fem code ed multifield has been used for implementing and testing the procedure copyright 2005 john wiley sons ltd

dynamical systems and non hermitian iterative eigensolvers simple preconditioned iterations can provide an efficient alternative to more elaborate eigenvalue algorithms we observe that these simple methods can be viewed as forward euler discretizations of well known autonomous differential equations that enjoy appealing geometric properties this connection facilitates novel results describing convergence of a class of preconditioned eigensolvers to the leftmost eigenvalue provides insight into the role of orthogonality and biorthogonality and suggests the development of new methods and analyses based on more sophisticated discretizations these results also highlight the effect of preconditioning on the convergence and stability of the continuous time system and its discretization

family of runge kutta based algorithms for unsteady incompressible flows a family of algorithms based on implicit runge kutta time integration suitable for unsteady incompressible flow is developed spatially discretized momentum equations are integrated in time using i

a computational stream function method for two dimensional incompressible viscous flows this work concerns the development of a numerical method based on the stream function formulation of the navier stokes equations to simulate two dimensional plane or axisymmetric viscous flows the main features of the proposed method are the use of the high order finite difference compact method for the discretization of the stream function equation the implicit pseudo transient newton krylov multigrid matrix free method for the stationary stream function equation and the fourth order runge kutta method for the integration of non stationary flows copyright 2005 john wiley sons ltd

extremal probabilistic problems and hotelling s t 2 test under a symmetry condition we consider the hotelling t 2 statistic for an arbitrary d dimensional sample if the sampling is not too deterministic or inhomogeneous then under the zero means hypothesis the limiting distribution for t 2 is chi 2 d it is shown that a test for the orthant symmetry condition introduced by efron can be constructed which does not differ essentially from the one based on chi 2 d and at the same time is applicable not only to large random homogeneous samples but to all multidimensional samples the main results are not limit theorems but exact inequalities corresponding to the solutions to certain extremal problems the following auxiliary result itself may be of interest chi d sqrt d 1 has a monotone likelihood ratio

antialiasing filters for coupled reynolds averaged large eddy simulations the increasing complexity of engineering problems makes the coupling of multiple simulation codes attractive in fluid mechanical applications the physical range of flow phenomena that can be modeled can be extended significantly by coupling flow solvers based on the reynolds averaged navier stokes rans approach and on large eddy simulations les these separate flow solvers run simultaneously and exchange information at the interface however because the les flow solver operates usually with a much smaller time step the les data have to be sampled to provide data for the rans flow solver in the sampling process aliasing errors can occur possibilities are investigated to suppress aliasing errors while preserving the amplitude and phase of the long wave spectrum

constraint consistent runge kutta methods for one dimensional incompressible multiphase flow new time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one dimensional two fluid model the methodology is based on halfexplicit runge kutta methods being explicit for the mass and momentum equations and implicit for the volume constraint these half explicit methods are constraint consistent i e they satisfy the hidden constraints of the two fluid model namely the volumetric flow incompressibility constraint and the poisson equation for the pressure a novel analysis shows that these hidden constraints are present in the continuous semi discrete and fully discrete equations next to constraint consistency the new methods are conservative the original mass and momentum equations are solved and the proper shock conditions are satisfied efficient the implicit constraint is rewritten into a pressure poisson equation and the time step for the explicit part is restricted by a cfl condition based on the convective wave speeds and accurate achieving high order temporal accuracy for all solution components masses velocities and pressure highorder accuracy is obtained by constructing a new third order runge kutta method that satisfies the additional order conditions arising from the presence of the constraint in combination with time dependent boundary conditions two test cases kelvin helmholtz instabilities in a pipeline and liquid sloshing in a cylindrical tank show that for time independent boundary conditions the half explicit formulation with a classic fourth order runge kutta method accurately integrates the two fluid model equations in time while preserving all constraints a third test case ramp up of gas production in a multiphase pipeline shows that our new third order method is preferred for cases featuring time dependent boundary conditions

a grassmann rayleigh quotient iteration for computing invariant subspaces the classical rayleigh quotient iteration rqi allows one to compute a one dimensional invariant subspace of a symmetric matrix a here we propose a generalization of the rqi which computes a p dimensional invariant subspace of a cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature

the dynamics of rayleigh quotient iteration this paper analyzes the rayleigh quotient iteration algorithm for symmetric matrices dynamical systems techniques are employed to characterize the sets of points for which the algorithm will converge to an eigenvector it is shown that these sets have full measure and that their geometric nature is related to the spacing of the eigenvalues

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

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

inflow and initial conditions for direct numerical simulation based on adjoint data assimilation a method for generating inflow conditions for direct numerical simulations dns of spatially developing flows is presented the proposed method is based on variational data assimilation and adjoint based optimization the estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system the approach s robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder the performance of the technique is also illustrated in a real world application by using noisy large scale piv measurements this method denoises experimental velocity fields and reconstructs a continuous trajectory of motion fields from discrete and unstable measurements

least squares matching problems abstract a large class of matching problems can be thought of in the following way one is given a group g which acts on a riemannian manifold and one is given two points x 1 and x 2 in the manifold the problem is to find g g such that d g x 1 x 2 is as small as possible if the group has finite cardinality this is a combinatorial optimization problem whereas if g is a lie group one can use the calculus to obtain necessary conditions our main results establish circumstances under which one can relax the combinatorial problem to an appropriate lie group problem and then solve it by the method of steepest descent an interesting class of applications involves embedding the permutation group on n letters in the orthogonal group o n with the latter acting on r n n 1 2 via a symmetricized tensor product the convergence properties of the descent equation which arises in this way are analyzed in some detail

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

unstructured grid arbitrarily shaped element method for fluid flow simulation a three dimensional unstructured grid arbitrarily shaped element method is developed for solving the navier stokes equations the proposed method is generally applicable to arbitrarily shaped elements and thus offers the potential to unify many of the different grid topologies into a single formulation examples of grid topologies include a structured hexahedral mesh unstructured tetrahedral mesh hybrid mesh using a combination of hexahedra tetrahedra prisms and pyramids cartesian mesh with elements cubes cut by flow boundaries and mixed arbitrary multiblock meshes the concept of such an arbitrary element method is developed and implemented into a pressure based finite volume solver it utilizes a collocated and cell centered storage scheme expressions for second order discretizations of the convection and diffusion terms are derived and presented for an arbitrarily shaped element the developed code as a first step is applied to two selected three dimensional viscous flows using a structured hexahedral mesh and an unstructured tetrahedral mesh it is demonstrated that the concept of the arbitrarily shaped element method can be viable and efficient

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

the projected gradient methods for least squares matrix approximations with spectral constraints the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure this paper describes a general procedure in using the projected gradient method it is shown that the projected gradient of the objective function on the manifold of constraints usually can be formulated explicitly this gives rise to the construction of a descent flow that can be followed numerically the explicit form also facilitates the computation of the second order optimality conditions examples of applications are discussed with slight modifications the procedure can be extended to solve least squares problems for general matrices subject to singular value constraints

a bridge between projection methods and simple type methods for incompressible navier stokes equations a bridge is built between projection methods and simple type methods semi implicit method for pressure linked equation a general second order accurate projection method is developed for the simulation of incompressible unsteady flows by employing a non linear update of pressure term as n pn 1 i n pn where n is a coefficient matrix which may depend on the grid size time step and even velocity it includes three and four step projection methods the standard simple method is written in a concise formula for steady and unsteady flows it is proven that simple type methods have second order temporal accuracy for unsteady flows the classical second order projection method and simple type methods are united within the framework of the general second order projection formula two iteration algorithms of simple type methods for unsteady flows are described and discussed in addition detailed formulae are provided for general projection methods by using the runge kutta technique to update the convective term and crank nicholson scheme for the diffusion term copyright 2007 john wiley sons ltd

generation of three dimensional turbulent inlet conditions for large eddy simulation a method for generating realistic i e reproducing in space and time the large scale coherence of the flows inflow conditions based on two point statistics and stochastic estimation is presented the method is based on proper orthogonal decomposition and linear stochastic estimation this method allows a realistic representation with a minimum of information to be stored most of the illustrations of this method are given for a plane turbulent mixing layer that contains most of the basic features of organized turbulent flows examples of the application of the method are given first for the generation of inflow conditions for direct numerical simulation dns and for large eddy simulation from experimental results second dns results are used to generate realistic inflow conditions for two and three dimensional dns retaining only a minimum size of relevant information

a unified formulation for continuum mechanics applied to fluid structure interaction in flexible tubes this paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid structure interaction in flexible tubes a review of current methods of fluid structure coupling highlights common limitations of high computational cost and solution instability it is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain a single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes the method is validated first by simulating dynamic oscillation of a clamped elastic beam it is then applied to study the case of interest wave propagation in highly flexible tubes in which a predicted wave speed of 8 58m s falls within 2 of an approximate analytical solution the method shows further good agreement with analytical solutions for tubes of increasing rigidity covering a range of wave speeds from those found in arteries to that in the undisturbed fluid

self similar flows abstract large classes of self similar isospectral flows can be viewed as continuous analogues of certain matrix eigenvalue algorithms in particular there exist families of flows associated with the qr lr and cholesky eigenvalue algorithms this paper uses lie theory to develop a general theory of self similar flows which includes the qr lr and cholesky flows as special cases also included are new families of flows associated with the sr and hr eigenvalue algorithms the basic theory produces analogues of unshifted single step eigenvalue algorithms but it is also shown how the theory can be extended to include flows which are continuous analogues of shifted and multiple step eigenvalue algorithms

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

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

the continuous time rayleigh quotient flow on the sphere a continuous time differential equation inspired by the rayleigh quotient iteration for a symmetric matrix a is studied the set of all continuous solutions termed the rayleigh quotient flow is shown to be a time scaled version of the newton flow for rayleigh quotient cost functional the scaling factor ensures that the rate of variation of the rayleigh quotient is constant and positive along solutions this interpretation leads to a precise phase portrait for the rayleigh quotient flow it is shown that a complete non degenerate solution of the rayleigh quotient flow visits each of the eigenvectors of a in ascending order

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

role of initial conditions in establishing asymptotic flow behavior the role of the details of initial or upstream conditions in establishing asymptotic behavior is reviewed the traditional view that at least simple shear flows reach universal asymptotic states is shown to be inconsistent with the abundant experimental and direct numerical simulation data even though scaled mean velocity profiles collapse the streamwise or temporal variation of the scaling parameters and spreading rates can vary widely for different upstream or initial conditions equilibrium similarity theory shows why the traditional view has arisen normalized mean velocity profiles can be universal even though the other moment profiles and scaling parameters are not decaying isotropic turbulence and applications of the proper orthogonal decomposition to free shear flows are used to show what parameters might control the downstream development it is argued that reynolds averaged navier stokes cannot account for these dependencies but large eddy simulation can

ordinary differential equations and the symmetric eigenvalue problem in this paper the authors develop a general framework for calculating the eigenvalues of a symmetric matrix using ordinary differential equations new algorithms are suggested and old algorithms including qr are interpreted

a finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement abstract this paper describes a finite volume method for simulating transport processes governed by convection diffusion type equations the formulation is based on a cell centred unstructured grid with an edge based data structure discretisation is independent of control volume or cell shape by using a surface vector decomposition at the midpoint of the interface between cells along with a deferred correction approach any cross diffusion due to grid skewness can be readily accounted for when discretising the diffusive flux for modelling fluid flow processes a collocated arrangement of variables is employed so that a single coefficient matrix applies for the momentum equations of each velocity component to avoid checkerboard oscillation arising from pressure velocity decoupling occurring under the collocated variable arrangement when a pressure based solution algorithm is employed a novel pseudo flux interpolation method is proposed for unstructured grids ensuring that the solution is both under relaxation factor and time step for transient calculation independent the methodology can be formulated within a framework whereby either a coupled or a decoupled solution algorithm can be employed the features and advantages of the method are demonstrated by solution of the navier stokes equations for two benchmark flow problems

a segregated implicit pressure projection method for incompressible flows in this paper a segregated implicit projection method is presented and investigated although high reynolds turbulent flow has been a motivating factor the present study is mainly restricted to the incompressible navier stokes equations the proposed method is analyzed for properties like stability accuracy and consistency aided by some test examples in addition two different flow cases are simulated to evaluate the ability and efficiency of the method compared with other results

a high resolution code for turbulent boundary layers a new high resolution code for the direct simulation of incompressible boundary layers over a flat plate is described it can accommodate a wide range of pressure gradients and general time dependent boundary conditions such as incoming wakes or wall forcing the consistency orders of the advective and pressure correction steps are different but it is shown that the overall resolution is controlled by the higher order advection step the formulation of boundary conditions to ensure global mass conservation in the presence of arbitrary forcing is carefully analyzed two validation boundary layers with and without a strong adverse pressure gradient are presented with maximum reynolds numbers re q 2000 they agree well with the available experiments turbulent inflow conditions for the zero pressure case are implemented by a recycling method and it is shown that at least the initial 300 momentum thicknesses have to be discarded before the effect of the artificial inflow is forgotten it is argued that this is not a defect of the method used to generate the inflow but a property of the boundary layer

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