symmetry preserving discretization of navier stokes equations on collocated unstructured grids a fully conservative discretization is presented in this paper the same principles followed by verstappen and veldman 2003 3 are generalized for unstructured meshes here a collocated mesh scheme is preferred over a staggered one due to its simpler form for such meshes the basic idea behind this approach remains the same mimicking the crucial symmetry properties of the underlying differential operators i e the convective operator is approximated by a skew symmetric matrix and the diffusive operator by a symmetric positive definite matrix a novel approach to eliminate the checkerboard spurious modes without introducing any non physical dissipation is proposed to do so a fully conservative regularization of the convective term is used the supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed finally the new discretization method is successfully tested for a buoyancy driven turbulent flow in a differentially heated cavity

development of an implicit method for multi fluid flow simulations a fully coupled implicit method has been developed for solving the viscous full multi fluid equations which incorporate transport and generation of mass and momentum for each component present in a system this work presents stability analysis and representative computational results of this algorithm the stability analyses demonstrate the performance of several iterative schemes applied to the solution of the linearized block system which arises in the fully implicit formulation these include block jacobi and symmetric block gauss siedel schemes using two forms of relaxation a hierarchy of increasing physical complexity is pursued starting with one dimensional two fluid systems with minimum inter field dynamic coupling and no mass transfer these analyses are then extended to systems employing physically important inter field forces drag dispersion virtual mass the effects of mass transfer multiple fields i e more than 2 and multiple dimensions are considered a two fluid navier stokes code has been developed guided by the stability analyses one dimensional and two dimensional results generated with this code are presented which verify the validity of the stability analyses presented for the coupled scheme and the effectiveness of the method for flows of engineering relevance

a new mixed basis navier stokes formulation for incompressible flows over complex geometries numerical modeling of complex geometries necessitates the use of curvilinear body fitted coordinates this article proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non orthogonal grids with the physical covariant velocity as the primary solution variable this results in an algorithm which has many advantages of orthogonal equations the conservation equations written in this form retains the diagonal dominance of the pressure equation the newly formed conservation equations are solved on a structured grid using the simpler algorithm and are shown to converge well for non orthogonal grids standard k model is used for the turbulence closure

on the influence of different stabilisation methods for the incompressible navier stokes equations two different stabilisation methods for the incompressible navier stokes equations are investigated both methods are based on a special interpolation scheme for the velocity components but with different effects and behaviour they introduce varying errors in the continuity equation but also the derivation of terms contributing to the special interpolation have a great influence on the quality of the results by means of various examples the two stabilisation methods and their contributing parts are compared

gain constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays this paper is concerned with the gain constrained recursive filtering problem for a class of time varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises the stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case the phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of bernoulli distributed random variables taking values of 1 or 0 which means that the sensors may experience randomly occurring delays with individual delay characteristics the process noise is finite step autocorrelated the purpose of the addressed gain constrained filtering problem is to design a filter such that for all probabilistic sensor delays stochastic nonlinearities gain constraint as well as correlated noises the cost function concerning the filtering error is minimized at each sampling instant where the filter gain satisfies a certain equality constraint a new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre specified filter gain constraint a simulation example is provided to illustrate the effectiveness of the proposed filter design approach

recursive estimators of signals from measurements with stochastic delays using covariance information least squares linear one stage prediction filtering and fixed point smoothing algorithms for signal estimation using measurements with stochastic delays contaminated by additive white noise are derived the delay is considered to be random and modelled by a binary white noise with values zero or one these values indicate that the measurements arrive in time or they are delayed by one sampling time recursive estimation algorithms are obtained without requiring the state space model generating the signal but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities

metrics on semistable and numerically effective higgs bundles we provide notions of numerical effectiveness and numerical flatness for higgs vector bundles on compact kahler manifolds in terms of fibre metrics we prove several properties of bundles satisfying such conditions and in particular we show that numerically flat higgs bundles have vanishing chern classes and that they admit filtrations whose quotients are stable flat higgs bundles we compare these definitions with those previously given in the case of projective varieties finally we study the relations between numerically effectiveness and semistability establishing semistability criteria for higgs bundles on projective manifolds of any dimension

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

multigrid acceleration for recirculating laminar and turbulent flows computed with a non orthogonal collocated finite volume scheme abstract a study has been undertaken of multigrid convergence acceleration in iterative calculations of recirculating laminar and turbulent flows the basic numerical platform is a 2d 3d non orthogonal collocated finite volume algorithm in which convection is approximated optionally by a non monotonic upstream weighted third order scheme or by a monotonie second order muscl tvd formulation and which iterates the solution towards the steady state by way of a pressure correction scheme the study investigates the performance of various multigrid implementations including the correction and full approximation multigrid variants the latter operated within a variety of cycles both with prescribed and residual driven relaxation sweeps at each grid level the multigrid implementation is documented in detail and includes a consideration of data structure issues and special algorithmic measures necessary to secure robust convergence for turbulent flows the performance characteristics of the multigrid variants are then exposed through a range of results arising from computations for laminar and turbulent conditions with turbulence being represented by the k model or full reynolds stress transport closure

a computational strategy for the regularized 13 moment equations with enhanced wall boundary conditions the challenge of modeling low speed rarefied gas flow in the transition regime is well known in this paper we propose a numerical solution procedure for the regularized 13 moment equations within a finite volume framework the stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first order approximation to model confined flows a complete set of wall boundary conditions for the 13 moment equations are derived based on the maxwell wall boundary model this has been achieved by expanding the molecular distribution function to fourth order accuracy in hermite polynomials empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation monte carlo data the numerical predictions obtained from the regularized 13 moment equations and the navier stokes fourier equations are compared with data generated using the direct simulation monte carlo method for planar couette flow for a range of wall velocities and knudsen numbers 0 012 1 0 the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation monte carlo data the results also highlight limitations that are caused by the use of a first order expansion of the third moment

implicit method for incompressible flow calculations in three dimensional ducts and cascades a method is presented for the numerical solution of the incompressible navier stokes equations in three dimensional ducts and cascades both laminar and turbulentows are resolved the latter through the k turbu lence model the method is based on an elliptic formulation which consists of the sequential solution of the mean ow and the turbulence equations through an approximate factorization technique the cost of factorization is minimized through the formation and inversion of a single matrix for all but the continuity equations the conti nuity constraint is enforced by means of thepressure correction technique forwhich a moreef cient variant of the approximate factorization scheme is employed the method exhibitsgood convergence characteristics asdepicted from the analyzed three dimensional problems the prediction capabilities of this method are demonstrated by analyzing thelaminarowin a three dimensional bend and theturbulentowin a linearcompressorcascade with zero and nonzero tip clearance for cascadeow problems with nonzero tip clearances a variant of the present method accommodating multiple patched subdomains is devised

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

a collocated grid finite volume method for aeroacoustic computations of low speed flows a numerical algorithm for simulation of acoustic noise generation based on collocated grids is described the approach that was originally developed using a viscous inviscid decomposition technique involves two steps comprising a viscous incompressible flow part and an inviscid or viscous acoustic part on collocated grids the inviscid solution is found to be mesh dependent due to unavoidable extrapolations of the acoustic pressure and density at walls differing from the case on staggered grids where no extrapolation is needed the situation is most pronounced when a sharp body is considered a viscous acoustic algorithm is proposed to overcome the difficulty numerical computations of flows past a circular cylinder and a naca 0015 airfoil show that a viscous viscous coupling is more natural and gives excellent results as compared to those obtained in previous computations based on viscous inviscid coupling on staggered grids the model is applied to the problem of an airfoil exposed to a gust and results are compared to the numerical results of lockard and morris aiaa j 36 6 1998 907

local mesh refinement within a multi block structured grid scheme for general flows abstract a multi level flow adaptive mesh refinement strategy has been formulated and implemented within a structured grid multiblock scheme for 2d laminar transitional and turbulent recirculating flow although the locally refined irregular grid portions are organised as block structured patches within coarse grid blocks a special data structure allows high storage economy to be achieved issues of particular interest in the study include the performance of different flow adaptation sensors based on solution properties and error and the response of the solution accuracy to inter grid interpolation practices based on bi linear bi quadratic and compact interpolation the effectiveness of the local refinement strategy especially in terms of cpu and memory resources is examined by reference to four test cases ranging from an analytically prescribed scalar field over a square domain to a transitional flow over a highly loaded compressor blade the study demonstrates that cpu and memory savings with a three level refinement for the compressor blade case are of order 70 and 90 respectively relative to the requirements of globally fine grids returning similar accuracy levels

a numerical method for large eddy simulation in complex geometries we discuss the development of a numerical algorithm and solver capable of performing large eddy simulation in the very complex geometries often encountered in industrial applications the algorithm is developed for unstructured hybrid grids is non dissipative yet robust at high reynolds numbers on highly skewed grids simulation results for a variety of flows are presented

large eddy simulation of an oscillating cylinder in a steady flow in this work large eddy simulation is used to study the flow around a circular cylinder undergoing streamwise sinusoidal oscillations this benchmark case is a first step toward studying engineering applications related to flow induced vibrations both the flow physics which correlate the flow development with the time varying loading of the cylinder at two different oscillation frequencies as well as a validation of the fluid structure interaction methodology through comparison with experimental data for the same configuration are described with the methodology used large eddy simulation based on a finite volume method capable of handling moving meshes gives force predictions that generally agree well with experimentally measured data both with respect to the overall flow development as with force magnitude

filtering for a class of nonlinear discrete time stochastic systems with state delays in this paper the filtering problem is investigated for a class of nonlinear discrete time stochastic systems with state delays we aim at designing a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square for all admissible nonlinearities and time delays first an algebraic matrix inequality approach is developed to deal with the filter analysis problem and sufficient conditions are derived for the existence of the desired filters then based on the generalized inverse theory the filter design problem is tackled and a set of the desired filters is explicitly characterized a simulation example is provided to demonstrate the usefulness of the proposed design method

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

recursive estimation of discrete time signals from nonlinear randomly delayed observations in this paper one stage prediction filtering and fixed point smoothing problems are addressed for nonlinear discrete time stochastic systems with randomly delayed measurements perturbed by additive white noise the observation delay is modelled by a sequence of independent bernoulli random variables whose values zero or one indicate that the real observation arrives on time or it is delayed one sampling time and hence the available measurement to estimate the signal is not updated assuming that the state space model generating the signal to be estimated is unknown and only the covariance functions of the processes involved in the observation equation are available recursive estimation algorithms based on linear approximations of the real observations are proposed

einstein hermitian connections on polystable principal bundles over a compact kahler manifold given a compact kahler manifold m and a connected reductive algebraic group g over inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i a prinlcipal g bundle over m admits an einstein hermitian connection if and only if the principal bundle is polystable if m is a projective manifold a higgs g bundle over m admits an einstein hermitian connection if and only if the higgs bundle is polystable

an effective explicit pressure gradient scheme implemented in the two level non staggered grids for incompressible navier stokes equations in this paper an improved two level method is presented for effectively solving the incompressible navier stokes equations this proposed method solves a smaller system of nonlinear navier stokes equations on the coarse mesh and needs to solve the oseen type linearized equations of motion only once on the fine mesh level within the proposed two level framework a prolongation operator which is required to linearize the convective terms at the fine mesh level using the convergent navier stokes solutions computed at the coarse mesh level is rigorously derived to increase the prediction accuracy this indispensable prolongation operator can properly communicate the flow velocities between the two mesh levels because it is locally analytic solution convergence can therefore be accelerated for the sake of numerical accuracy momentum equations are discretized by employing the general solution for the two dimensional convection diffusion reaction model equation the convective instability problem can be simultaneously eliminated thanks to the proper treatment of convective terms the converged solution is thus very high in accuracy as well as in yielding a quadratic spatial rate of convergence for the sake of programming simplicity and computational efficiency pressure gradient terms are rigorously discretized within the explicit framework in the non staggered grid system the proposed analytical prolongation operator for the mapping of solutions from the coarse to fine meshes and the explicit pressure gradient discretization scheme which accommodates the dispersion relation preserving property have been both rigorously justified from the predicted navier stokes solutions

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

projective manifolds whose tangent bundles are numerically effective in 1979 mori mo proved the so called hartshorne frankel conjecture every projective n dimensional manifold with ample tangent bundle is isomorphic to the complex projective space p a differential geometric analogon assuming the existence of a k ihler metric on x with positive holomorphic bisectional curvature is independently due to siu yau sy thus it seems natural to classify projective manifolds x whose tangent bundle tx satisfy a degenerate condition of ampleness numerical effectivity abbreviated by nef this means that the tautological quotient line bundle d 1 on f tx is numerically effective i e c 0

calculation of flow in transition duct using second order closure and wall functions our purpose is to determine whether the deficiences reported in a previous study could be overcome by using an alternative high reynolds number second order closure that will be described next

finite volume method for coupled subsurface flow problems i darcy problem abstract the article introduces a finite volume method for the darcy problem in heterogeneous anisotropic media the method is based on the mixed formulation for the pressure and its gradient the method is stable despite collocation of both pressure and its gradient at cell centers and demonstrates the first order convergence on numerous benchmarks as well as good monotonicity property the method produces quasi definite matrix which is numerically shown to have good asymptotics of the condition number our flux discretization method is a realization of our more general concept of stable flux discretization for saddle point systems with vector of several unknowns in this paper this vector is composed of pressure and its gradient and the saddle point system is the mixed formulation of the darcy problem

computational method of second moment turbulence closures in complex geometries this paper presents a finite volume numerical method to calculate turbulent flows using second moment turbulence closures the numerical method is formulated for a collocated grid arrangement and on body fitted coordinate grids a special interpolation scheme is derived to resolve the potential decoupling between momentum and reynolds stress transport equations this interpolation scheme naturally leads to stability promoting terms in the momentum equations in the form of anisotropic eddy viscosities issues such as the implementation of boundary conditions with a body fitted coordinate grid are also discussed applications are given to demonstrate the robustness of the numerical method and the performance of a second moment turbulence closure computational results are compared with available experimental data and to those of the standard two equation turbulence model good results have been obtained with the second moment turbulence closure

numerical prediction of fluid resonant oscillation at low mach number a method governing equation set and numerical procedure suited to the numerical simulation of fluid resonant oscillation at low mach numbers is constructed the new equation set has been derived under the assumption that the compressibility effect is weak because the derived equations are essentially the same as the incompressible navier stokes equations except for an additional term we can apply almost the same numerical procedure developed for incompressible flow equations without difficulty with application of a pressure based method that treats the continuity equation as a constraint equation for pressure the stiffness problem that arises in solving the usual compressible flow equations under low mach number conditions has been alleviated to verify the present method we apply it to the flows over a three dimensional open cavity

evaluation of a bounded high resolution scheme for combustor flow computations the present paper is concerned with the application of a high resolution scheme for a finite volume discretization method the capability of the chosen scheme is evaluated for the numerical simulation of three dimensional flowfields special emphasis lies in the calculation of the processes in the mixing zone of gas turbine combustors thus numerical results are compared with detailed measurements of velocity and temperature in a model mixing zone the velocity field as well as the temperature field strongly depend on the scheme used for the discretization of the momentum and energy equations the proposed high resolution scheme and the well known quick scheme yield similar results which are superior to those obtained with the simple upwind scheme for the simulation of turbulent transport the standard fc model is employed the effect of numerical diffusion caused by the usual upwind discretization of the convective transport of a and e is assessed by the application of the high resolution scheme of the discretization of the a and e equations as a result it is found that the velocity and temperature fields are insensitive to the scheme that is applied for the discretization of the a and e equations

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

can adaptive grid refinement produce grid independent solutions for incompressible flows abstract this paper studies if adaptive grid refinement combined with finite volume simulation of the incompressible rans equations can be used to obtain grid independent solutions of realistic flow problems it is shown that grid adaptation based on metric tensors can generate series of meshes for grid convergence studies in a straightforward way for a two dimensional airfoil and the flow around a tanker ship the grid convergence of the observed forces is sufficiently smooth for numerical uncertainty estimation grid refinement captures the details of the local flow in the wake which is shown to be grid converged on reasonably sized meshes thus grid convergence studies using automatic refinement are suitable for high reynolds incompressible flows

semistable and numerically effective principal higgs bundles we study miyaoka type semistability criteria for principal higgs g bundles e on complex projective manifolds of any dimension we prove that e has the property of being semistable after pullback to any projective curve if and only if certain line bundles obtained from some characters of the parabolic subgroups of g are numerically effective one also proves that these conditions are met for semistable principal higgs bundles whose adjoint bundle has vanishing second chern class in a second part of the paper we introduce notions of numerical effectiveness and numerical flatness for principal higgs bundles discussing their main properties for non higgs principal bundles we show that a numerically flat principal bundle admits a reduction to a levi factor which has a flat hermitian yang mills connection and as a consequence that the cohomology ring of a numerically flat principal bundle with coefficients in r is trivial to our knowledge this notion of numerical effectiveness is new even in the case of non higgs principal bundles

multigrid methods for incompressible heat flow problems with an unknown interface finite volume multigrid methods are presented for solving incompressible heat flow problems with an unknown melt solid interface mainly in solidification applications using primitive variables on collocated grids the methods are implemented based on a multiblock and multilevel approach allowing the treatment of a complicated geometry the inner iterations are based on the simple scheme in which the momentum interpolation is used to prevent velocity pressure decoupling the outer iterations are set up for interface update through the isotherm migration method v cycle and full multigrid fmg methods are tested for both two and three dimensional problems and are compared with a global newton s method and a single grid method the effects of prandtl and rayleigh numbers on the performance of the schemes are also illustrated among these approaches fmg has proven to be superior on performance and efficient for large problems sample calculations are also conducted for horizontal bridgman crystal growth and the performance is compared with that of traditional single grid methods

influence of momentum interpolation methods on the accuracy and convergence of pressure velocity coupling algorithms in openfoam checkerboard pressure is one of the most significant problems arising from the use of collocated grids for fluid dynamic simulations using the finite volume method the original rhie chow momentum interpolation technique termed original momentum interpolation method omim was proposed to eliminate the non physical saw tooth pressure oscillations however it was soon proved that the steady state solutions obtained with this technique were under relaxation factor dependent nevertheless standard omim is still commonly used in several cfd codes like openfoam the software used for this work in this paper the omim and a possible correction for under relaxation dependency which has been implemented in openfoam are discussed in detail the proposed methodology is compared and contrasted with omim in terms of accuracy of the solution and speed of convergence for several classical pressure velocity segregated algorithms for steady state solvers namely simple simple c simple r and piso a classical laminar 2d cavity is used as the base test case the study is then extended to a more complex 2d airfoil profile naca0012 in the cases considered mesh uniformity and orthogonality are progressively reduced and turbulence starts playing an important role limiting therefore the convergence of the cases and the performance of the correction

recursive filtering with random parameter matrices multiple fading measurements and correlated noises this paper is concerned with the recursive filtering problem for a class of discrete time nonlinear stochastic systems with random parameter matrices multiple fading measurements and correlated noises the phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval b k c k such a probability distribution could be any commonly used discrete distribution over the interval b k c k that covers the bernoulli distribution as a special case the process noise and the measurement noise are one step autocorrelated respectively the process noise and the measurement noise are two step cross correlated the purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices stochastic nonlinearity and multiple fading measurements as well as correlated noises intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation the proposed scheme is of a form suitable for recursive computation in online applications a simulation example is given to illustrate the effectiveness of the proposed filter design scheme

approximation of nonlinear filters for markov systems with delayed observations the aim of this paper is to give some approximation results for a class of nonlinear filtering problems with delay in the observation first we point out some general results on the approximation problem for the filter in nonlinear filtering in particular we give a general procedure for obtaining some upper bounds for the different approximations we consider this procedure is then applied in the case of nonlinear filtering problems with delay x y which can be represented by means of a markov system x hat y in the sense that y t hat y a t finally these upper bounds are computed explicitly in the particular case of markov jump process with counting observations

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

optimal control of continuous time linear systems with a time varying random delay abstract we study a finite horizon optimal control problem for a class of linear systems with a randomly varying time delay the systems of this type may arise in embedded control applications and in certain applications in economics the delay value is treated as an unknown variable but with known statistical properties modelled by a markov process with a finite number of states the probabilistic delay averaging approach is employed to determine the optimal control in the form which is independent of the delay value

extended and unscented filtering algorithms using one step randomly delayed observations in this paper the least squares filtering problem is investigated for a class of nonlinear discrete time stochastic systems using observations with stochastic delays contaminated by additive white noise the delay is considered to be random and modelled by a binary white noise with values of zero or one these values indicate that the measurement arrives on time or that it is delayed by one sampling time using two different approximations of the first and second order statistics of a nonlinear transformation of a random vector we propose two filtering algorithms the first is based on linear approximations of the system equations and the second on approximations using the scaled unscented transformation these algorithms generalize the extended and unscented kalman filters to the case in which the arrival of measurements can be one step delayed and hence the measurement available to estimate the state may not be up to date the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

letter to the editor a collocated finite volume scheme to solve free convection for general non conforming grids we present a new collocated numerical scheme for the approximation of the navier stokes and energy equations under the boussinesq assumption for general grids using the velocity pressure unknowns this scheme is based on a recent scheme for the diffusion terms stability properties are drawn from particular choices for the pressure gradient and the non linear terms convergence of the approximate solutions may be proven mathematically numerical results show the accuracy of the scheme on irregular grids

kalman filtering for multiple time delay systems this paper is to study the linear minimum variance estimation for discrete time systems with instantaneous and l time delayed measurements by using re organized innovation analysis a simple approach to the problem is presented in this paper it is shown that the derived estimator involves solving l 1 different standard kalman filtering with the same dimension as the original system

numerical appraisal of three low mach number algorithms for radiative convective flows in enclosures abstract the present study investigates three different algorithms for the numerical simulation of non boussinesq convection with thermal radiative heat transfer based on a low mach number formulation the solution methodology employs a fractional step approach based on the finite volume method on arbitrary polyhedral meshes the three algorithms compute the coupled governing equations in a segregated manner using the conservative form of momentum equations in conjunction with a variable coefficient pressure poisson equation the first algorithm algorithm a uses conservation of mass and energy equation to compute density and temperature the other two algorithms algorithm b and algorithm c calculates temperature and density from the equation of state respectively and solves a conservative form of the continuity and energy equation to obtain density and temperature respectively the energy and mass conservation errors arising due to the use of algorithms b and c are derived concerning various non dimensional parameters governing the flow and heat transfer the significance of these errors is highlighted by performing investigations over a range of rayleigh prandtl and planck numbers for various two and three dimensional natural convection problems with radiative heat transfer finally the role of balancing of the pressure and buoyancy terms is emphasized for robust calculations of large temperature difference thermo buoyant convection with radiative heat transfer

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 comparison of higher order bounded convection schemes this paper presents a comparison of recently developed four higher order bounded convection schemes soucup hlpa smarter and lppa which employ different characteristics in a normalized variable diagram all the schemes are formulated on a non uniform non orthogonal grid and their relative performances are compared through applications to the several test problems the results of numerical experiments show that all the tested bounded schemes resolve the boundedness problem retaining the accuracy of the higher order scheme the hlpa smarter and lppa schemes result in nearly the same solution behaviours and the soucup scheme is shown to be relatively more diffusive than the other three bounded schemes

direct numerical simulation of scalar transport using unstructured finite volume schemes an unstructured finite volume method for direct and large eddy simulations of scalar transport in complex geometries is presented and investigated the numerical technique is based on a three level fully implicit time advancement scheme and central spatial interpolation operators the scalar variable at cell faces is obtained by a symmetric central interpolation scheme which is formally first order accurate or by further employing a high order correction term which leads to formal second order accuracy irrespective of the underlying grid in this framework deferred correction and slope limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation the accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori a direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method in spite of the linear character of the scalar transport equation the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral properties of interpolation schemes although the results show an improved spectral resolution and greater spatial accuracy for the high order operator in the analysis of basic scalar transport problems the low order central scheme is found superior for high fidelity simulations of turbulent scalar transport