implicit schemes and lu decompositions implicit methods for hyperbolic equations are analyzed by constructing lu factorizations it is shown that the solution of the resulting tridiagonal systems in one dimension is well conditioned if and only if the lu factors are diagonally dominant stable implicit methods that have diagonally dominant factors are constructed for hyperbolic equations in n space dimesnions only two factors are required even in three space dimensions acceleration to a steady state is analyzed when the multidimensional backward euler method is used with large time steps it is shown that the scheme approximates a newton raphson iteration procedure

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

subset construction complexity for homogeneous automata position automata and zpc structures the aim of this paper is to investigate how subset construction performs on specific families of automata a new upper bound on the number of states of the subset automaton is established in the case of homogeneous automata the complexity of the two basic steps of subset construction i e the computation of deterministic transitions and the set equality tests is examined depending on whether the nondeterministic automaton is an unrestricted one an homogeneous one a position one or a zpc structure which is an implicit construction for a position automaton copyright 2001 elsevier science b v

diagonally inverted lower upper factored implicit multigrid scheme for the three dimensional navier stokes equations an approximately factored implicit multigrid algorithm is developed to calculate three dimensional compressible viscous flows this scheme solves the full reynolds averaged navier stokes equations with a k e model of turbulence the flow equations are solved within the framework of the multigrid method using a four grid level w cycle while the k e equations are solved only on the finest grid and uncoupled from the flow calculations

near wall turbulence models for complex flows including separation results of a computational experiment designed to investigate the performance of different near wall treatments in a single turbulence model with a common numerical method are reported the complete fully elliptic reynoldsaveraged navier stokes equations have been solved using a low reynolds number model a new two layer model and a two point wall function method in thek s turbulence model for the boundary layer and wake of two axisymmetric bodies these tests enable the evaluation of the performance of the different approaches in flows involving longitudinal and transverse surface curvatures streamwise and normal pressure gradients viscous inviscid interaction and separation the two layer approach has been found to be quite promising for such flows and can be extended to other complex flows

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

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

efficient and robust reynolds stress model computation of three dimensional compressible flows thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynoldsstressclosure thee vemean e owandseventurbulencetransportequationsarediscretizedinspace ona structured multiblock grid using an o x 3 e nitevolumeupwind biased muscl schemewithvanleere ux vectorsplitting and van albada limiters time integration is based on an implicit dual time stepping procedure with alternating direction implicit subiterations a particular treatment of the approximate jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase sothatthecomputationaloverhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration for steady e ow computations local time steps are used for both the subiterations and the time marching with courant friedrichs lewynumbersof o 10 20 fortheo 1 20 subiterationsneededand o 100 500 forthetime marching the robustness of the method is ensured by appropriate positivity boundedness and reynolds stress realizability constraints the numerical method is illustrated by computing and conducting numerical studies for a high subsonic m 0 7 three dimensional e ow with large separation and for a transonic three dimensional shock wave boundary layer interaction

large deviations for expanding transformations with additive white noise large deviations estimates for the autocorrelations of order kof the random process zn xn n n 0 are obtained the processes xn n 0and n n 0are independent n n 0 are i i d bounded random variables xn tn x0 n mathbb n t m mis expanding leaving invariant a gibbs measure on a compact set m and m mathbb r is a continuous function a possible application of this result is the case where mis the unit circle and the gibbs measure is the one absolutely continuous with respect to the lebesgue measure on the circle the case when tis a uniquely ergodic map was studied in carmona et al 1998 in the present paper tis an expanding map however it is possible to derive large deviations properties for the autocorrelations samples 1 n n 1j 0zjzj k but the deviation function is quite different from the uniquely ergodic case because it is necessary to take into account the entropy of invariant measures for tas an important information the method employed here is a combination of the variational principle of the thermodynamic formalism with donsker and varadhan s large deviations approach

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

two dimensional inlet simulation using a diagonal implicit algorithm a modification of an implicit approximate factorization finite difference algorithm applied to the two dimensional euler and navier stokes equations in general curvilinear coordinates is presented for supersonic freestream flow about and through inlets the modification transforms the coupled system of equations into an uncoupled diagonal form which requires less computation work for steady state applications the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm solutions are given for inviscid and laminar flow about a two dimensional wedge inlet configuration comparisons are made between computed results and exact theory

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

lu implicit multigrid algorithm for the three dimensional euler equations an lu implicit multigrid scheme is developed for the calculation of three dimensi onal transonic flow through rotating cascades this numerical method solves the unsteady euler equations in finite volume form with added adaptive artificial dissipation the implicit scheme allows one to take a much larger time step than is normally permitted in most explicit schemes while the multigrid method is incorporated to accelerate the convergence rate for steady state calculations using this method computational storage requirements are comparable to those of explicit schemes while operation counts are considerably less than those found in the more widely used alternating direction implicit schemes

numerical analysis of three dimensional viscous internal flows a 3 d navier stokes code has been developed for analysis of turbomachinery blade rows and other internal flows the navier stokes equations are written in a cartesian coordinate system rotating about the x axis and then mapped to a general body fitted coordinate system streamwise viscous terms are neglected using the thin layer assumption and turbulence effects are modeled using the baldwin lomax turbulence model the equations are discretized using finite differences on stacked c type grids and are solved using a multistage runge kutta algorithm with a spatially varying time step and implicit residual smoothing calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer comparisons are made with experimental data taken by eckerle and langston for a circular cylinder under similar conditions computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane calculated details of the primary vortex show excellent agreement with the experimental data the calculations also show a small secondary vortex not seen experimentally

partial derivatives of regular expressions and finite automaton constructions we introduce a notion of a partial derivative of a regular expression it is a generalization to the non deterministic case of the known notion of a derivative invented by brzozowski we give a constructive definition of partial derivatives study their properties and employ them to develop a new algorithm for turning regular expressions into relatively small nfa and to provide certain improvements to brzozowski s algorithm constructing dfa we report on a prototype implementation of our algorithm constructing nfa and present some examples

an efficient null free procedure for deciding regular language memebership we present a new algorithm to determine whether a given word belongs to the language denoted by a regular expression it is based on our zpc representation of the glushkov automaton of a regular expression this procedure requires a specific representation of the glushkov automaton of the expression the representation is computed in linear time and space using the zpc algorithm designed by ziadi et al

a level 1 large deviation principle for the autocovariances of uniquely ergodic transformations with additive noise a large deviation principle ldp at level 1 for random means of the type m n equiv frac 1 n sum limits j 0 n 1 z j z j 1 text n 1 2 is established the random process zn n 0 is given by zn xn n n 0 1 2 where xn n 0 and n n 0 are independent random sequences the former is a stationary process defined by xn tn x0 x0 is uniformly distributed on the circle s1 t s1 s1 is a continuous uniquely ergodic transformation preserving the lebesgue measure on s1 and n n 0 is a random sequence of independent and identically distributed random variables on s1 is a continuous real function the ldp at level 1 for the means mn is obtained by using the level 2 ldp for the markov process vn xn n n 1 n 0 and the contraction principle for establishing this level 2 ldp one can consider a more general setting t 0 1 0 1 is a measure preserving lebesgue measure phi left 0 left 1 right right to mathbb r is a real measurable function and n are independent and identically distributed random variables on mathbb r for instance they could have a gaussian distribution with mean zero and variance 2 the analogous result for the case of autocovariance of order k is also true

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

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

the development of a free surface capturing approach for multidimensional free surface flows in closed containers a new surface capturing method is developed for numerically simulating viscous free surface flows in partially filled containers the method is based on the idea that the flow of two immiscible fluids within a closed container is governed by the equations of motion for an incompressible viscous nonhomogeneous variable density fluid by computing the flow fields in both the liquid and gas regions in a consistent manner the free surface can be captured as a discontinuity in the density field thereby eliminating the need for special free surface tracking procedures the numerical algorithm is developed using a conservative implicit finite volume discretization of the equations of motion the algorithm incorporates the artificial compressibility method in conjunction with a dual time stepping strategy to maintain a divergence free velocity field a slope limited high order muscl scheme is adopted for approximating the inviscid flux terms while the viscous fluxes are centrally differenced the capabilities of the surface capturing method are demonstrated by calculating solutions to several two and three dimensional problems

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

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