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

resolution of the 2d navier stokes equations in velocity vorticity form by means of an influence matrix technique abstract an influence matrix technique is proposed to enforce both the continuity equation and the definition of the vorticity in the treatment of the 2d incompressible navier stokes equations it is shown and supported by numerical experiments that at each time step the divergence is actually equal to zero within machine accuracy the same result is obtained for the definition of the vorticity

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

optimal design for non newtonian flows using a topology optimization approach we study non newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach the flow is modeled with the single relaxation hydrodynamic lattice boltzmann method and the shear dependence of viscosity is included through the carreau yasuda model for non newtonian fluids to represent the viscosity of blood in this model we use non newtonian similarity further we introduce a scaling to decrease the effects of the non newtonian model in porous regions in order to stabilize the coupling of the lbm porosity and non newtonian flow models for the resulting flow model we derive the non newtonian sensitivity analysis for steady state conditions and illustrate the non newtonian effect on channel layouts for a 2d dual pipe design problem at different reynolds numbers

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

group actions on geodesic ptolemy spaces in this paper we study geodesic ptolemy metric spaces x which allow proper and cocompact isometric actions of crystallographic or more generally virtual polycyclic groups we show that x is equivariantly roughly isometric to a euclidean space

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

new finite element finite volume level set formulation for modelling two phase incompressible flows we present a new level set method for modelling two phase incompressible flows with moving interface boundaries the method is based on a finite element fe treatment of the equations governing the motion of the interface separating two immiscible phases and a finite volume fv description of the fluid flow equations the performance of the method is demonstrated and validated using several sample problems involving two phase isothermal flows with density ratios of the order of 102 103 and viscosity ratios as high as 7 104 surface tension effects are included the present formulation displays good convergence properties and it is relatively simple to program this allows the method to be implemented into existing commercial fv based computational fluid dynamics cfd software thereby extending their application range we have successfully implemented the method in the code cfx 4

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

an efficient solution method for incompressible n s equations using non orthogonal collocated grid an efficient strategy for the solution of n s equations using collocated non orthogonal grids is presented the governing equations have been discretized in the physical plane itself without co ordinate transformation thereby retaining the lucidity of the basic finite volume method the non orthogonal terms and quick type corrections for the convective terms in the momentum equations are treated explicitly while the other terms are taken in implicit form in the pressure correction equation the non orthogonal terms have been dropped altogether the discretized equations have been solved by the preconditioned conjugate gradient square method the specific combination of above steps has resulted in better convergence properties as compared to those of existing algorithms even for highly skewed grids the scheme has been validated against benchmark solutions such as lid driven flow in square and skewed cavities and experi mental results of flow over a single cylinder its applicability has also been illustrated for flow through a bank of staggered cylinders with anti symmetric inlet and outlet boundary conditions copyright 1999 john wiley sons ltd

a shift transformation for fully conservative methods turbulence simulation on complex unstructured grids abstract operator transformations are presented that allow matrix operators for collocated variables to be transformed into matrix operators for staggered variables while preserving symmetries these shift transformations permit conservative skew symmetric convective operators and symmetric positive definite diffusive operators to be obtained for staggered variables using collocated operators shift transformations are not limited to uniform or structured meshes and this formulation leads to a generalization of the works of perot j comput phys 159 2000 58 and verstappen and veldman j comput phys 187 2003 343 a set of shift operators have been developed for and applied to a time adaptive cartesian mesh method with a fractional step algorithm the resulting numerical scheme conserves mass to machine error and conserves momentum and energy to second order in time a mass conserving interpolation is used for the variables during mesh adaptation the interpolation conserves momentum and energy to second order in space turbulent channel flow simulations were conducted at re 180 using direct numerical simulation dns the dns results from the adaptive method compare favourably with spectral dns results despite the use of a formally second order accurate scheme

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

topology optimization for turbulent flow with spalart allmaras model abstract in this research a new finite element fe based topology optimization to for turbulent flow was developed using the spalart allmaras s a equation which is one of the reynolds averaged navier stokes rans equations despite many innovative works on the subject of fluidic to it is rare to consider the influence of turbulent flow in to to consider the effect of complex turbulent fluid motion this research considered the s a model developed mainly for aerodynamic flows for a successful to one primary issue is modification of the s a turbulent model to account for topological evolution during the optimization process to address this issue we proposed the addition of penalization terms to the original governing equations to show the validity of the present approach and the effect of turbulent flow on optimal layouts some two dimensional benchmark designs studied for laminar flow were reconsidered by considering the effect of turbulent flow the eddy viscosity values were increased at some local regions due to the boussinesq hypothesis and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow it was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs

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

a numerical model for flow in meandering channels with natural bed topography a finite volume numerical model is presented for the calculation of three dimensional turbulent flow in meandering channels with natural bed configuration the governing equations are written in a general curvilinear coordinate system so that all singly connected geometrical configurations can be accommodated for simplicity the cartesian velocity components are retained as dependent variables the numerical procedure is very general so that it can deal with complex cross sections and separated flow turbulence closure is through the standard k model computed results show good agreement with experimental data in meandering channels with rectangular and natural bed configurations this work provides a hydrodynamic basis for the study of the mechanisms for the formation of river meanders

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

hyperbolicity cat 1 spaces and the ptolemy inequality using a four points inequality for the boundary of cat 1 spaces we study the relation between gromov hyperbolic spaces and cat 1 spaces

topology optimization of the shear thinning non newtonian fluidic systems for minimizing wall shear stress this paper suggests the topology optimization process to minimize wall shear stress by considering shear thinning non newtonian fluid effects in the systematic design of fluidic systems dealing with blood topology optimization was originally developed for mechanical design problems and within the last decade the method has been extended to a range of fluidic applications in this paper the carreau yasuda constitutive equation model is used for shear thinning non newtonian fluid modeling the fundamental idea is that the material density of each element or grid point is a design variable thus the geometry is parameterized in a pixel like pattern then material interpolation functions for inverse permeability and dynamic viscosity are used to ensure convergence of the solution and resolve non linearity in order to define wall shear stress on implicit boundary between solid and fluid i e blood occurring in fluidic topology optimization the relaxation method of wall shear stress is first proposed in this study we then apply the proposed fluidic topology optimization to actual fluidic systems dealing with blood e g a femoral bypass graft these design examples validate the efficiency of the proposed approach and show that topology optimization can be used for the initial conceptual design of various fluidic systems

development of a finite volume particle method for 3 d fluid flow simulations the finite volume particle method fvpm is a meshless method for simulating fluid flows which includes many of the desirable features of mesh based finite volume methods fvpm benefits from particle interaction vectors to weight conservative fluxes exchanged between particles these vectors are equivalent to the intercell area vectors in mesh based finite volume methods to compute the interaction vectors either numerical or exact integration has been used numerical integration based on quadrature rules is approximate and costly whereas the exact method employing a top hat kernel is precise and fast to date quadrature integration has not been used in 3 d due to its excessive cost and the exact method has been developed only for 2 d computations in this study we develop a new 3 d fvpm formulation which features a rectangular top hat kernel to compute interaction vectors exactly and efficiently we also introduce a new boundary condition enforcement technique based on a single layer of boundary particles in this technique no slip wall boundary conditions with complex geometries are precisely enforced by overlaying a layer of particles on wall surfaces employing ausm for inviscid fluxes weakly compressible fluid flow is studied with the proposed method to achieve more accurate results the solution can be refined near the wall boundary by splitting the fluid particles this formulation is validated for lid driven cavity flow a moving square and jet impingement test cases

numerical simulation of isotropic turbulence using a collocated approach and a nonorthogonal grid system we studied the effect of using a nonorthogonal grid coordinate system and a finite volume approach in the simulation of decaying isotropic turbulence calculations were performed in distorted periodic cubic boxes and with a turbulent reynolds number based on the taylor microscale and on a root mean square turbulent velocity of approximately 40 a preliminary study showed that in the nonorthogonal grids some fourier modes of the discretized derivatives can have greater amplitude or the phase inverted relatively to the modes of the exact derivative contrary to what occurs with a cartesian grid system however in the simulations the statistical distributions of velocity pressure and longitudinal and lateral velocity derivatives were always identical regardless of the grid distortion the temporal evolution of the energy was also similar and the differences at the end of the simulations after about two eddy turnover times did not exceed 1 furthermore the grid nonorthogonality affected neither the isotropy of the fields nor the correlation between the vorticity and the principal rates of strain we concluded that the finite volume approach in nonorthogonal grid systems may be used in the numerical simulation of complex turbulent flows with either the direct numerical simulation or large eddy simulation methodologies

kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow the collocated mesh scheme is often favored over the staggered mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates the collocated mesh scheme does not conserve kinetic energy however and few careful checks of the impact of these errors have been made in this work analysis is used to identify two sources of kinetic energy conservation error in the collocated mesh scheme 1 errors arising from the interpolations used to estimate the velocity on the cell faces and 2 errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes it is shown that the interpolation error can be eliminated through the use of first order accurate centered interpolation operators with mesh independent weights the pressure error appears to be intrinsic to the scheme and it is shown to scale as o t2 x2 the effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the cartesian mesh is stretched in only one direction the inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error the standard second order centered interpolation is shown to lead to severe numerical oscillations while the kinetic energy conserving first order centered interpolation produces solutions that are almost as smooth as those obtained with a third order upwind interpolation when compared in channel flow simulations however the first order centered interpolation is shown to be far superior to the third order upwind interpolation the latter being adversely affected by numerical dissipation only slight differences were noted when comparing channel flow simulations using first order and second order centered interpolations these results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly constructed non dissipative centered interpolations

a lagged implicit segregated data reconstruction procedure to treat open boundaries the problem of treating open boundaries is still a challenging one applying fully developed condition is constrained to long enough domains without having enough physical evidence about what happens on boundaries the domain extent could not be shortened and computational costs could not be reduced from the advent of free open boundary conditions they were confined to mixed finite element procedures recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction a wider class of flow solvers available however rely on the segregated procedure where the velocity components and pressure are solved in succession moreover many finite volume algorithms do not use the shape function reconstruction in this work by proposing a lagged implicit procedure we have extended the application of the open boundary condition to these wider classes of flow solvers the proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement which is easily applicable to any segregated and coupled flow solver to validate the compatibility of this extension benchmark problem of backward facing step is solved on successively truncated domains where open boundary may pass through recirculation zones results show that the proposed extension works fine for that problem it reduced the computational domain length and hence memory by a factor of 4 6 and the required computational time by a factor of 21 flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well

performance comparison of the nwf and dc methods for implementing high resolution schemes in a fully coupled incompressible flow solver this paper reports on the use of the normalized weighting factor nwf method and the deferred correction dc approach for the implementation of high resolution hr convective schemes in an implicit fully coupled pressure based flow solver four hr schemes are realized within the framework of the nwf and dc methods and employed to solve the following three laminar flow problems i lid driven flow in a square cavity ii sudden expansion in a square cavity and iii flow in a planar t junction over three grid systems with sizes of 104 5i 104 and 3i 105 control volumes the merit of both approaches is demonstrated by comparing the computational costs required to solve these problems using the various hr schemes on the different grid systems whereas previous attempts to use the nwf method in a segregated flow solver failed to produce converged solutions current results clearly demonstrate that both methods are suitable for utilization in a coupled flow solver in terms of cpu efficiency there is no global and consistent superiority of any method over another even though the dc method outperformed the nwf method in two of the three test problems solved

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

combination of topology optimization and optimal control method this paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control in the presented method the material topology is determined using the simp solid isotropic material with penalization method which has been popularly used in topology optimization in the simp method the design variable is relaxed and bounded in the interval 0 1 and the evolution of the design variable is usually implemented by the method of moving asymptotes mma which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable in the combination of topology optimization and optimal control method the control variable appears along with the design variable in order to evolve the control variable and design variable using mma simultaneously the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval 0 1 which is the same as the bound constraint of the design variable the optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity during the optimization procedure the design and control variables are filtered by the helmholtz filters to ensure the smoothness of the distribution to ensure the minimum scale length and remove the gray area in the material topology the filtered design variable is projected by the threshold method the feasibility and robustness of the combination of these two methods are demonstrated by several test problems including heat transfer fluid flow and compliance minimization

topology optimization of unsteady incompressible navier stokes flows this paper discusses the topology optimization of unsteady incompressible navier stokes flows an optimization problem is formulated by adding the artificial darcy frictional force into the incompressible navier stokes equations the optimization procedure is implemented using the continuous adjoint method and the finite element method the effects of dynamic inflow reynolds number and target flux on specified boundaries for the optimal topology of unsteady navier stokes flows are presented numerical examples demonstrate the feasibility and necessity of this topology optimization method for unsteady navier stokes flows

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

topology optimization based on a two dimensional swirl flow model of tesla type pump devices abstract tesla pumps are composed of rotating disks without blades and are based on the boundary layer effect i e viscous friction forces acting on the fluid and coand effect the tesla pump has various applications however the efficiency of its operation is quite low which makes room for the optimization of its design this way novel configurations of devices based on this working principle can be developed thus in this work a topology optimization formulation is proposed to optimize the rotor of a tesla type pump device by using a 2d swirl flow model which is a specific model that presents an axisymmetric flow with or without flow rotation around the axisymmetric axis the 2d swirl laminar fluid flow modeling is solved by using the finite element method a traditional material model is adopted by considering nodal design variables and is extended to take into account the fact that the optimization is performed in a rotating reference frame and the relative tangential velocity behaves differently than the other velocity components since the 2d swirl flow model is axisymmetric a multi objective function is defined in order to minimize energy dissipation and vorticity an extra term is proposed to the vorticity function to reduce the generation of grayscale results an interior point optimization algorithm ipopt is applied to solve the optimization problem numerical results taking into account different aspects of the design of the rotor of a tesla type device are presented

topology optimization of creeping fluid flows using a darcy stokes finite element a new methodology is proposed for the topology optimization of fluid in stokes flow the binary design variable and no slip condition along the solid fluid interface are regularized to allow for the use of continuous mathematical programming techniques the regularization is achieved by treating the solid phase of the topology as a porous medium with flow governed by darcy s law fluid flow throughout the design domain is then expressed as a single system of equations created by combining and scaling the stokes and darcy equations the mixed formulation of the new darcy stokes system is solved numerically using existing stabilized finite element methods for the individual flow problems convergence to the no slip condition is demonstrated by assigning a low permeability to solid phase and results suggest that auxiliary boundary conditions along the solid fluid interface are not needed the optimization objective considered is to minimize dissipated power and the technique is used to solve examples previously examined in literature the advantages of the darcy stokes approach include that it uses existing stabilization techniques to solve the finite element problem it produces 0 1 void solid topologies i e there are no regions of artificial material and that it can potentially be used to optimize the layout of a microscopically porous material copyright 2005 john wiley sons ltd

unified formulation of the momentum weighted interpolation for collocated variable arrangements abstract momentum weighted interpolation mwi is a widely used discretisation method to prevent pressure velocity decoupling in simulations of incompressible and low mach number flows on meshes with a collocated variable arrangement despite its popularity a unified and consistent formulation of the mwi is not available at present in this work a discretisation procedure is devised following an in depth analysis of the individual terms of the mwi derived from physically consistent arguments based on which a unified formulation of the mwi for flows on structured and unstructured meshes is proposed including extensions for discontinuous source terms in the momentum equations as well as discontinuous changes of density as shown by the presented analysis and numerical results the mwi enforces a low pass filter on the pressure field which suppresses oscillatory solutions furthermore the numerical dissipation of kinetic energy introduced by the mwi is shown to converge with third order in space and is independent of the time step if the mwi is derived consistently from the momentum equations in the presence of source terms the low pass filter on the pressure field can be shaped by a careful choice of the interpolation coefficients to ensure the filter only acts on the driving pressure gradient that is associated with the fluid motion which is shown to be vitally important for the accuracy of the numerical solution to this end a force balanced discretisation of the source terms is proposed that precisely matches the discretisation of the pressure gradients and preserves the force applied to the flow using representative test cases of incompressible and low mach number flows including flows with discontinuous source terms and two phase flows with large density ratios the newly proposed formulation of the mwi is favourably compared against existing formulations and is shown to significantly reduce or even eliminate solution errors with an increased stability for flows with large density ratios

immersed boundary method for generalised finite volume and finite difference 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

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

a cartesian grid method with transient anisotropic adaptation a cartesian grid method with solution adaptive anisotropic refinement and coarsening is developed for simulating time dependent incompressible flows the cartesian grid cells and faces are managed using an unstructured data approach and algorithms are described for the time accurate transient anisotropic refinement and coarsening of the cells the governing equations are discretized using a collocated cell centered arrangement of velocity and pressure and advanced in time using the fractional step method significant savings in the memory requirement of the method can be realized by advancing the velocity field using a novel approximate factorization technique although an iterative technique is also presented the pressure poisson equation is solved using additive correction multigrid and an efficient coarse grid selection algorithm is presented finally the cartesian cell geometry allows the development of relatively simple analytic expressions for the optimal cell dimensions based on limiting the velocity interpolation error the overall method is validated by solving several benchmark flows including the 2d and 3d lid driven cavity flows and the 2d flow around a circular cylinder in this latter case an immersed boundary method is used to handle the embedded cylinder boundary

derivation of a modified hybrid approximation to assess the present algorithm as compared with the btdmia we give in table 1 their storage needs and operation counts per grid point when both are applied without and with bordering to the inverse boundary layer problem described earlier for fair comparison when m m the two methods should operate in opposite directions the forward sweep of the present algorithm is to be carried out starting from the side with m conditions whereas its counterpart of the most efficient form of the btdmia is to be carried out starting from the other side the conclusion is twofold non bordering is superior to bordering the present algorithm is more efficient than the btdmia

lattice boltzmann method for simulating the viscous flow in large distensible blood vessels a lattice boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries the mass conservation for the boundary condition is tested in detail the viscous flow in elastic vessels is simulated with a pressure radius relationship similar to that of the pulmonary blood vessels the numerical results for steady flow agree with the analytical prediction to very high accuracy and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally the model is expected to find many applications for studying blood flows in large distensible arteries especially in those suffering from atherosclerosis stenosis aneurysm etc

an adjoint based lattice boltzmann method for noise control problems in this paper optimal control of acoustic problems is addressed within the lattice boltzmann method framework to this end an adjoint based lattice boltzmann method is proposed to solve the adjoint problem the adjoint state provides an easy access to the optimization gradients the line search step in newton s descent method is performed through a combination of complex differentiation and adjoint problem in the lattice boltzmann method the implementation of an active noise reduction method for two dimensional weakly compressible low mach number flows is discussed and the applicability of the method is assessed

topology optimization using the lattice boltzmann method incorporating level set boundary expressions this paper presents a topology optimization method for fluid dynamics problems based on the level set method and using the lattice boltzmann method lbm in this optimization method the optimization problems are formulated based on the original boltzmann equation and the design sensitivities are precisely obtained without the time consuming numerical operations encountered when dealing with a large scale asymmetric matrix in contrast to previous research in which the lbm uses the lattice boltzmann equation lbe for the formulations of optimization problems and the derivation of their adjoint equations that is we newly derive sensitivity formulations from the original boltzmann equation not the lbe that can be said to be an approximated equation and these formulations yield strictly correct sensitivities that are error free based on the above formulations we construct a level set based topology optimization method incorporating a fictitious interface energy for the design of a fluid channel that minimizes flow friction furthermore two and three dimensional numerical examples are provided to confirm the validity and utility of the presented method

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

level set based topology optimization of transient flow using lattice boltzmann method considering an oscillating flow condition abstract topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering specifically the development of energy dissipation devices with vibration control remains a key consideration the aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real world engineering designs although several studies have examined topology optimization to minimize dissipated kinetic energy this study introduces an objective function for maximizing the dissipated kinetic energy in time varying fluid flows via velocity gradients

quantifying and reducing model form uncertainties in reynolds averaged navier stokes simulations despite their well known limitations reynolds averaged navier stokes rans models are still the workhorse tools for turbulent flow simulations in today s engineering analysis design and optimization while the predictive capability of rans models depends on many factors for many practical flows the turbulence models are by far the largest source of uncertainty as rans models are used in the design and safety evaluation of many mission critical systems such as airplanes and nuclear power plants quantifying their model form uncertainties has significant implications in enabling risk informed decision making in this work we develop a data driven physics informed bayesian framework for quantifying model form uncertainties in rans simulations uncertainties are introduced directly to the reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints e g realizability smoothness and symmetry an iterative ensemble kalman method is used to assimilate the prior knowledge and observation data in a bayesian framework and to propagate them to posterior distributions of velocities and other quantities of interest qois we use two representative cases the flow over periodic hills and the flow in a square duct to evaluate the performance of the proposed framework both cases are challenging for standard rans turbulence models simulation results suggest that even with very sparse observations the obtained posterior mean velocities and other qois have significantly better agreement with the benchmark data compared to the baseline results at most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds the framework is a major improvement over existing black box physics neutral methods for model form uncertainty quantification where prior knowledge and details of the models are not exploited this approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes proposed a physics informed framework to quantify uncertainty in rans simulations framework incorporates physical prior knowledge and observation data based on a rigorous bayesian framework yet fully utilizes physical model applicable for many complex physical systems beyond turbulent flows

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

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

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

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

on the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates abstract the issues of adopting the velocity components as dependent velocity variables including the cartesian and culvilinear ones for the navier stokes flow computations are investigated the viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form it is demonstrated that with the curvilinear velocity vectors the curvatures of the grid lines introduce extra source terms into the governing equations with the cartesian velocity vector on the other hand the governing equations in curvilinear coordinates can retain the full conservation law form and honor the physical conservation laws the nonlinear combinations of the metric terms also cause the algorithms based on curvilinear velocity components to be more difficult to satisfy the geometric conservation law and hence more sensitive to grid skewness effect for the combined utilization of the cartesian velocity vector and the staggered grid arrangement the implications of spurious pressure oscillation arising from the 90 turning are discussed it is demonstrated that these spurious oscillations can possibly appear only under a very specific circumstance namely the meshes in the region with 90 turning must be parallel to the cartesian coordinates and of uniform spacing along coordinates otherwise no spurious oscillations can appear several flow solutions for domain with 90 and 360 turnings are presented to demonstrate that satisfactory results can be obtained by using the cartesian velocity components and the staggered grid arrangement

enhancement of an industrial finite volume code for large eddy type simulation of incompressible high reynolds number flow using near wall modelling abstract we present a validation strategy for enhancement of an unstructured industrial finite volume solver designed for steady rans problems for large eddy type simulation with near wall modelling of incompressible high reynolds number flow different parts of the projection based discretisation are investigated to ensure les capability of the numerical method turbulence model parameters are calibrated by using a minimisation of least squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow then the method is applied to the flow over a backward facing step at reh 37 500 of special interest is the role of the spatial and temporal discretisation error for low order schemes for wall bounded flows present results confirm existing best practice guidelines for mesh design for free shear layers a sensor to quantify the resolution quality of the les based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at reh 37 500

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

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

the integrated space time finite volume method and its application to moving boundary problems abstract the integrated space time finite volume method for predicting time dependent fluid flow problems is developed by enforcing discrete conservation over space time control volumes which fill the space time domain this method satisfies global conservation in space time while automatically satisfying the leibnitz rule and geometrical conservation law the method is validated using a variety of two dimensional problems featuring both prescribed and free boundary motion advances in other aspects of cell centered finite volume discretization most notably in the modelling of diffusion terms and free surface flows are also described

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

experimental investigation of turbulent flow through a circular to rectangular transition duct an experimental study was conducted to investigate incompressible turbulent flow through a circular torectangular transition duct having the same inlet and outlet cross sectional areas an overall length to diameter ratio of 4 5 and an aspect ratio of 3 0 at the exit plane downstream of the inlet the local cross sectional area increased to a value 15 above the inlet value and then decreased to the exit value mean flow and turbulence data were obtained by means of pressure probe and hot wire instrumentation for an operating bulk reynolds number of 3 9 x 10 5 the results show that curvature of the duct walls induces a relatively strong pressuredriven crossflow that develops into a contrarotating vortex pair near the diverging side walls of the duct this vortex pair significantly distorts both the primary mean velocity and reynolds stress fields law of the wall behavior was observed in the near wall region at the duct exit plane and to a lesser extent immediately after the end of transition analysis of the results shows that caution must be observed if conventional wall functions are used to predict the present flow situation

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

a new reynolds stress algebraic equation model a new reynolds stress algebraic equation modeltsan hsing shih and jiang zhucenter for modeling of turbulence and transitioninstitute for computational mechanics in propulsionnasa lewis research center cleveland ohiojohn l lumleycornell university ithaca new yorkabstracta general turbulent constitutive relation shih and lumley 1993 is directly appliedto propose a new reynolds stress algebraic equation model in the development of thismodel the constraints based on rapid distortion theory and realizability i e the positivityof the normal reynolds stresses and the schwarz inequality between turbulent velocitycorrelations are imposed model coefficients are calibrated using well studied basic flowssuch as homogenous shear flow and the surface flow in the inertial sublayer the performanceof this model is then tested in complex turbulent flows including the separated flow over abackward facing step and the flow in a confined jet the calculation results are encouragingand point to the success of the present model in modeling turbulent flows with complexgeometries 1 introductionthe present study concentrates on complex turbulent shear flows which are of greatinterest in propulsion systems the particular flows presented in this paper are for thebackward facing step and the confined jet both of which have complex structures forexample a confined jet combines several types of flow structure and flow phenomena suchas a shear layer jet recirculation separation and reattachment accurate prediction ofthese flows is of great importance in all the key elements of engine design the turbulence model developed in this study is a reynolds stress algebraic equationmodel which is based on a turbulent constitutive relation shill and lum ey 1993 a result ofrapid distortion theory reynolds 1987 and the turbulent realizability principle schumann1977 lumley 1978 the constitutive relation is obtained using the invariance theory incontinuum mechanics for flows including a passive scalar this theory leads to a generalconstitutive relation for the reynolds stress tensor uiuj in terms of the mean deformationrate tensor ui j and the turbulent velocity and length scales characterized by the turbulentkinetic energy k and its dissipation rate s pope 1975 applied a similar constitutiverelation to rodi s algebraic reynolds stress formulation rodi 1972 in conjunction withthe lrr second order closure model launder et ai 1975 and obtained an explicit algebraic

projection methods for two velocity two pressure models for flows of heterogeneous mixtures in this paper a numerical analysis of two velocity two pressure models for flows of solid particles and fluids is presented first a formal exploitation of the weak formulation of such models asserts that they are amenable to integration via projection methods the challenging issues in the algorithm development for these models are then documented and suitable numerical methodologies for their remedy are devised subsequently an algorithm for the integration of the models of interest is proposed this is a two phase projection method on collocated grids that utilizes a fractional step time marching scheme it is further endowed with an interface detection and treatment methodology to properly account for the stiffness induced by the presence of moving and deforming material interfaces the efficiency and robustness of the proposed numerical method are assessed in a series of numerical experiments that are delineated in the last part of this paper

pressure based navier stokes solver using the multigrid method apressure based implicit procedure to solve steadystate navier stokes equations is developed a multistep pressure correction procedure with an implicit density treatment is used to establish the pressure and velocity fields a multigrid relaxation scheme is used to solve the scalar matrices resulting from the finite volume formulation the algorithm is valid for all mach number flows ranging from incompressible to supersonic flow regimes

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

an accurate compact treatment of pressure for colocated variables we propose a new scheme for the pressure treatment in computations of incompressible flow using a colocated grid arrangement to avoid oscillations associated with the sparse non compact stencil we introduce a compact fourth order equivalent of this stencil and study its advantages over the classical second order averaging procedure

lattice boltzmann method for non newtonian power law fluids we study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models we extensively test the accuracy of the method for the case of shear thinning and shear thickening truncated power law fluids in the parallel plate geometry and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution finally we also tested the method in the reentrant flow geometry in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points in this geometry we also found excellent agreement with the solutions obtained by standard finite element methods and the agreement improves with higher lattice resolution

a flat strip theorem for ptolemaic spaces a metric space x d is called ptolemaic space pt space if the inequality xy zw xz yw xw yz holds for each quadruple of points x y z and w in x here xy d x y denotes the distance of two points x and y the main result proven in the paper is the following if x d is a pt space which is also a geodesic space i e for each pair x y there exists a geodesic connecting x and y and if x is moreover homeomorphic to 0 1 then x is isometric to a flat strip 0 a 2 with its euclidean metric the authors also give a new short proof of the fact that a proper geodesic pt space is always strictly distance convex see also th foertsch and v schroeder trans am math soc 363 no 6 2891 2906 2011 zbl 1220 53092 this also indicates a positive answer to the open question if every proper geodesic pt space is also a cat 0 space