parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

a global meshless collocation particular solution method for solving the two dimensional navier stokes system of equations the two dimensional navier stokes system of equations for incompressible fluids is solved by the method of approximate particular solutions maps in its global formulation the fluid velocity and pressure fields are approximated by a linear superposition of particular solutions of a stokes non homogeneous system of equations with multiquadric mq radial basis function as the source term the nonlinear convective terms of the momentum equations are linearly approximated by using a guess value of the velocity field and the resulting linear system of equations is solved by a simple direct iterative scheme picard iteration with the velocity guess given by the solution at the previous iteration although the continuity equation is not explicitly imposed in the resulting formulation the scheme is mass conservative because the particular solutions exactly satisfy the mass conservation equation the proposed numerical scheme is validated by comparison of the obtained numerical results with the corresponding analytical solution of the kovasznay flow problem at different reynolds numbers re from this analysis it is observed that the maps results are stable and accurate for a wide range of shape parameter values in addition lid driven cavity flow problems in rectangular and triangular domains up to re 3200 and re 1000 respectively and the backward facing step at re 800 are solved and the results obtained are compared with corresponding benchmark numerical solutions showing excellent agreement

a sum of disjoint products algorithm for reliability evaluation of flow networks abstract this paper proposes a revised algorithm to evaluate the unreliability of a flow network in which capacities of arcs are assumed to be independent binary valued random variables such a problem is a generalization of the well known np hard two terminal reliability problem which evaluates the probability of the connection from a source node to a sink node the proposed algorithm is motivated by rueger both in a branching manner the proposed and rueger s algorithms express the system unreliability in terms of a sum of disjoint products where each product is derived from a branching condition b via a d cutb in o m log m time and via the first system failure under b in o d n2 2m time respectively where d is the demand n and m are the numbers of nodes and arcs in the network respectively experimental experiences show that the proposed algorithm drastically reduces the execution time and performs more robustly when compare to rueger s algorithm but the number of disjoint products derived by it will be a little bit larger

stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

a class of parallel two level nonlinear schwarz preconditioned inexact newton algorithms we propose and test a new class of two level nonlinear additive schwarz preconditioned inexact newton algorithms aspin the two level aspin combines a local nonlinear additive schwarz preconditioner and a global linear coarse preconditioner this approach is more attractive than the two level method introduced in cai keyes and marcinkowski nonlinear additive schwarz preconditioners and applications in computational fluid dynamics international journal numerical methods in fluids 40 2002 1463 1470 which is nonlinear on both levels since the coarse part of the global function evaluation requires only the solution of a linear coarse system rather than a nonlinear coarse system derived from the discretization of original partial dierential equations the overall computational cost is reduced considerably our parallel numerical results based on an incompressible lid driven flow problem show that the new two level aspin is quite scalable with respect to the number of processors and the fine mesh size when the coarse mesh size is fine enough and in addition the convergence is not sensitive to the reynolds numbers

high order compact computation and nonuniform grids for streamfunction vorticity equations abstract fourth order compact difference schemes for steady streamfunction vorticity formulation of 2d incompressible navier stokes equations on nonuniform grids are derived using maple software package especially we deduce fourth order compact difference scheme of the first partial derivative terms in order to resolve boundary layers grid transformation techniques are used which maps a nonuniform grid onto a uniform one for use with the fourth order compact difference scheme a krylov subspace iterative method with an ilut preconditioning technique is employed to solve the resulting linear system the proposed high accuracy computation method is applied to two model problems computational results are compared with results computed by other schemes in the literature

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

developing numerical techniques for solving low mach number fluid acoustic problems conservation equations applicable to this regime are derived by applying four simplifying assumptions to the fully compressible form of the navier stokes and energy equations isentropic state changes adiabatic flow negligible density variation inertial terms and stokes hypothesis the resulting equations termed acoustic compressible are similar to the traditional pseudocompressible equations except for two distinctions pseudocompressible solutions use artificially high mach numbers for computational convenience and neglect the pressure convection term in the mass conservation equation

moffatt eddies in the driven cavity a quantification study by an hoc approach abstract in this paper we establish moffatt likeness of the corner vortices in the lid driven square cavity for stokes flow and flow for moderate reynolds numbers in the pre asymptotic regime the flow is computed by using an efficient transient navier stokes n s solver on compact non uniform space grids the quantification of the corner vortices in succession as moffatt vortices follows from them following a fixed geometric ratio in sizes and intensities in the process we also provide more detailed benchmarking results for the corner vortices in the cavity flow the accuracy of the scale resolution of the vortices has been verified by a novel approach to grid independence analysis this approach utilizes the concept of adverse pressure gradients as a tool to validate that the separation zones in the neighborhood of the corners are consistent with the vortices obtained from our computed solution of the n s equations

the complexity of counting cuts and of computing the probability that a graph is connected several enumeration and reliability problems are shown to be p complete and hence at least as hard as np complete problems included are important problems in network reliability analysis namely computing the probability that a graph is connected and counting the number of minimum cardinality s t cuts or directed network cuts also shown to be p complete are counting vertex covers in a bipartite graph counting antichains in a partial order and approximating the probability that a graph is connected and the probability that a pair of vertices is connected

a new family of 5 5 cc 4oc schemes applicable for unsteady navier stokes equations in this paper a new family of implicit compact finite difference schemes for computation of unsteady convection diffusion equation with variable convection coefficient is proposed the schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady navier stokes system the proposed schemes where transport variable and its first derivatives are carried as the unknowns combine virtues of compact discretization and pade scheme for spatial derivative these schemes which are based on a five point stencil with constant coefficients named as 5 5 constant coefficient 4th order compact 5 5 cc 4oc give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods these schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable they efficiently capture both transient and steady solutions of linear and nonlinear convection diffusion equations with dirichlet as well as neumann boundary conditions subsequently the proposed schemes are applied to problems governed by the incompressible navier stokes equations the results obtained are in excellent agreement with analytical and available numerical results in all cases establishing efficiency and accuracy of the proposed schemes

isogeometric boundary element analysis of steady incompressible viscous flow part 1 plane problems abstract a novel approach is presented to the boundary element analysis of steady incompressible flow nurbs basis functions are used for describing the geometry of the problem and for approximating the unknowns in addition the arising volume integrals are treated differently to published work that is volumes are described by bounding nurbs curves instead of cells and a mapping is used the advantage of our approach is that non trivial boundary shapes can be described with very few parameters and that no generation of cells is required for the solution of the non linear equations both classical and modified newton raphson methods are used a comparison of the two methods is made on the classical example of a forced cavity flow where accurate solutions are available in the literature the results obtained agree well with published ones for moderate reynolds numbers using both methods but it is found that the latter requires a relaxation scheme and considerably more iterations to converge finally it is shown on a practical example of an airfoil how more complex boundary shapes can be approximated with few parameters and a solution obtained with a small number of unknowns

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

convex computation of the region of attraction of polynomial control systems we address the long standing problem of computing the region of attraction roa of a target set e g a neighborhood of an equilibrium point of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints we show that the roa can be computed by solving an infinite dimensional convex linear programming lp problem over the space of measures in turn this problem can be solved approximately via a classical converging hierarchy of convex finite dimensional linear matrix inequalities lmis our approach is genuinely primal in the sense that convexity of the problem of computing the roa is an outcome of optimizing directly over system trajectories the dual infinite dimensional lp on nonnegative continuous functions approximated by polynomial sum of squares allows us to generate a hierarchy of semialgebraic outer approximations of the roa at the price of solving a sequence of lmi problems with asymptotically vanishing conservatism this sharply contrasts with the existing literature which follows an exclusively dual lyapunov approach yielding either nonconvex bilinear matrix inequalities or conservative lmi conditions the approach is simple and readily applicable as the outer approximations are the outcome of a single semidefinite program with no additional data required besides the problem description the approach is demonstrated on several numerical examples

design of state feedback control for polynomial systems with quadratic performance criterion and control input constraints abstract this paper presents a novel convex optimization approach to design state feedback control for polynomial systems design criteria are comprised of a quadratic cost function and bounded magnitudes of control inputs specifically we formulate a control synthesis of closed loop systems operated in a given bounded domain characterized by a semi algebraic set we consider an extended class of rational lyapunov functions and derive an upper bound of the cost function together with a state feedback control law by exploiting bounds on the control input magnitudes the controller design condition can be cast as a parameter dependent linear matrix inequality pdlmi which is convex optimization and can be efficiently solved by sum of squares sos technique in addition we derive a sufficient condition to compute a lower bound of the cost function when choosing polynomial structure of the solution candidate the lower bound can also be written as pdlmi numerical examples are provided to illustrate the effectiveness of the proposed design

an implicit scheme for solving the convection diffusion reaction equation in two dimensions in this paper we consider a passive scalar transported in two dimensional flow the governing equation is that of the convection diffusion reaction equation for purposes of computational efficiency we apply an alternating direction implicit scheme akin to that proposed by polezhaev use of this implicit operator splitting scheme allows the application of a tridiagonal thomas solver to obtain the solution within each solution step a semidiscretization scheme is applied to discretize the differential equation in one dimension we approximate the time derivative term using a forward time stepping scheme the resulting inhomogeneous differential equation has only the spatial derivative terms and is solved using a newly proposed nodally exact steady state convection diffusion reaction scheme details on the development of the flux discretization scheme are provided modified equation analysis fourier stability analysis and a study on scheme monotonicity are also performed to shed further light on the proposed transient scheme to validate the proposed scheme we first consider test problems which are amenable to analytic solutions good agreement is obtained with both one and two dimensional steady unsteady problems thus demonstrating the validity of the method c 2000 academic press

a divergence free condition compensated method for incompressible navier stokes equations the present study aims to develop a new formulation to effectively calculate the incompressible navier stokes solutions in non staggered grids the distinguished feature of the proposed method which avoids directly solving the divergence free equation is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility for the sake of numerical accuracy dispersion relation preserving upwind scheme developed within the two dimensional context was employed to approximate the convection terms the validity of the proposed mass preserving navier stokes method is justified by solving two benchmark problems at high reynolds and rayleigh numbers based on the simulated navier stokes solutions the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of cpu time 2007 elsevier b v all rights reserved

stability regions of nonlinear autonomous dynamical systems a topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented the stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points and or closed orbits on the stability boundary several necessary and sufficient conditions are derived to determine whether a given equilibrium point or closed orbit is on the stability boundary a method for finding the stability region on the basis of these results is proposed the method when feasible will find the exact stability region rather than a subset of it as in the lyapunov theory approach several examples are given to illustrate the theoretical prediction

on the role of the helmholtz decomposition in mixed methods for incompressible flows and a new variational crime abstract according to the helmholtz decomposition the irrotational parts of the momentum balance equations of the incompressible navier stokes equations are balanced by the pressure gradient unfortunately nearly all mixed methods for incompressible flows violate this fundamental property resulting in the well known numerical instability of poor mass conservation the origin of this problem is the lack of l 2 orthogonality between discretely divergence free velocities and irrotational vector fields therefore a new variational crime for the nonconforming crouzeix raviart element is proposed where divergence free lowest order raviart thomas velocity reconstructions reestablish l 2 orthogonality this approach allows to construct a cheap flow discretization for general 2d and 3d simplex meshes that possesses the same advantageous robustness properties like divergence free flow solvers in the stokes case optimal a priori error estimates for the velocity gradients and the pressure are derived moreover the discrete velocity is independent of the continuous pressure several detailed linear and nonlinear numerical examples illustrate the theoretical findings

an asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows it is well known that any viscous fluid flow near a corner consists of infinite series of eddies with decreasing size and intensity unless the angle is larger than a certain critical angle h k moffat j fluid mech 18 1964 pp 1 18 the objective of the current work is to simulate such infinite series of eddies occurring in steady flows in domains with corners the problem is approached by high order finite element method with exponential mesh refinement near the corners coupled with analytical asymptotics of the flow near the corners such approach allows one to compute position and intensity of the eddies near the corners in addition to the other main features of the flow the method was tested on the problem of the lid driven cavity flow as well as on the problem of the backward facing step flow the results of computations of the lid driven cavity problem show that the proposed method computes the central eddy with accuracy comparable to the best of existing methods and is more accurate for computing the corner eddies than the existing methods the results also indicate that the relative error of finding the eddies intensity and position decreases uniformly for all the eddies as the mesh is refined i e the relative error in computation of different eddies does not depend on their size

reduction of average path length in binary decision diagrams by spectral methods this paper deals with analytic methods for the calculation and reduction of the average path lengths apls in binary decision diagrams bdds usually information theoretic measures and information theoretic techniques are used to construct bdds of minimal apls specifically the mutual information between a boolean function and its variables and the shannon fano prefix coding are utilized this paper deals with the problem of the apl reduction by using spectral techniques particularly methods based on the properties of the walsh spectrum of a boolean function and its autocorrelation function are discussed it is shown that the apl is a linear function of the autocorrelation values that is the apl depends on the boolean function s properties in the time domain autocorrelation rather on the boolean function s properties in the frequency domain walsh spectrum in addition it is shown that information theoretic criteria like the mutual information or the conditional entropy are equivalent to frequency domain criteria consequently existing information theoretic approaches for apl reduction that are based on mutual information criterion or the walsh transform coefficients may derive a suboptimal apl the representation of the apl as a function of the autocorrelation values opens a way to determine the optimal ordering of the input variables analytically two procedures for apl reduction by ordering and by using linear combinations of the input variables are presented 1 minimization by using the autocorrelation values and 2 minimization by using the mutual information between the boolean function and a linear function of the input variables the time domain approach may derive a linearized bdd of a lower apl whereas the information theoretic approach has a lower computational complexity with comparable performance experimental results show the efficiency of the suggested techniques

robust region of attraction estimation we propose a method to compute invariant subsets of the region of attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty parameter independent lyapunov functions are used to characterize invariant subsets of the robust region of attraction a branch and bound type refinement procedure reduces the conservatism we demonstrate the method on an example from the literature and uncertain controlled short period aircraft dynamics

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

syrel a symbolic reliability algorithm based on path and cutset methods symbolic terminal reliability algorithms are important for analysis and synthesis of computer networks in this paper we present a simple and efficient algorithm syrel to obtain compact terminal reliability expressions between a terminal pair of computers of complex networks this algorithm incorporates conditional probability set theory and boolean algebra in a distinct approach in which most of the computations performed are directly executable boolean operations the conditibnal probability is used to avoid applying at each iteration the most time consuming step in reliability algorithms which is making a set of events mutually exclusive the algorithm has been implemented on a vax 11 750 and can analyze fairly large networks with modest memory and time requirements

a newton method with adaptive finite elements for solving phase change problems with natural convection we present a new numerical system using finite elements with mesh adaptivity for the simulation of solid liquid phase change systems in the liquid phase the natural convection flow is simulated by solving the incompressible navier stokes equations with boussinesq approximation a variable viscosity model allows the velocity to progressively vanish in the solid phase through an intermediate mushy region the phase change is modeled by introducing an implicit enthalpy source term in the heat equation the final system of equations describing the liquid solid system by a single domain approach is solved using a newton iterative algorithm the space discretization is based on a p2 p1 taylor hood finite elements and mesh adaptivity by metric control is used to accurately track the solid liquid interface or the density inversion interface for water flows the numerical method is validated against classical benchmarks that progressively add strong non linearities in the system of equations natural convection of air natural convection of water melting of a phase change material and water freezing very good agreement with experimental data is obtained for each test case proving the capability of the method to deal with both melting and solidification problems with convection the presented numerical method is easy to implement using freefem software using a syntax close to the mathematical formulation

rational lyapunov functions for estimating and controlling the robust domain of attraction this paper addresses the estimation and control of the robust domain of attraction rda of equilibrium points through rational lyapunov functions lfs and sum of squares sos techniques specifically continuous time uncertain polynomial systems are considered where the uncertainty is represented by a vector that affects polynomially the system and is constrained into a semialgebraic set the estimation problem consists of computing the largest estimate of the rda lerda provided by a given rational lf the control problem consists of computing a polynomial static output controller of given degree for maximizing such a lerda in particular the paper shows that the computation of the best lower bound of the lerda for chosen degrees of the sos polynomials which requires the solution of a nonconvex optimization problem with bilinear matrix inequalities bmis can be reformulated as a quasi convex optimization problem under some conditions moreover the paper provides a necessary and sufficient condition for establishing tightness of this lower bound lastly the paper discusses the search for optimal rational lfs using the proposed strategy

discrete exterior calculus discretization of incompressible navier stokes equations over surface simplicial meshes a conservative discretization of incompressible navier stokes equations is developed based on discrete exterior calculus dec a distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product the governing equations are first rewritten using the exterior calculus notation replacing vector calculus differential operators by the exterior derivative hodge star and wedge product operators the discretization is then carried out by substituting with the corresponding discrete operators based on the dec framework numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured triangular meshes and first order accuracy for otherwise unstructured meshes by construction the method is conservative in that both mass and vorticity are conserved up to machine precision the relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a singularity avoiding moving least squares scheme for two dimensional unstructured meshes moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data in particular they are often employed when solving partial differential equations on unstructured meshes which are typically needed when the geometry defining the domain is complex it is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements however little research has specifically addressed this issue in this paper a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions and the precise conditions under which singularities occur are identified the theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner while attempting to maintain stencil symmetry as closely as possible finally the scheme is applied in a convection diffusion equation solver and an incompressible navier stokes solver and the results are shown to compare favourably with known analytical solutions and previously published results

estimating the domain of attraction for uncertain polynomial systems estimating the domain of attraction da of equilibrium points is a problem of fundamental importance in systems engineering several approaches have been proposed for the case of known polynomial systems allowing one to find the largest estimate of the da leda for a given lyapunov function lf however the problem of estimating the robust da rda that is the da guaranteed for all possible uncertainties in an uncertain system it is still an unsolved problem in this paper lmi methods are proposed for estimating the rda in the case of systems depending polynomially in the state and in the uncertainty which is supposed to belong to a polytope specifically the issue of computing the robust leda rleda that is the intersection of all ledas is considered for common and parameter dependent lfs providing constant and parameter dependent lower bounds the computation of approximations with simple shape of the rleda in the case of parameter dependent lfs is also discussed

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

region of attraction analysis of nonlinear stochastic systems using polynomial chaos expansion abstract a method is presented to estimate the region of attraction roa of stochastic systems with finite second moment and uncertainty dependent equilibria the approach employs polynomial chaos pc expansions to represent the stochastic system by a higher dimensional set of deterministic equations we first show how the equilibrium point of the deterministic formulation provides the stochastic moments of an uncertainty dependent equilibrium point of the stochastic system a connection between the boundedness of the moments of the stochastic system and the lyapunov stability of its pc expansion is then derived defining corresponding notions of a roa for both system representations we show how this connection can be leveraged to recover an estimate of the roa of the stochastic system from the roa of the pc expanded system two optimization programs obtained from sum of squares programming techniques are provided to compute inner estimates of the roa the first optimization program uses the lyapunov stability arguments to return an estimate of the roa of the pc expansion based on this result and user specifications on the moments for the initial conditions the second one employs the shown connection to provide the corresponding roa of the stochastic system the method is demonstrated by two examples

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part ii application in part i of this paper a preconditioned artificial compressibility scheme was developed for modelling laminar steady state and transient incompressible flows for a wide range of reynolds and rayleigh numbers in this part several examples of laminar incompressible problems are solved and discussed the influence of various ac parameters on robustness and convergence rates are assessed for a complex category of problems it is shown that the scheme developed in part i is an accurate robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes copyright 2002 john wiley sons ltd

a deferred correction multigrid algorithm based on a new smoother for the navier stokes equations abstract an algorithm which brings together the techniques of multigrid and deferred correction through their common relationship with imperfect newton iteration manages to combine the ease of calculation of a low order with the accuracy of a high order difference approximation of any given differential equation problem a stable explicit gauss seidel relaxation algorithm for the navier stokes equations based on an appropriate kind of upwinding of as well as derivatives especially developed for use as a multigrid smoother in this context is presented and the complete algorithm is tested on the standard conservative second order discretization of the driven cavity problem

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

paper maximal lyapunov functions and domains of attraction for autonomous nonlinear systems in this paper we present various theoretical and computational methods for estimating the domain of attraction of an autonomous nonlinear system these methods are based on the concept of a maximal lyapunov function which is introduced in this paper a partial differential equation characterizing a maximal lyapunov function is derived and the relationships of this equation as compared to zubov s partial differential equation are discussed an iterative procedure is given for solving the new partial differential equation this procedure yields lyapunov function candidates that are rational functions rather than polynomials the method is applied to four two dimensional examples and one three dimensional example and it is shown that the estimates obtained using this method are in many cases substantially better than those obtained using known methods

practical sequential bounds for approximating two terminal reliability with increasing emphases on better and more reliable services network systems have incorporated reliability analysis as an integral part in their planning design and operation this article first presents a simple exact decomposition algorithm for computing the np hard two terminal reliability which measures the probability of successful communication from specified source node to sink node in the network then a practical bounding algorithm which is indispensable for large networks is presented by modifying the exact algorithm for obtaining sequential lower and upper bounds on two terminal reliability based on randomly generated large networks computational experiments are conducted to compare the proposed algorithm to the well known and widely used edge packing approximation model and to explore the performance of the proposed bounding algorithm computational results reveal that the proposed bounding algorithm is superior to the edge packing model and the trade off of accuracy for execution time ensures that an exact difference between upper and lower bounds on two terminal reliability can be obtained within an acceptable time

on a high order newton linearization method for solving the incompressible navier stokes equations the present study aims to accelerate the non linear convergence to incompressible navier stokes solution by developing a high order newton linearization method in non staggered grids for the sake of accuracy the linearized convection diffusion reaction finite difference equation is solved line by line using the nodally exact one dimensional scheme the matrix size is reduced and at the same time the cpu time is considerably saved owing to the reduction of stencil points this newton linearization method is computationally efficient and is demonstrated to outperform the classical newton method through computational exercises copyright 2005 john wiley sons ltd

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

gas kinetic scheme with discontinuous derivative for low speed flow computation the present paper concerns the improvement of the gas kinetic scheme gks for low speed flow computation in the modified gks scheme the flow distributions with discontinuous derivatives are used as an initial condition at the cell interface for the flux evaluation this discontinuity is determined by considering both the flow characteristic and grid s resolution compared with gks method with a continuous slope for the flow variables at a cell interface the new scheme is more robust and accurate in the under resolved flow computation the new scheme presents much less numerical oscillation the extension of the current scheme to unstructured mesh is straightforward to validate the method both computations of 2d lid driven cavity flow and 3d flow past a sphere are performed the numerical results validate the current method

adaptive variational multiscale methods for incompressible flow based on two local gauss integrations we consider variational multiscale vms methods with h adaptive technique for the stationary incompressible navier stokes equations the natural combination of vms with adaptive strategy retains the best features of both methods and overcomes many of their deficits a reliable a posteriori projection error estimator is derived which can be computed by two local gauss integrations at the element level finally some numerical tests are presented to illustrate the method s efficiency

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

fast computation of bounds for two terminal network reliability in this paper an algorithm for the fast computation of network reliability bounds is proposed the evaluation of the network reliability is an intractable problem for very large networks and hence approximate solutions based on reliability bounds have assumed importance the proposed bounds computation algorithm is based on an efficient bdd representation of the reliability graph model and a novel search technique to find important minpaths mincuts to quickly reduce the gap between the reliability upper and lower bounds furthermore our algorithm allows the control of the gap between the two bounds by controlling the overall execution time therefore a trade off between prediction accuracy and computational resources can be easily made in our approach the numerical results are presented for large real example reliability graphs to show the efficacy of our approach

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

a unified gas kinetic scheme for continuum and rarefied flows iv fluid dynamic equations are valid in their respective modeling scales such as the particle mean free path scale of the boltzmann equation and the hydrodynamic scale of the navier stokes ns equations with a variation of the modeling scales theoretically there should have a continuous spectrum of fluid dynamic equations even though the boltzmann equation is claimed to be valid in all scales many boltzmann solvers including direct simulation monte carlo method require the cell resolution to the order of particle mean free path scale therefore they are still single scale methods in order to study multiscale flow evolution efficiently the dynamics in the computational fluid has to be changed with the scales a direct modeling of flow physics with a changeable scale may become an appropriate approach the unified gas kinetic scheme ugks is a direct modeling method in the mesh size scale and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path the cell size of ugks is not limited by the particle mean free path with the variation of the ratio between the numerical cell size and local particle mean free path the ugks recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale the previous ugks is mostly constructed from the evolution solution of kinetic model equations even though the ugks is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time it still has space to develop more accurate flow solver in the region where the time step is comparable with the local particle mean free time in such a scale there is dynamic difference from the full boltzmann collision term and the model equations this work is about the further development of the ugks with the implementation of the full boltzmann collision term in the region where it is needed the central ingredient of the ugks is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled the newly developed ugks has the asymptotic preserving ap property of recovering the ns solutions in the continuum flow regime and the full boltzmann solution in the rarefied regime in the mostly unexplored transition regime the ugks itself provides a valuable tool for the non equilibrium flow study the mathematical properties of the scheme such as stability accuracy and the asymptotic preserving will be analyzed in this paper as well

a fully dynamic algorithm for distributed shortest paths we propose a fully dynamic distributed algorithm for the all pairs shortest paths problem on general networks with positive real edge weights if is the number of pairs of nodes changing the distance after a single edge modification insert delete weight decrease or weight increase then the message complexity of the proposed algorithm is o n in the worst case where n is the number of nodes of the network if o n2 this is better than recomputing everything from scratch after each edge modification up to now only a result of ramarao and venkatesan was known stating that the problem of updating shortest paths in a dynamic distributed environment is as hard as that of computing shortest paths

evaluations of quantiles of system lifetime distributions abstract for each coherent and mixed system with exchangeable components we provide sharp bounds on the deviations of system lifetime distribution quantiles from the respective quantiles of single component lifetime distributions the bounds are expressed in the scale units generated by the absolute moments of various orders of the component lifetime centered about the median of its distribution

sph with the multiple boundary tangent method in this article we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics sph method benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries as well current sph boundary approaches do not properly treat curved boundaries in complicated flow domains these drawbacks have been remedied in a new boundary treatment method presented in this article called the multiple boundary tangent mbt approach in this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions the two benchmark problems chosen are the lid driven cavity problem and flow over a cylinder the sph solutions using the mbt approach and the results from literature are in very good agreement these solutions involved solid boundaries but the approach presented herein should be extendable to time evolving free surface boundaries copyright 2008 john wiley sons ltd

a compact monotonic discretization scheme for solving second order vorticity velocity equations abstract this paper presents a numerical method for solving the steady state navier stokes equations for incompressible fluid flows using velocities and vorticity as working variables the method involves solving a second order differential equation for the velocity and a convection diffusion equation for the vorticity in cartesian grids the key to the success of the numerical simulation of this class of flow equations depends largely on proper simulation of vorticity transport equation subject to proper boundary vorticity in this paper we present a monotonic advection diffusion multi dimensional scheme and a theoretically rigorous implementation of vorticity boundary conditions while the derivation of the proposed integral vorticity boundary condition is more elaborate and is more difficult to solve than conventional local approaches the present approach offers significant advantages in this study both lid driven and backward facing step problems have been selected for comparison and validation purposes

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

power law fluid flow in driven enclosures with undulation using mrt lattice boltzmann method abstract in this article the flow of non newtonian fluid which is represented by the power law model in two dimensional 2d driven enclosures is studied the enclosure consists of regular rectangular shaped undulations on the bottom wall multiple relaxation time mrt collision model for the lattice boltzmann equation method lbm is employed first numerical validation is performed by comparing the mrt lbm results of power law fluid flow inside the wall driven square enclosure no undulation and flow inside diagonally flipped l shaped enclosure with the literature the strain rate profiles for square enclosure without undulations are compared using various equations available for strain rate calculation in the lbm literature further the effect of different values of the non hydrodynamic relaxation parameters on the flow is examined then for the undulated enclosures flow features and eddy dynamics are analyzed and discussed for the variations in the power law index n to represent shear thinning and shear thickening fluids the effects of various parameters such as reynolds numbers wall undulation heights and wavelength of undulations on the power law fluid flow are analyzed also the variation of viscosity with spatial location for steady state flow and total kinetic energy within the computational domain are presented for various values of power law index

linear stability of incompressible flow using a mixed finite element method we analyzed the linear stability for incompressible flow using the mixed finite element method first by means of the fractional step finite element method the two dimensional base flows were numerically computed over a range of reynolds numbers and then they were perturbed with three dimensional disturbances by using linear stability and normal mode analysis we obtained the partial differential equations governing the evolution of perturbation from linearized navier stokes equations with slight compressibility in terms of the mixed finite element discretization in which six node quadratic lagrange triangular elements with quadratic interpolation for velocities p2 and three node linear lagrange triangular elements for pressure p1 were used a nonsingular generalized eigenproblem was formulated from these equations whose solution gives the dispersion relationship between the complex growth rate and the wave number we examined the stability of lid driven cavity flow in this study the stability results obtained from thep2p1elements were compared with those fromp1p1elements the spatial distribution of the pressure disturbance can be smoothed by using ap2p1element such as that in the simulation of incompressible flows by the mixed finite element method however the choice of elemental type has little influence on the stability results this study presents stability curves to identify the critical reynolds number and the critical wavelength of the neutral mode and discusses the instability mechanism the taylor goertler like vortices in the cavity were obtained by means of the reconstruction of three dimensional flows the stability results and the reconstructed three dimensional flows were in agreement with the observed ones and the other numerical stability results respectively

performance assessment and reliability analysis of dependable and distributed computing systems based on bdd and recursive merge system reliability evaluation sensitivity analysis failure frequency analysis importance measures and optimal design are important issues that have become research topics for distributed dependable computing finding all of the minimal file spanning trees mfst and avoiding repeatedly computing the redundant mfsts have been key techniques for evaluating the reliability of a distributed computing system dcs in previous works however identifying all of the disjointed mfsts is difficult and time consuming for large scale networks although existing algorithms have been demonstrated to work well on medium scale networks they have two inherent drawbacks first they do not support efficient manipulation of boolean algebra the sum of disjoint products method used by these algorithms is inefficient when dealing with large boolean functions second the tree based partitioning algorithm does not merge isomorphic sub problems and therefore redundant computations cannot be avoided in this paper we propose a new efficient algorithm for the reliability evaluation of a dcs based on the recursive merge and the binary decision diagram bdd using the bdd substitution method we can easily apply our algorithm to a network with imperfect nodes the experimental results show a significant improvement in the execution time compared to previous works

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

on the role of polynomials in rbf fd approximations ii numerical solution of elliptic pdes rbf generated finite differences rbf fd have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of pdes we find in the present study that combining polyharmonic splines phs with multivariate polynomials offers an outstanding combination of simplicity accuracy and geometric flexibility when solving elliptic equations in irregular or regular regions in particular the drawbacks on accuracy and stability due to runge s phenomenon are overcome once the rbf stencils exceed a certain size due to an underlying minimization property test problems include the classical 2 d driven cavity and also a 3 d global electric circuit problem with the earth s irregular topography as its bottom boundary the results we find are fully consistent with previous results for data interpolation

local stability analysis for uncertain nonlinear systems we propose a method to compute provably invariant subsets of the region of attraction for the asymptotically stable equilibrium points of uncertain nonlinear dynamical systems we consider polynomial dynamics with perturbations that either obey local polynomial bounds or are described by uncertain parameters multiplying polynomial terms in the vector field this uncertainty description is motivated by both incapabilities in modeling as well as bilinearity and dimension of the sum of squares programming problems whose solutions provide invariant subsets of the region of attraction we demonstrate the method on three examples from the literature and a controlled short period aircraft dynamics example

region of attraction analysis with integral quadratic constraints abstract a general framework is presented to estimate the region of attraction of attracting equilibrium points the system is described by a feedback connection of a nonlinear polynomial system and a bounded operator the input output behavior of the operator is characterized using an integral quadratic constraint this allows to analyze generic problems including for example hard nonlinearities and different classes of uncertainties adding to the state of practice in the field which is typically limited to polynomial vector fields the iqc description is also nonrestrictive with the main result given for both hard and soft factorizations optimization algorithms based on sum of squares techniques are then proposed with the aim to enlarge the inner estimates of the roa numerical examples are provided to show the applicability of the approaches these include a saturated plant where bounds on the states are exploited to refine the sector description and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft iqcs

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

stability region analysis using polynomial and composite polynomial lyapunov functions and sum of squares programming we propose using bilinear sum of squares programming for obtaining inner bounds of roas for dynamical systems with polynomial vector fields we search for polynomial as well as composite lyapunov functions comprised of pointwise maximums of polynomial functions results for several examples from the literature are presented using the proposed methods and the penbmi solver

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

development of bem for convective viscous flow problems abstract three kinds of boundary element approaches for an unsteady flow problem of incompressible viscous fluid are presented the first approach which is the so called boundary domaintype is based on the use of fundamental solution for the only linear differential operator and the newton raphson iterative procedure the second one is based on the time splitting technique of the governing equations in which the fundamental equations are split into the convection equation and the stokes equations the third one is based on the well known fractional step fs method which is one of the time splitting techniques in order to show the applicability and effectiveness of our approaches numerical results of the driven cavity flow example are demonstrated through a comparison with other numerical results

finding the k shortest paths we give algorithms for finding the k shortest paths not required to be simple connecting a pair of vertices in a digraph our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges in time o m n log n k we can also find the k shortest paths from a given source s to each vertex in the graph in total time o m n log n kn we describe applications to dynamic programming problems including the knapsack problem sequence alignment maximum inscribed polygons and genealogical relationship discovery

numerical simulation of incompressible fluid flow using locally solenoidal elements in this paper we present a numerical study of the performance of a discontinuous galerkin formulation for the navier stokes equations this method is characterized by the fact that the velocity field is approximated using piecewise polynomial functions that are totally discontinuous across interelement boundaries and which are pointwise divergence free on each element locally solenoidal in particular numerical results are presented for two well known benchmark problems

vorticity boundary condition and related issues for finite difference schemes this paper discusses three basic issues related to the design of finite difference schemes forunsteadyviscous incompressible flows using vorticity formulations the boundary condition for vorticity an efficient time stepping procedure and the relation between these schemes and the ones based on velocity pressure formulation we show that many of the newly developed global vorticity boundary conditions can actually be written as some local formulas derived earlier we also show that if we couple a standard centered difference scheme with third or fourth order explicit runge kutta methods the resulting schemes havenocell reynolds number constraints for high reynolds number flows these schemes are stable under the cfl condition given by the convective terms finally we show that the classical mac scheme is the same as thom s formula coupled with second order centered differences in the interior in the sense that one can define discrete vorticity in a natural way for the mac scheme and get the same values as the ones computed from thom s formula we use this to derive an efficient fourth order runge kutta time discretization for the mac scheme from the one for thom s formula we present numerical results for driven cavity flow at high reynolds number 105

region of attraction estimation using invariant sets and rational lyapunov functions this work addresses the problem of estimating the region of attraction ra of equilibrium points of nonlinear dynamical systems the estimates we provide are given by positively invariant sets which are not necessarily defined by level sets of a lyapunov function moreover we present conditions for the existence of lyapunov functions linked to the positively invariant set formulation we propose connections to fundamental results on estimates of the ra are presented and support the search of lyapunov functions of a rational nature we then restrict our attention to systems governed by polynomial vector fields and provide an algorithm that is guaranteed to enlarge the estimate of the ra at each iteration

supg stabilized finite element resolution of the navier stokes equations applications to water treatment engineering in this paper an analysis of the viscous incompressible flow has been carried out from the very definition of the governing equations up to the resolution of some practical problems passing through the comprehensive study of the stabilized finite element techniques used in their resolution as a consequence of this analysis a code based upon a realistic interpretation of the forces has been written which allows for the modelling of the open channel flow with optimum results in the resolution of some benchmark and real flow problems related with the wastewater industry