response variability of stochastic frame structures using evolutionary field theory the integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so called variability response function vrf and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory the vrf is a function depending on deterministic parameters related to the geometry boundary conditions mean material properties and loading of the structural system no approximations are involved in the derivation of the integral form however a conjecture has to be made that is validated using monte carlo simulations the uncertain system property considered is the inverse of the elastic modulus flexibility closed form expressions can be derived in principle for the vrf of any statically determinate or indeterminate frame system using a flexibility based formulation alternatively a fast monte carlo simulation approach is provided to numerically evaluate the vrf it is shown in closed form and numerically that the vrf for statically indeterminate structures is a function of the standard deviation ff of the stochastic field modeling the inverse of the elastic modulus although the vrf depends on ff it appears to be independent of the functional form of the spectral density function of the stochastic field modeling the uncertain system properties for statically determinate structures the vrf is independent of ff the integral form can be used to compute the variance of the system response as well as its upper bound with minimal computational effort it also provides an excellent insight into the mechanisms controlling the response variability the upper bounds for the response variance are spectral and probability distribution free requiring knowledge of only the variance of the inverse of the elastic modulus the proposed bounds are realizable in the sense that it is possible to determine the probabilistic characteristics of the stochastic field that produces them several numerical examples are provided demonstrating the capabilities of the methodology

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

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

extension of the certain generalized stresses method for the stochastic analysis of homogeneous and laminated shells abstract the paper presents an extension of the certain generalized stresses method cgsm for the static finite element analysis of homogeneous and laminated shells with variability the basic assumption is that the generalized stresses do not depend on input parameters perturbation the cgsm is a non intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest the uncertain input parameters are material and physical properties uniform random parameters as well as random fields are considered the displacements statistical results mean value standard deviation and distribution are obtained by monte carlo simulations using a semi analytical formula two examples are treated the scordelis lo shell roof and an automotive windscreen the method provides results of good quality and is very economical from a computational time point of view

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

efficient numerical strategies for spectral stochastic finite element models the use of spectral stochastic finite element models results in large systems of equations requiring specialized solution strategies this paper discusses three different numerical algorithms for solving these large systems of equations it presents a trade off of these algorithms in terms of memory usage and computation time it also shows that the structure of the spectral stochastic stiffness matrix can be exploited to accelerate the solution process while keeping the memory usage to a minimum copyright 2005 john wiley sons ltd

a new perspective on the solution of uncertainty quantification and reliability analysis of large scale problems abstract this work revisits the computational performance of non intrusive monte carlo versus intrusive galerkin methods of large scale stochastic systems in the framework of high performance computing environments the purpose of this work is to perform an assessment of the range of the relative superiority of these approaches with regard to a variety of stochastic parameters in both approaches the solution of the resulting algebraic equations is performed with a combination of primal and dual domain decomposition methods implementing specifically tailored preconditioners the solution of repeated simulations of the monte carlo method is accelerated with an a orthogonalization procedure aiming at reducing the iterations of subsequent simulations while the solution of the augmented equations of the stochastic galerkin method is enhanced with preconditioners which combine the block diagonal features of the resulting matrices as well as the sparsity pattern of the off block diagonal terms numerical results are presented demonstrating the efficiency of the proposed implementations on a large scale 3d problem with different stochastic characteristics and useful conclusions are derived regarding the ranges of stochastic parameters in which non intrusive solvers have a superior performance compared to intrusive ones and vice versa

a multigrid method with unstructured adaptive grids for steady euler equations the multigrid method based on multi stage jacobi relaxation earlier developed by the authors for structured grid calculations with euler equations is extended to unstructured grid applications the meshes are generated with delaunay triangulation algorithms and are adapted to the flow solution

stochastic flows associated to coalescent processes we study a class of stochastic flows connected to the coalescent processes that have been studied recently by mohle pitman sagitov and schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size we define a bridge to be a right continuous process b r r 0 1 with nondecreasing paths and exchangeable increments such that b 0 0 and b 1 1 we show that flows of bridges are in one to one correspondence with the so called exchangeable coalescents this yields an infinite dimensional version of the classical kingman representation for exchangeable partitions of we then propose a poissonian construction of a general class of flows of bridges and identify the associated coalescents we also discuss an important auxiliary measure valued process which is closely related to the genealogical structure coded by the coalescent and can be viewed as a generalized fleming viot process

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

a high order semi implicit imex weno scheme for the all mach isentropic euler system abstract in this paper new high order schemes are constructed and analyzed for the numerical solution of euler equations of isentropic gas dynamics material waves are treated explicitly while acoustic waves are treated implicitly thus avoiding severe cfl restrictions for low mach flows high order accuracy in space is obtained by finite difference weno schemes while high order in time is obtained by imex methods with semi implicit linearization treatment the schemes are proven to be asymptotic preserving and asymptotic accurate as the mach number vanishes several tests in one and two space dimensions illustrate the effectiveness of the proposed schemes

stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters the research work presents the study on non deterministic problems in the presence of the multiple imprecise random field uncertainties by extending the spectral stochastic finite element framework the standard random field is expanded to characterize the behaviour of physical model with imprecise randomness more appropriately for real engineering problems based on available sources of uncertainty the young s modulus and body force of structures are considered as imprecise random fields with bounded statistical moments mathematical expressions and solution procedure are developed to produce the uncertain but bounded statistical characteristics of responses namely interval mean value interval standard deviation and bounding distribution functions the bounding probability density and cumulative distribution of the imprecise random response are then effectively visualized by means of polynomial chaos expansion the feasibility and effectiveness of the presented method are illustrated by three numerical examples

schemes to compute unsteady flashing flows some ways to compute flashing flows in variable cross section ducts are provided focusing on the homogeneous relaxation model the basic numerical method relies on a splitting technique that is consistent with the overall entropy inequality the cross section is assumed to he continuous and the finite volume approach is applied to approximate homogeneous equations several suitable schemes to account for complex equation of state are discussed namely the rusanov scheme an approximate form of the roe scheme and the volumes finis roe vfroe scheme with the help of nonconservative variables to evaluate respective accuracy the homogeneous euler equations are computed first and the l1 error norm of transient solutions of shock tube experiments are plotted it is shown that the rusanov scheme is indeed less accurate which balances its interesting properties inasmuch as it preserves the positivity of the mean density and the maximum principle for the vapor quality computations of real cases are presented which account for the mass transfer term and the time space dependent cross sections

on ruelle s probability cascades and an abstract cavity method we construct in this work a markov process which describes a clustering mechanism through which equivalence classes on are progressively lumped together this clustering process gives a new description of ruelle s continuous probability cascades it also enables to introduce an abstract cavity method which mimicks certain features of the cavity method developed by physicists in the context of the sherrington kirkpatrick model

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

random field finite elements the probabilistic finite element method pfem is formulated for linear and non linear continua with inhomogeneous random fields analogous to the discretization of the displacement field in finite element methods the random field is also discretized the formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization furthermore it is shown that a reduced set of the uncorrelated variables is sufficient for the second moment analysis based on the linear formulation of the pfem the method is then extended to transient analysis in non linear continua the accuracy and efficiency of the method is demonstrated by application to a one dimensional elastic plastic wave propagation problem and a two dimensional plane stress beam bending problem the moments calculated compare favourably with those obtained by monte carlo simulation also the procedure is amenable to implementation in deterministic fem based computer programs

implicit multigrid algorithms for incompressible turbulent flows on unstructured grids an implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described the foundation of the code is a backward euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned generalized minimal residual gmres technique for the gmres calculations several techniques are investigated for forming the matrix vector product convergence acceleration is achieved through a multigrid scheme that uses nonnested coarse grids that are generated using a technique described in the present paper convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four element airfoil viscous results which are compared with experimental data include the turbulent flow over a naca 4412 airfoil a three element airfoil for which mach number effects are investigated and three dimensional flow over a wing with a partial span flap

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

a copula based perturbation stochastic method for fiber reinforced composite structures with correlations abstract under most circumstances there are correlations among random variables for composite structures and these correlations can have a considerable effect on the reliability analysis result consequently a copula based perturbation stochastic method is proposed to amend the disability of traditional perturbation stochastic method on correlation problems as a statistical tool copula function meets the intrinsic demand of fiber reinforced composite structures on variable s correlation and allows the choice of joint cumulative distribution functions cdfs to be separate from the marginal cdfs with the aid of change of variable technique copula is introduced straightly into the framework to describe the relevance without any special transformation besides the probability curves and reliability index of multi variables of gaussian and non gaussian can be achieved easily furthermore in order to significantly improve the efficiency and capability to resist the mesh distortion compared with the traditional stochastic fem strain matrices are reconstructed by the edge based smoothing technique the overall uncertain condition coupled by stochastic fiber orientations material parameters and external loads is analyzed several examples are provided to verify the validity of the method

a high order godunov method for multiple condensed phases presented in this work is a nonlinear adaptive nonreflecting boundary condition nrbc that when compared with classical local nrbcs further reduces the wave reflection error at far fields in the numerical simulation of wave dominated problems a nonlinear procedure can considerably improve the accuracy of nrbcs even if the problem itself is linear as in the case of the 2d wave equation in fact the first and second order nrbcs of engquist and majda can be modified by adding proper weights to the coefficients of the difference equations the weights are adaptively determined in such a way that the angle of complete absorption is locally coincident with the outgoing wave direction the theoretical reflection coefficients and the numerical experiments show that a considerable reduction of the numerical error due to wave reflections is achieved by applying the present adaptive algorithm

stochastic finite element method for random harmonic analysis of composite plates with uncertain modal damping parameters abstract damping parameters of fiber reinforced composite possess significant uncertainty due to the structural complexity of such materials considering the parameters as random variables this paper uses the generalized polynomial chaos gpc expansion to capture the uncertainty in the damping and frequency response function of composite plate structures a spectral stochastic finite element formulation for damped vibration analysis of laminate plates is employed experimental modal data for samples of plates is used to identify and realize the range and probability distributions of uncertain damping parameters the constructed gpc expansions for the uncertain parameters are used as inputs to a deterministic finite element model to realize random frequency responses on a few numbers of collocation points generated in random space the realizations then are employed to estimate the unknown deterministic functions of the gpc expansion approximating the responses employing modal superposition method to solve harmonic analysis problem yields an efficient sparse gpc expansion representing the responses the results show while the responses are influenced by the damping uncertainties at the mid and high frequency ranges the impact in low frequency modes can be safely ignored utilizing a few random collocation points the method indicates also a very good agreement compared to the sampling based monte carlo simulations with large number of realizations as the deterministic finite element model serves as black box solver the procedure can be efficiently adopted to complex structural systems with uncertain parameters in terms of computational time

response variability of laminate composite plates due to spatially random material parameter young s modulus is at the center of attention in the stochastic finite element analysis since the parameter plays an important role in determining structural behavior however the other material parameter of poisson s ratio is another independent material parameter that governs the behavior of structural systems accordingly the independent estimation of the influence of this parameter on the uncertain response of a system is of importance from the perspective of stochastic analysis to this end we propose a formulation to determine the response variability in laminated composite plates due to the spatial randomness of poisson s ratio to filter out the independent contribution of random poisson s ratio a decomposition of the constitutive matrix into several sub matrices by using the taylor s expansion is needed which makes the random poisson s ratio simple enough to be included in the formulation to validate the adequacy of the proposed formulation several examples are chosen and the results are compared with those given by monte carlo analysis by means of the formulation suggested here it is expected that an extension of the formulation to include the effect of correlations between random poisson s ratio and other structural and or geometrical parameters will be achieved with ease resulting in a more practical estimation of the response variability of laminated composite plates

wave structure similarity of the hllc and roe riemann solvers application to low mach number preconditioning the approximate riemann solver of roe and the solver of harten lax van leer hll and its variants such as the hllc solver are widely used as building blocks of finite volume godunov type methods for the solution of the euler equations of gas dynamics and related hyperbolic flow models the hllc solver has gained increasing popularity over the last two decades since it possesses some of the good properties of the roe solver and in addition satisfies important entropy and positivity conditions with no need of special fixes in this work we rewrite the classical hllc riemann solver in a novel form that highlights the formal mathematical similarity of its wave structure with the one of the roe solver this similarity might be useful to extend to the hllc method some numerical techniques devised specifically for the roe method as an example of application we illustrate the design of a turkel type low mach number preconditioning technique for the hllc scheme by exploiting methodologies proposed in the l

steady state convergence acceleration of the generalized lattice boltzmann equation with forcing term through preconditioning several applications exist in which lattice boltzmann methods lbm are used to compute stationary states of fluid motions particularly those driven or modulated by external forces standard lbm being explicit time marching in nature requires a long time to attain steady state convergence particularly at low mach numbers due to the disparity in characteristic speeds of propagation of different quantities in this paper we present a preconditioned generalized lattice boltzmann equation glbe with forcing term to accelerate steady state convergence to flows driven by external forces the use of multiple relaxation times in the glbe allows enhancement of the numerical stability particular focus is given in preconditioning external forces which can be spatially and temporally dependent in particular correct forms of moment projections of source forcing terms are derived such that they recover preconditioned navier stokes equations with non uniform external forces as an illustration we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic prandtl numbers which imposes lorentz forces on the flow of conducting fluids computational studies particularly in three dimensions for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning in addition the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation

probabilistic nonlinear finite element analysis of composite structures a probabilistic finite element analysis procedure for laminated composite shells is developed a total lagrangian finite element formulation employing a degenerated three dimensional laminated composite shell element with the full green lagrange strains and first order shear deformable kinematics is used the first order second moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response reliability calculations are made by using the first order reliability method combined with sensitivity derivatives from the finite element analysis both ply level and micromechanics level random variables are incorporated the latter by means of the aboudi micromechanics model two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type structure combinations in general the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

the carleman type singular integral equations we present a consolidated account of carleman type singular integral equations we have started from the most basic equation of this type and have at first attempted to integrate from the existing literature the progress which has been made so far in this field many different techniques are presented to solve these types of integral equations both in the real and the complex domains in the complex domain both closed and open contours for integrals are considered in the process of this study we find that many known methods need to be polished and extended we attempt to accomplish this and then interrelate different concepts and solutions thereby we obtain solutions of more general singular integral equations of the carleman type many interesting examples are presented to illustrate the general theory

numerical solution of spectral stochastic finite element systems abstract this paper addresses the issues involved in solving systems of linear equations which arise in the context of the spectral stochastic finite element ssfem formulation two efficient solution procedures are presented that dramatically reduce the amount of computations involved in numerically solving these problems a brief review is first provided of the underlying spectral approach which highlights the peculiar structure of the matrices generated and how their properties are related to both the level of approximation involved as well as to the convergence behavior of the proposed solution procedure the differences between these matrices from their deterministic finite element counterparts are illustrated an iterative solution scheme is proposed which utilizes their specific properties for efficient memory management and enhanced convergence behavior results from numerical tests are presented comparisons with standard algorithms illustrate the efficiency of the proposed algorithm the second solution procedure presented in this paper is based on hierarchical basis concepts results from numerical tests are again provided and the limitations of this approach are assessed the performance of both proposed algorithms indicates that the linear algebraic systems from the underlying ssfem formulation can be solved with considerably less effort in memory and computation time than their size suggests furthermore the data structures and the hierarchical concept introduced in this study are found to have great potential for the future development of adaptive procedures in stochastic fem

stochastic finite element analysis of shells with combined random material and geometric properties abstract in this work an extended stochastic formulation of the triangular composite facet shell element tric is presented for the case of combined uncertain material young s modulus poisson s ratio and geometric thickness properties these properties are assumed to be described by uncorrelated two dimensional homogeneous stochastic fields the stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with monte carlo simulation mcs for the computation of the response variability useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

simulation of synthetic jets using unsteady reynolds averaged navier stokes equations an unsteady reynolds averaged navier stokes solver is applied for the simulation of a synthetic zero net mass flow jet created by a single diaphragm piezoelectric actuator in quiescent air this configuration was designated as case 1 for the computational fluid dynamics validation 2004 cfdval2004 workshop held at williamsburg virginia in march 2004 time averaged and instantaneous phase averaged data for this case were obtained at nasa langley research center using multiple measurement techniques computational results from two dimensional simulations with one equation spalart allmaras and two equation menter s turbulence models are presented along with the experimental data the effect of grid refinement preconditioning and time step variation are also examined

on the stationary distribution of the block counting process for population models with mutation and selection abstract we consider two population models subject to the evolutionary forces of selection and mutation the moran model and the wright fisher model in such models the block counting process traces back the number of potential ancestors of a sample of the population at present under some conditions the block counting process is positive recurrent and its stationary distribution is described via a linear system of equations in this work we first characterise the measures leading to a geometric stationary distribution the bolthausen sznitman model being the most prominent example having this feature next we solve the linear system of equations corresponding to the moran model for the wright fisher model we show that the probability generating function associated to the stationary distribution of the block counting process satisfies an integro differential equation we solve the latter for the kingman model and the star shaped model

preconditioned multigrid methods for unsteady incompressible flows a highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3d steady and time dependent incompressible flows thek turbulence model is used to estimate the effects of turbulence the model equations are solved together with the n s equations in a strongly coupled way and acceleration techniques like the multigrid method are also used for the turbulence model equations for unsteady problems a dual time stepping procedure is adopted to satisfy the divergence free constraint and to obtain a time accurate solution to improve the performance of this approach for small physical time steps a modification to residual smoothing parameters is proposed the numerical algorithm and the turbulence model are validated first by calculating unsteady inviscid flow around an oscillating cylinder unsteady laminar flow past a circular cylinder and steady high reynolds number turbulent flow over a 6 1 prolate spheroid then the three dimensional time dependent turbulent flow over a spheroid when it is undergoing a pitch up maneuver is calculated and compared with experimental data

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

generalized flux vector splitting and roe average for an equilibrium real gas abstract the flux vector splittings of steger warming and van leer and roe s approximate riemann solver are generalized to arbitrary equilibrium gas laws comparisons with other formulations are made

a flux vector splitting scheme for low mach number flows in preconditioning method abstract the stiffness of euler equations system increases with the decreasing of mach number which results in poor convergence when solving steady flow problems numerically in order to accelerate the convergence a preconditioning method is proposed a flux vector splitting scheme is derived from the classic steger warming scheme and the roe flux difference splitting scheme and preconditioned systems developed for the two schemes separately numerical results are presented and it is shown that flux vector splitting scheme can be preconditioned as successfully as flux difference splitting and exhibits similar convergence acceleration and accurate solution

computation of flows with arbitrary equations of state the extension of time marching computations to fluids with arbitrary equations of state is demonstrated by means of stability analyses simplified problems and practical applications most of the examples use the properties of supercritical hydrogen for which the density varies by more than an order of magnitude for small changes in pressure and temperature but representative computations for incompressible fluids and perfect gases are also given to demonstrate the generality of the procedure because representative flow velocities in typical supercritical fluids applications are much lower than the speed of sound convergence enhancement through eigenvalue control is often necessary this is accomplished through a generalization of earlier preconditioning methods that enables efficient computation of arbitrary equation of state fluids perfect gases and incompressible fluids by a single procedure the present approach thus provides a single method that is uniformly applicable to all equations of state

accurate computation of contact discontinuities in flows with general equations of state abstract the evolution of a contact discontinuity in a real fluid flow is particularly difficult to compute with a conservative scheme indeed godunov type schemes involve an averaging step which may create an intermediate state with an incorrect pressure spurious acoustic waves are then generated these waves affect transient simulations as well as implicit time marching procedures for steady state computations however a formulation involving the pressure as a dependent variable can be used to restore a fast convergence for steady state computations

hybrid multifluid algorithms extensions of many successful single component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components a new algorithm based on the compressible euler equations for multicomponent fluids augmented by the pressure evolution equation is presented the extended set of equations offers two alternative ways to update the pressure field i using the equation of state or ii using the pressure evolution equation in a numerical implementation these two procedures generally yield different answers the former is a standard conservative update but may produce oscillations near material interfaces the latter is nonconservative but becomes exact near interfaces and automatically maintains pressure equilibrium a hybrid scheme which selects from the two pressure update procedures is presented the scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite very small number of grid cells computed solutions exhibit oscillation free interfaces and have em negligible relative conservation errors in total energy even for very strong shocks the proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one s favourite scheme to solve multifluid dynamics

spectral stochastic finite element analysis for laminated composite plates abstract a spectral stochastic finite element formulation with consideration of multi layer effect and spatial variability of material properties is developed for probabilistic analysis of laminated composite plates the material properties of each lamina are modeled as a set of random fields and represented by the karhunen loeve expansion the expansion is incorporated into a spatial discretization in accordance with a standard finite element procedure based on the first order shear deformation theory a spectral expansion with use of polynomial chaos is employed to represent the stochastic nodal displacements in terms of standard normal random variables a preconditioning matrix is then proposed for the solution of spectral stochastic finite element equations with use of a preconditioning conjugate gradient technique the various statistics of interest of the system responses are finally obtained by means of the coefficients of the spectral expansion the numerical accuracy and the computational efficiency of the method are demonstrated by comparison with monte carlo simulation

acceleration of uncertainty updating in the description of transport processes in heterogeneous materials the prediction of thermo mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters such materials occur e g in historic buildings and the durability assessment of these therefore needs a reliable and probabilistic simulation of transport processes which is related to the suitable identification of material parameters in order to include expert knowledge as well as experimental results one can employ an updating procedure such as bayesian inference the classical probabilistic setting of the identification process in bayes form requires the solution of a stochastic forward problem via computationally expensive sampling techniques which makes the method almost impractical in this paper novel stochastic computational techniques such as the stochastic galerkin method are applied in order to accelerate the updating procedure the idea is to replace the computationally expensive forward simulation via the conventional finite element fe method by the evaluation of a polynomial chaos expansion pce such an approximation of the fe model for the forward simulation perfectly suits the bayesian updating the presented uncertainty updating techniques are applied to the numerical model of coupled heat and moisture transport in heterogeneous materials with spatially varying coefficients defined by random fields

explicit solution to the stochastic system of linear algebraic equations α1a1 α2a2 αmam x b abstract this paper presents a novel solution strategy to the stochastic system of linear algebraic equations 1 a 1 2 a 2 m a m x b arising from stochastic finite element modelling in computational mechanics in which i i 1 m denote random variables a i i 1 m real symmetric deterministic matrices b a deterministic random vector and x the unknown random vector to be solved the system is first decoupled by simultaneously diagonalizing all the matrices a i via a similarity transformation and then it is trivial to invert the sum of the diagonalized stochastic matrices to obtain the explicit solution of the stochastic equation system unless all the matrices a i share exactly the same eigen structure the joint diagonalization can only be approximately achieved hence the solution is approximate and corresponds to a particular average eigen structure of the matrix family specifically the classical jacobi algorithm for the computation of eigenvalues of a single matrix is modified to accommodate multiple matrices and the resulting jacobi like joint diagonalization algorithm preserves the fundamental properties of the original version including its convergence and an explicit solution for the optimal givens rotation angle three numerical examples are provided to illustrate the performance of the method

modified sub interval perturbation finite element method for 2d acoustic field prediction with large uncertain but bounded parameters abstract based on the sub interval perturbation analysis a modified sub interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2d acoustic field with large uncertain but bounded parameters in the proposed method the inversion of the invertible sub interval dynamic stiffness matrix is approximated by a modified approximate interval value sherman morrison woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in neumann series the modified sub interval perturbation procedures are implemented in a numerical finite element framework numerical results on a 2d acoustic tube and a 2d acoustic cavity of a car with large uncertain but bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method