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

an exact method for the calculation of certain titchmarsh weyl m functions we consider the second order linear differential equation where q is real valued in the case we calculate the titchmarsh weyl m function associated with

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

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

oscillation and asymptotic behavior of second order difference equations abstract the oscillation of the second order difference equation c n y n p n y v n 1 0 n 0 1 2 1 1 is investigated where yn yn 1 yn v is a quotient of odd positive integers some necessary and sufficient conditions for oscillation of 1 1 with v 1 and v

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

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

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

the form of the spectral functions associated with a class of sturm liouville equations with integrable coefficient we consider the second order linear differential equation in the case where roughly q l 1 0 we devise a representation for the spectral function t associated with which is valid for t sufficiently large our results are the best possible

oscillation criteria for two dimensional dynamic systems on time scales we establish some oscillation criteria for the two dimensional dynamic system x d t b t g y s t y d t a t f x t on a time scale t our results not only unify the oscillation of two dimensional differential systems and difference systems but include the oscillation results for differential systems and provide new oscillation criteria for difference systems several examples are considered to illustrate the main results

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

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

the asymptotic form of the titchmarsh weyl m function associated with a second order differential equation with locally integrable coefficient on deduit un developpement asymptotique pour la m fonction de titchmarsh weyl associee a l equation differentielle lineaire d ordre 2 y qy y sur 0 dans le cas ou la seule restriction sur la fonction a valeur reelle q est q l 1 0 e pour e 0

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

an inverse problem involving the titchmarsh weyl m function let m denote the titchmarsh weyl m function associated with the differential equation with neumann boundary condition at 0 in the case q c m 0 e for some integer m and e 0 we prove the following result theorem 2 1 if for some integer 3 we know that im l 2 m 0 0 on the ray e i then q v 0 0 for all v in the set 0 1 m for which 2 mod

a second order nonlinear difference equation oscillation and asymptotic behavior discrete analogues are investigated for well known results on oscillation growth and asymptotic behavior of solutions of y q t y 0 for q t 0 and for q t 0 the analogue of atkinson s oscillation criterion is shown to be true for 2yn 1 qn yn 0 but the analogue for atkinson s nonoscillation criterion is shown to be false

a three dimensional modified strongly implicit procedure for heat conduction the application of discretizatio n techniques frequently leads to a system of algebraic equations having a welldefined coefficient structure a modified strongly implicit procedure for solving the system resulting from the modeling of heat conduction in three dimensions is presented in this work the method is derived for a 19 point scheme with the more common 7 point scheme emerging as a special case of the procedure in this way the asymmetric influence of the additional terms in the lu matrix product is weakened as a consequence the method is less sensitive to the iteration parameter and mesh aspect ratio and in addition provides considerably more rapid convergence than does the strongly implicit procedure the increased convergence is exhibited by a significant reduction in the computational cost the characteristics of the method are examined through application to several model problems and application is made to a more complex three dimensional problem comparisons with the sip strongly implicit and adi alternating direction implicit methods are provided

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

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

a property of the asymptotic series for a class of titchmarsh weyl m functions in an earlier paper 6 we showed that if q c n 0 e for some e 0 then the titchmarsh weyl m function associated with the second order linear differential equation has the asymptotic expansion as a in a sector of the form 0 we show that if the real valued function q admits the expansion in a neighbourhood of 0 then

existence of bounded positive solutions for a system of difference equations abstract this paper deals with the second order nonlinear neutral delay system of difference equations a n x n b n x n f n x h 1 n x h kn y w 1 n y w kn c n n n 0 p n y n q n y n g n x s 1 n x s kn y t 1 n y t kn r n n n 0 by virtue of the banach fixed point theorem and some natural modifications of the techniques in the literature we prove the existence results of uncountably many bounded positive solutions for the system of difference equations seven examples are constructed to explain the main results presented in this paper

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

classification schemes for nonoscillatory solutions of two dimensional nonlinear difference systems abstract classification schemes for nonoscillatory solutions of a class of nonlinear two dimensional nonlinear difference systems are given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of these solutions are also provided

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

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

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

oscillation of two dimensional difference systems abstract the authors consider the nonlinear two dimensional difference system x n b n g y n y n 1 a n f x n n n o no no 1 where n 0 n 1 2 a n and b n n n n 0 are real sequences and f g r r are continuous with uf u 0 and ug u 0 for u 0 a solution x n y n of the system is oscillatory if both components are oscillatory the authors obtain sufficient conditions for all solutions of the system to be oscillatory some of their results allow a n to oscillate examples to illustrate the results are included

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

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

oscillation and asymptotic behavior of two dimensional difference systems this paper is concerned with the oscillation behavior of solutions of the nonlinear two dimesional difference system dx n b ng y n dy n 1 a nf x n n n n 0 n 0 n 0 1 some necessary and sufficient conditions are given for the oscillation of all solution of the system our result improve and generalize some results in the literature examples to illustrate the result are included

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

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

the asymptotic form of the spectral functions associated with a class of sturm liouville equations on utilise une forme modifiee de la formule d inversion de stieltjes avec des resultats recents sur la forme asymptotique des m fonctions de titchmarch weyl pour obtenir une expression asymptotique pour les fonctions spectrales t associees a l equation differentielle y q x y y o x b