a parallel implicit method for the direct numerical simulation of wall bounded compressible turbulence a new second order accurate implicit temporal numerical scheme for the direct numerical simulation of turbulent flows is presented the formulation of the implicit method and the corresponding tunable parameters are introduced the numerical simulation results are compared with the results given by explicit runge kutta schemes theoretical results and published experimental and numerical data an assessment of the accuracy and performance of the method to simulate turbulent flows is made for temporally decaying isotropic turbulence and subsonic and supersonic turbulent boundary layers whereas no significant advantage over typical explicit time integration methods are found for the incompressible flows it is shown that the implicit scheme yields significant reduction in computer cost while assuring time accurate solutions for compressible turbulence simulations

three dimensional incompressible navier stokes solver using lower upper symmetric gauss seidel algorithm a numerical method based on the pseudocompressibility concept is developed for solving the three dimensional incompressible navier stokes equations using the lower upper symmetric gauss seidel implicit scheme very high efficiency is achieved in a new flow solver ins3d lu code by accomplishing the complete vectorizability of the algorithm on obiique planes of sweep in three dimensions

efficient cell vertex multigrid scheme for the three dimensional navier stokes equations a cell vertex scheme for the three dimensional navier stokes equations which is based on central difference approximations and runge kutta time stepping is described by using local time stepping implicit residual smoothing with locally varying coefficients a multigrid method and carefully controlled dissipative terms very good convergence rates are obtained for two and three dimensional flows details of the acceleration techniques which are important for convergence on meshes with high aspect ratio cells are discussed emphasis is placed on the analysis of the implicit smoothing of the explicit residuals with coefficients which depend on cell aspect ratios

multigrid solution of the euler equations using implicit schemes on utilise une methode multigrille du type factorisation approchee couplee a un schema de direction alternee implicite pour resoudre les equations d euler pour l ecoulement transsonique sur un profil aerodynamique on obtient une convergence tres rapide

diagonal implicit multigrid algorithm for the euler equations a multigrid implementation of the alternating direction implicit algorithm has been developed to solve the euler equations of inviscid compressible flow the equations are approximated using a finite volume spatial approximation with added dissipation provided by an adaptive blend of second and fourth differences for computational efficiency the equations are diagonalized by a local similariity transformation so that only a decoupled system of scalar pentadiagonal systems need be solved along each line results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the basic scheme and convergence histories to demonstrate the efficiency of the method

application of simultaneous perturbation stochastic approximation method for aerodynamic shape design optimization aerodynamic shape design optimization problems such as inverse and constrained airfoil design and axisymmetric nozzle design are investigated by applying the simultaneous perturbation stochastic approximation spsa method to objective functions that are estimated during each design iteration using a finite volume computational fluid dynamics technique for solving the compressible navier stokes equations the spsa method has been demonstrated in the literature as having significant advantages over stochastic global optimization methods such as the simulated annealing sa method in this work the spsa is compared with sa method for a class of twodimensional and axisymmetric aerodynamic design optimization problems the numerical studies show that the spsa method is robust in reaching optimal aerodynamic shapes is easy to implement and is highly efficient the spsa method can also decrease the computational costs significantly compared with the sa method

bayesian prediction tests for structural stability abstract a bayesian prediction test for structural stability is proposed which has several advantages over classical procedures in particular the small sample distribution of the test statistic is known under the null hypothesis the same test statistic is appropriate for both regression and time series models the test is valid even for nonstationary multivariate ar and var models and the test is robust to certain forms of nonnormality in the error distribution a comparison of the bayesian and classical tests indicates that the bayesian test is equivalent to the predictive chow test for regression models

implicit time stepping methods for the navier stokes equations a novel two factor approximate factorization for three dimensional flows is described the method uses a preconditioned conjugate gradient solver for one of the factors and this solution is based on a method developed for two dimensional flows this two dimensional method is described and its performance is summarized for steady and unsteady flows the two factor method is then given larger time steps can be used with this method than is possible with the more conventional three factor method test results for the transonic steady flow over the onera m6 wing are given

a multidimensional gas kinetic bgk scheme for hypersonic viscous flow this paper concerns the development and application of a gas kinetic scheme based on the bhatnagar gross krook bgk model for the navier stokes equations in the study of hypersonic viscous flow firstly we extend the gas kinetic navier stokes solver k xu a gas kinetic bgk scheme for the navier stokes equations and its connection with artificial dissipation and godunov method j comput phys 171 2001 289 335 by implementing a multidimensional particle propagation mechanism in the flux evaluation where the gradients of flow variables in both normal and tangential directions of a cell interface are explicitly included with the construction of a time averaged flux function an implicit bgk scheme with lu sgs method is constructed the main purpose of the current research is to pave the way to extend the current approach directly to the flow computation with unstructured mesh where the flow gradients in both parallel and perpendicular directions around a cell interface can be explicitly taken into account in a viscous flow computation in the numerical parts we concentrate on the computation of heat flux in laminar hypersonic viscous flows where complicated flow phenomena i e shock boundary layer interaction flow separation and viscous inviscid interaction will be encountered the cases studied include the type iv shock shock interaction around a circular cylinder and hypersonic flow passing through a double cone geometry in the hypersonic viscous flow in comparison with the capturing of velocity and pressure fields the accurate computation of stress and heat flux bears large difficulties in all cases studied here the heat fluxes obtained across body surfaces have good agreement with the experimental measurements

analytic approach to the critical density in cellular automata for traffic flow the jamming transition in the stochastic traffic cellular automaton of nagel and schreckenberg j phys i 2 2221 1992 is examined we argue that most features of the transition found in the deterministic limit do not persist in the presence of noise and suggest instead to define the transition to take place at that critical density ensuremath rho c at which a large initial jam just fails to dissolve we show that ensuremath rho c v j v j v f where v f is the velocity of noninteracting vehicles and v j is the speed of the dissolution wave moving into the jam an approximate analytic calculation of v j in the framework of a simple renormalization scheme is presented which explicitly displays the effect of the interaction between vehicles during the acceleration stage of the nagel schreckenberg rules with maximum velocity v mathrm max g1 the analytic prediction is compared to numerical simulations we find a remarkable correspondence between the analytic expression for v j and a phase diagram obtained numerically by l ubeck et al phys rev e 57 1171 1998

aerodynamic shape optimization using computational fluid dynamics and parallel simulated annealing algorithms aerodynamic shape design using stochastic optimization methods such as simulated annealing method to optimize objective functions evaluated by modern state of the art computational fluid dynamics solvers normally requires enormous computation time to search for the global optimal design aerodynamic shape optimization of internal flow systems is studied using euler navier stokes solvers and parallel simulated annealing algorithm which is implemented on parallel computing platforms a variety of inverse and direct design of internal flow systems are carried out to examine the efficiency and speedup of the parallel simulated annealing algorithms

cellular automata models for general traffic conditions on a line abstract by the use of the methods proposed in a recent article we were able to shed some light on the experimentally obtained flux density relation in traffic flow we suggest an order parameter showing the existence of two regimes in freeway traffic we also introduce the case of traffic at signal condition analysing the effects of convenient traffic parameters on the flux density diagram

overrelaxation applied to lower upper symmetric gauss seidel method for hypersonic flow an implicit time marching method for acceleration of the convergence of solution for the compressible navier stokes equations is presented this is based on the lower upper symmetric gauss seidel lu sgs method proposed by yoon and jameson a very simple overrelaxation is additionally executed in the lu sgs method coupled with diagonal flux splitting then an overrelaxation parameter w a parameter similar to that in the well known successive overrelaxation method is introduced the calculated results for a hypersonic viscous flows around a cylinder and through a compression corner indicate that the convergence is accelerated by a proper value of 1 2 this method is also applied to a hypersonic thermochemical nonequilibrium flow around a sphere

the ergodic theory of traffic jams we introduce and analyze a simple probabilistic cellular automaton which emulates the flow of cars along a highway our traffic ca captures the essential features of several more complicated algorithms studied numerically by k nagel and others over the past decade as prototypes for the emergence of traffic jams by simplifying the dynamics we are able to identify and precisely formulate the self organized critical evolution of our system we focus here on the cruise control case in which well spaced cars move deterministically at maximal speed and we obtain rigorous results for several special cases then we introduce a symmetry assumption that leads to a two parameter model described in terms of acceleration and braking probabilities based on the results of simulations we map out the phase diagram identifying three qualitatively distinct varieties of traffic which arise and we derive rigorous bounds to establish the existence of a phase transition from free flow to jams many other results and conjectures are presented from a mathematical perspective traffic ca provides local particle conserving one dimensional dynamics which cluster and converge to a mixture of two distinct equilibria

parallel computations of high lift airfoil flows using two equation turbulence models this work was partially sponsored by the korea aerospace research institute and the korea research foundation

prediction tests for structural stability abstract three groups of test statistics for testing structural stability are compared the statistics are based on predictions from univariate time series models the first group ignores the specification and estimation variability the second group ignores only the specification uncertainty while the statistics in the third group take into account both specification and estimation variability although corresponding statistics in the three groups have identical asymptotic distributions their small sample distributions differ markedly it is suggested to use the statistics in the third group in practice

multigrid convergence of an implicit symmetric relaxation scheme the multigrid method has been applied to an existing three dimensional compressible euler solver to accelerate the convergence of the implicit symmetric relaxation scheme this lower upper symmetric gauss seidel implicit scheme is shown to be an effective multigrid driver in three dimensions a grid refinement study is performed including the effects of large cell aspect ratio meshes performance figures of the present multigrid code on cray computers including the new c90 are presented a reduction of three orders of magnitude in the residual for a three dimensional transonic inviscid flow using 920 k grid points is obtained in less than 4 min on a cray c90 23 refs

data parallel lower upper relaxation method for the navier stokes equations the lower upper symmetric gauss seidel method is modified for the simulation of viscous flows on massively parallel computers the resulting diagonal data parallel lower upper relaxation dp lur method is shown to have good convergence properties on many problems however the convergence rate decreases on the high cell aspect ratio grids required to simulate high reynolds number flows therefore the diagonal approximation is relaxed and a full matrix version of the dp lur method is derived the full matrix method retains the data parallel properties of the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid both methods are implemented on the thinking machines cm 5 and a large fraction of the peak theoretical performance of the machine is obtained the low memory use and high parallel efficiency of the methods make them attractive for large scale simulation of viscous flows

wavenumber optimized immersed boundary method for aeroacoustic analysis based on cartesian mesh an immersed boundary method ibm suitable for aeroacoustic analysis is developed using the block structured cartesian mesh method called the building cube method the ibm using a ghost cell approach in conjunction with an image point is employed a hybrid interpolation scheme combining the wavenumber based method and inverse distance weighting method is introduced to the ibm this method is evaluated using four test cases the results of interpolation at an image point indicate that the wavenumber based method provides more accurate results than standard interpolation methods for aeroacoustic problems the results of acoustic scattering around a sphere show that the proposed ibm achieves better than second order accuracy in the case of noise propagation from a generic inlet the proposed ibm is shown to yield more accurate predictions for the far field sound pressure level than the inverse distance weighting based ibm in a different application involving the jt15d nacelle the far field sound pressure

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

lower upper implicit scheme for high speed inlet analysis on developpe une methode numerique d analyse du champ d ecoulement non visqueux d une entree a grande vitesse par resolution des equations d euler le schema se revele efficace et robuste aussi bien pour les faibles nombres de mach que pour les ecoulements transsoniques

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

lower upper symmetric gauss seidel method for the euler and navier stokes equations on developpe un schema de relaxation multigrille application a des ecoulements transsoniques

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

prediction from the dynamic simultaneous equation model with vector autoregressive errors the asymptotic distribution of prediction is derived for the general simultaneous equation model with lagged endogenous variables and vector autoregressive errors the results turn out to be particularly simple when no lagged endogenous variables are present errors it seems worthwhile to extend schmidt s results since the estimation of dynamic simultaneous equation models with autoregressive errors is now fairly commonplace in the literature also as noted by schmidt 5 the effects of parameter estimation can produce a significant effect on forecast confidence intervals in fact the results we obtain are computationally feasible making it possible to calculate the term due to parameter estimation in a forecast confi dence interval for the seemingly unrelated regression model with vector autore gressive errors but with no lagged dependent variables the results turn out to be particularly straightforward generalizations of those obtained by baillie 1 who

implicit solution method for incompressible navier stokes equations including two layer k tau turbulence model the two dimensional incompressible navier stokes equations including a low reynolds number two layer k turbulence model are solved by an implicit time stepping routine using the method of artificial compressibility the two layer model uses a transport equation for the turbulent kinetic energy k and a new algebraic relationship for the turbulent time scale near the wall but reverts to the two equation k turbulence model in the bulk of the flow away from the wall the algebraic relationship for the turbulent time scale and the eddy viscosity damping function f are validated by direct numerical simulation data and asymptotic analysis of near wall turbulence a fifth order upwind biased differencing scheme is used to discretize the convective and pressure terms and second order central differences are employed for other spatial derivatives the nonlinear equations are solved using the preconditioned generalized minimal residual technique in conjunction with numerical linearization a ld 1 u factorization of the approximate jacobian matrix is used as preconditioning matrix

parallelization of rotorcraft aerodynamics navier stokes codes the modie cation of unsteady three dimensional navier stokes codes for application on massively parallel and distributed computing environments is investigated previously theeulermode of thenavier stokescode turns hasbeenparallelized fortheefe cientimplementation ofthenavier stokesmodeofturns onparallelcomputing systems several algorithmic changes should be made the main modie cation is done on the implicit operator lower upper symmetric gauss seidel two new implicit operators are used because of convergence problems of traditional operators with high cell aspect ratio grids needed for viscous calculations results for navier stokes cases are presented for various operators the message passing interface protocol is used because of its portability to various parallel architectures nomenclature a speed of sound e total energy p pressure pr prandtl number re reynolds number u v w cartesian velocities x y z cartesian coordinates specie c heat ratio dynamic viscosity generalized coordinates density 9 rotor azimuth angle

partially implicit scheme for chemically reacting flows at all mach numbers chemical reactions make computations of chemically reacting e ows stiff the degree of stiffness increases as the mach number decreases because the e ow timescale increases while the reaction timescales remain constant thus the computation of reacting e ows at low mach numbers is more dife cult than that in high mach number in the present study a new implicit scheme that employs partially implicit treatment of chemical source terms at mixed time levels has been developed the chemical jacobian is reduced to a partial form of the full chemical jacobian a lower triangular matrix and thus saves timein matrix inversion in addition robust calculation of the reacting e ows is made possible because a negative real eigenvalue of the partial chemical jacobian allows larger time step sizes than the full chemical jacobian for applications at all mach numbers a preconditioned lower upper symmetric gauss seidel scheme employing an approximate e ux jacobian splitting is incorporated for high mach number e ows the partially implicit scheme maintains similar convergence rates to the fully implicit one therefore it enhances computational efe ciency by reducing computing time per iteration for low machnumber reacting e ows it also enables robust calculation of reactions as well as the fully implicit one however its convergence rate is rather slow furthermore more stable and efe cient computations are possible when the fully implicit scheme is coupled with the partially implicit one

an implicit scheme for nonideal magnetohydrodynamics a new implicit algorithm is developed for solving the time dependent nonideal magnetohydrodynamic equations it can also be used as an efficient relaxation scheme for steady state solutions the algorithm is a finite volume scheme that uses an approximate riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non ideal terms i e resistivity and viscosity in one dimension the scheme is second order accurate in space and time in two or three dimensions the accuracy is between first and second order for the class of problems considered the implicit formulation is stable for any size time step thus allowing efficient tracking of slower transients the implicit operator is inverted using a lower upper symmetric gauss seidel iteration results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme

artificial dissipation models for the euler equations various artificial dissipation models that are used with central difference algorithms for the euler equations are analyzed for their effect on accuracy stability and convergence rates in particular linear and nonlinear models are investigated using an implicit approximate factorization code arc2d for transonic airfoils fully implicit application of the dissipation models is shown to improve robustness and convergence rates the treatment of dissipation models at boundaries will be examined it will be shown that accurate error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model i introduction t he solution of the euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme this is because the euler equations do not provide any natural dissipation mechanism such as viscosity in the navier stokes equations that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks a variety of numerical algorithms and computer codes for the euler equations have been developed methods such as maccormack s1 explicit

convergence acceleration of a navier stokes solver for efficient static aeroelastic computations new capabilities have been developed for a navier stokes solver to perform steady state simulations more efficiently the flow solver for solving the navier stokes equations is based on a combination of the lower upper factored symmetric gauss seidel implicit method and the modified harten lax van leer einfeldt upwind scheme a numerically stable and efficient pseudo time marching method is also developed for computing steady flows over flexible wings results are demonstrated for transonic flows over rigid and flexible wings

data parallel lower upper relaxation method for reacting flows the implicit lower upper symmetric gauss seidel lu sgs method of yoon and jameson is modified for use on massively parallel computers the method has been implemented on the thinking machines cm s and the maspar mp 1 and mp 2 where large percentages of the theoretical peak floating point performance are obtained it is shown that the new data parallel lu relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations the convergence is also improved for five species reacting air computations the performance of the method on various partitions of the cm s and on the maspar computers is discussed the new method shows promise for the efficient simulation of very large perfect gas and reacting flows

comparison of nonequilibrium solution algorithms applied to chemically stiff hypersonic flows three solution algorithms explicit under relaxation point implicit and lower upper symmetric gauss seidel are used to compute nonequilibrium flow around the apollo 4 return capsule at the 62 km altitude point in its descent trajectory by varying the mach number the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness the performance of the solution algorithms degraded as the mach number and stiffness of the flow increased at mach 15 and 30 the lower upper symmetric gauss seidel method produces an eight order of magnitude drop in the energy residual in one third to one half the cray c 90 computer time as compared to the point implicit and explicit under relaxation methods the explicit under relaxation algorithm experienced convergence difficulties at mach 30 and above at mach 40 the performance of the lower upper symmetric gauss seidel algorithm deteriorates to the point that it is out performed by the point implicit method the effects of the viscous terms are investigated grid dependency questions are explored

approximate factorization with source terms a comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error while two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized the third method used generates the lowest approximate factorization error this method may be preferred when the norms of source terms are large and transient solutions are of interest

optimizing a boundary layer ingestion offset inlet by discrete adjoint approach a large amount of low momentum boundary layer flow ingesting into a flush mounted inlet can cause significant total pressure loss and distortion to the extent beyond operability of a fan compressor to improve the quality of incoming flow into the engine shape optimization of the surface geometry at the inlet entrance has been carried out using the discrete adjoint method the inlet floor shape is parameterized by the use of control points on b spline surface patches to resolve the complicated geometry flexibly and wall bounded turbulent flow accurately an overset mesh system is well suited for integrating the flow analysis code sensitivity analysis code and grid modification tools to enhance the convergence characteristics of the sensitivity analysis code additional numerical dissipation for the discrete adjoint formulation is introduced after using this optimization procedure the new inlet yields a significant improvement in performance a more than 50 reduction in flow distortion and a 3 increase in total pressure recovery high performance at off design conditions is also realized with only slight degradation confirming the capability of the adjoint method for a practical design problem finally the physical meaning and implication of the performance improvement are elaborated upon in relation to the flow characteristics resulting from the new design

convergence characteristics of preconditioned euler equations the convergence characteristics of the preconditioned euler equations were studied a perturbation analysis was conducted to search for the relationships between the convergence characteristics and the flow mach numbers also the influence of cancellation errors on the convergence characteristics was investigated the governing equations were the preconditioned two dimensional euler equations flows in a two dimensional channel with a 10 circular bump in the middle of the channel were calculated at different speeds roe s fds scheme was used for spatial discretization and the lu sgs lower upper symmetric gauss seidel scheme was used for time integration it was shown that the convergence characteristics of continuity and momentum equations were maintained regardless of the mach numbers but the convergence characteristics of energy equation were strongly dependant on the mach numbers and worsened as the mach number decreased the convergence characteristics were well explained by the perturbation analysis the convergence characteristics were strongly dependant on the characteristics of the preconditioning matrix cancellation errors caused a serious convergence problem especially in the calculation of the energy equation at very low mach numbers the relative treatments and a higher precision of floating point variables alleviated cancellation problems to some extent however the convergence rate was not affected by the relative treatments or by the precision of floating point variables

fully implicit chebyshev time spectral method for general unsteady flows an efficient fully implicit chebyshev time spectral method tsm is developed to solve general unsteady flows with or without periodicity high accuracy of the chebyshev time spectral operator is d

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

particle hopping models of vehicular traffic distributions of distance headways and distance between jams we calculate the distribution of the distance headways i e the instantaneous gap between successive vehicles as well as the distribution of instantaneous distance between successive jams in the nagel schreckenberg ns model of vehicular traffic when the maximum allowed speed vmax of the vehicles is larger than unity over an intermediate range of densities of vehicles our monte carlo mc data for the distance headway distribution exhibit two peaks which indicate the coexistence of free flowing traffic and traffic jams our analytical arguments clearly rule out the possibility of occurrence of more than one peak in the distribution of distance headways in the ns model when vmax 1 as well as in the asymmetric simple exclusion process modifying and extending an earlier analytical approach for the ns model with vmax 1 and introducing a novel transfer matrix technique we also calculate the exact analytical expression for the distribution of distance between the jams in this model the corresponding distributions for vmax 1 have been computed numerically through mc simulation

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

on modified block ssor iteration methods for linear systems from steady incompressible viscous flow problems abstract in order to solve the large sparse systems of linear equations arising from numerical solutions of two dimensional steady incompressible viscous flow problems in primitive variable formulation we present block ssor and modified block ssor iteration methods based on the special structures of the coefficient matrices in each step of the block ssor iteration we employ the block lu factorization to solve the sub systems of linear equations we show that the block lu factorization is existent and stable when the coefficient matrices are block diagonally dominant of type ii by columns under suitable conditions we establish convergence theorems for both block ssor and modified block ssor iteration methods in addition the block ssor iteration and af adi method are considered as preconditioners for the nonsymmetric systems of linear equations numerical experiments show that both block ssor and modified block ssor iterations are feasible iterative solvers and they are also effective for preconditioning krylov subspace methods such as gmres and bicgstab when used to solve this class of systems of linear equations

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

a reconstructed discontinuous galerkin method for incompressible flows on arbitrary grids abstract the discontinuous galerkin dg methods have attained increasing popularity for solving the incompressible navier stokes ins equations in recent years however the dg methods have their own weakness due to the high computational costs and storage requirements in this work we develop a high order hybrid reconstructed dg rdg method for solving the ins equations on arbitrary grids to be specific the inviscid term of the ins equations is discretized by applying the third order hybrid rdg p 1 p 2 method with a simplified artificial compressibility flux while the viscous term of the ins equations is discretized by using the simple direct dg ddg method a number of incompressible flow problems in both steady and unsteady forms for a variety flow conditions are computed to numerically assess the performance of the hybrid rdg p 1 p 2 method which confirm its ability to achieve the optimal third order of accuracy at a significantly reduced computational costs furthermore a detailed comparison of a variety of different reconstructed strategies is performed and presented numerical results demonstrate that the hybrid rdg p 1 p 2 method outperforms the rdg p 1 p 2 method based on either the original least squares reconstruction or the green gauss reconstruction for solving the ins equations

ballistic annihilation and deterministic surface growth a model of deterministic surface growth studied by krug and spohn a model of the annihilating reactiona b inert studied by elskens and frisch a one dimensional three color cyclic cellular automaton studied by fisch and a particular automaton that has the number 184 in the classification of wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation this automaton is defined by the following rules at timet 0 one particle is put at each integer point of to each particle a velocity is assigned in such a way that it may be either 1 or 1 with probabilities 1 2 independent of the velocities of the other particles as time goes on each particle moves along at the velocity assigned to it and annihilates when it collides with another particle in the present paper we compute the distribution of this automaton for each timet we then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above we also show the relation of this limit process to the process which we call moving local minimum of brownian motion the latter is the processb min x defined byb min min b y x 1 y x 1 for everyx whereb x x is the standard brownian motion withb 0 0

implicit boundary equations for conservative navier stokes equations abstract co existence of the physical and numerical boundary conditions makes implicit boundary treatment a particularly difficult problem in modern cfd simulations previous studies adopted space time extrapolation or specially designed partial differential equations on the boundaries that are different from those of interior points they are often formulated in terms of primitive variables and are very challenging for complicated boundary types to be converted to and implemented in the conservative variables that are preferred in numerical simulations more importantly different boundary equations or different extrapolation techniques may compromise the stability accuracy or convergence rate of the a stable schemes that are developed for interior points a new methodology for implicit boundary treatment is proposed in this study by introducing a simple correction matrix t a set of generalized equations q t i t r are developed in terms of conservative variables it is applicable for both the interior domain t 0 and the boundaries t 0 it is in a partial differential equation form satisfies the boundary conditions accurately independent of the time and spatial discretizations any one sided schemes can be used on the boundaries but still maintain the upwind property implicit solution techniques are made significantly easy to implement using for example the data parallel lower upper relation method and the newton method combined with the gmres method for subsidiary iterations numerical experiments show that the proposed methodology produces stable simulations for very large cfl numbers and preserve the imposed boundary values accurately

traffic model with an absorbing state phase transition we consider a modified nagel schreckenberg ns model in which drivers do not decelerate if their speed is smaller than the headway number of empty sites to the car ahead in the original ns model such a reduction in speed occurs with probability p independent of the headway as long as the current speed is greater than zero in the modified model the free flow state with all vehicles traveling at the maximum speed v max is absorbing for densities smaller than a critical value c 1 v max 2 the phase diagram in the p plane is reentrant for densities in the range c c both small and large values of p favor free flow while for intermediate values a nonzero fraction of vehicles have speeds v max in addition to representing a more realistic description of driving behavior this change leads to a better understanding of the phase transition in the original model our results suggest an unexpected connection between traffic models and stochastic sandpiles

implicit unified gas kinetic scheme for steady state solutions in all flow regimes this paper presents an implicit unified gas kinetic scheme ugks for non equilibrium steady state flow computation the ugks is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function by solving the macroscopic equations implicitly a predicted equilibrium state can be obtained first through iterations with the newly predicted equilibrium state the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well the lower upper symmetric gauss seidel lu sgs factorization method is implemented to solve both macroscopic and microscopic equations which improves the efficiency of the scheme since the ugks is a direct modeling method and its physical solution depends on the mesh resolution and the local time step a physical time step needs to be fixed before using an implicit iterative technique with a pseudo time marching step therefore the physical time step in the current implicit scheme is determined by the same way as that in the explicit ugks for capturing the physical solution in all flow regimes but the convergence to a steady state speeds up through the adoption of a numerical time step with large cfl number many numerical test cases in different flow regimes from low speed to hypersonic ones such as the couette flow cavity flow and the flow passing over a cylinder are computed to validate the current implicit method the overall efficiency of the implicit ugks can be improved by one or two orders of magnitude in comparison with the explicit one

jamming transition in a cellular automaton model for traffic flow the cellular automaton model for traffic flow exhibits a jamming transition from a free flow phase to a congested phase in the deterministic case this transition corresponds to a critical point with diverging correlation length in the presence of noise however no consistent picture has emerged up to now we present data from numerical simulations that suggest the absence of critical behavior the transition of the deterministic case is smeared out and one only observes the remnants of the critical point

deterministic models for traffic jams abstract we study several deterministic one dimensional traffic models for integer positions and velocities we find the typical high and low density phases separated by a simple transition if positions and velocities are continuous variables the model shows self organized critically driven by the slowest car

decoupled implicit method for aerothermodynamics and reacting flows we propose a new implicit computational fluid dynamics method for steady state compressible reacting flows the concept is to decouple the total mass momentum and energy conservation equations from the species mass and internal energy equations and to solve the two equation sets sequentially with certain approximations to the implicit system it is possible to dramatically reduce the cost of the solution with little to no penalty on the convergence properties importantly the cost of the decoupled implicit problem scales linearly with the number of species as opposed to the quadratic scaling for the conventional fully coupled method furthermore the new approach reduces the memory requirements by a significant factor the decoupled implicit method shows promise for the application to aerothermodynamics problems and reacting flows

implicit navier stokes solver for three dimensional compressible flows a three dimensional numerical method based on the lower upper symmetric gauss seidel implicit scheme in conjunction with the flux limited dissipation model is developed for solving the compressible navier stokes equations a new computer code based on this method requires only 9 s per grid point per iteration on a single processor of a cray ymp computer and executes at the sustained rate of 175 mflops a reduction of three orders of magnitude in the residual for a high reynolds number flow using 636k grid points is obtained in 38 min

cellular automation models and traffic flow a cellular automaton model for the description of traffic flow is investigated it generalizes asymmetric exclusion models which have attracted a lot of interest in the past the authors calculate the so called fundamental diagram flow versus density for parallel dynamics using an improved mean field approximation which takes into account short range correlations for maximum velocity they find that the simplest of these non trivial approximations gives the exact result for higher velocities their results are in excellent agreement with numerical data

data parallel line relaxation method for the navier stokes equations the gauss seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers the resulting data parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata parallel relaxation methods but it reaches a steady state solution in much less time for all cases tested to date in addition the data parallel line relaxation method shows good convergence properties even on the high cell aspect ratio grids required to simulate high reynolds number e ows the new method is implemented using message passing on the cray t3e and the parallel performance of the method on this machine is discussed the data parallel line relaxation method combines the fast convergence of the gauss seidel line relaxation method with a high parallel efe ciency and thus shows promise for large scale simulation of viscous e ows

cellular automata models of single lane traffic the jamming transition in the stochastic cellular automation model nagel schreckenberg model j phys france i 2 2221 1992 of highway traffic is analyzed in detail by studying the relaxation time a mapping to surface growth problems and the investigation of correlation functions three different classes of behavior can be distinguished depending on the speed limit v mathrm max for v mathrm max 1 the model is closely related to the kardar parisi zhang class of surface growth for 1l v mathrm max l ensuremath infty the relaxation time has a well defined peak at a density of cars ensuremath rho somewhat lower than the position of the maximum in the fundamental diagram this density can be identified with the jamming point at the jamming point the properties of the correlations also change significantly in the v mathrm max ensuremath infty limit the model undergoes a first order transition at ensuremath rho ensuremath rightarrow 0 it seems that in the relevant cases 1l v mathrm max l ensuremath infty the jamming transition is under the influence of a second order phase transition in the deterministic model and a first order transition for v mathrm max ensuremath infty

implicit treatment of diffusion terms in lower upper algorithms a method is presented which allows diffusion terms to be treated implicitly in the lower upper lu algorithm which is a commonly used method for solving compressible euler and navier stokes equations so that the algorithm s good stability properties will not be impaired the new method generalizes the concept of lu factorization from that associated with the sign of eigenvalues to that associated with backward and forward difference operators without regard to eigenvalues the method is verified in a turbulent boundary layer study

on preconditioned iterative methods for unsteady incompressible navier stokes equations when the implicit finite difference scheme and linearization technique in conjunction with the artificial compressibility method are employed to discretize the unsteady incompressible navier stokes equations in each pseudo time step a structured system of linear equations is obtained and needs to be solved numerically in this paper preconditioning techniques are applied to solve such linear systems numerical example is given to illustrate the effectiveness of the proposed method we also find that a combination of the linearization technique with the preconditioned gmres method is quite efficient for the implicit finite difference discretization of the incompressible navier stokes equations

geometric multigrid with applications to computational fluid dynamics an overview is given of the development of the geometric multigrid method with emphasis on applications in computational fluid dynamics over the last ten years both compressible and incompressible flow problems and their corresponding multigrid solution methods are discussed the state of the art is described with respect to methods employed in industry as well as the multigrid efficiency obtained in academic applications