symmetry preserving discretization of navier stokes equations on collocated unstructured grids a fully conservative discretization is presented in this paper the same principles followed by verstappen and veldman 2003 3 are generalized for unstructured meshes here a collocated mesh scheme is preferred over a staggered one due to its simpler form for such meshes the basic idea behind this approach remains the same mimicking the crucial symmetry properties of the underlying differential operators i e the convective operator is approximated by a skew symmetric matrix and the diffusive operator by a symmetric positive definite matrix a novel approach to eliminate the checkerboard spurious modes without introducing any non physical dissipation is proposed to do so a fully conservative regularization of the convective term is used the supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed finally the new discretization method is successfully tested for a buoyancy driven turbulent flow in a differentially heated cavity

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

nonlinear dynamics delay times and embedding windows in order to construct an embedding of a nonlinear time series one must choose an appropriate delay time d often d is estimated using the autocorrelation function however this does not treat the nonlinearity appropriately and it may yield an incorrect value for d on the other hand the correct value of d can be found from the mutual information but this process is rather cumbersome computationally here we suggest a simpler method for estimating d using the correlation integral we call this the c c method and we test it on several nonlinear time series obtaining estimates of d in agreement with those obtained using the mutual information furthermore some researchers have suggested that one should not choose a fixed delay time d independent of the embedding dimension m but rather one should choose an appropriate value for the delay time window w d m 1 which is the total time spanned by the components of each embedded point unfortunately w cannot be estimated using the autocorrelation function or the mutual information and no standard procedure for estimating w has emerged however we show that the c c method can also be used to estimate w basically w is the optimal time for independence of the data while d is the first locally optimal time as tests we apply the c c method to the lorenz system a three dimensional irrational torus the rossler system and the rabinovich fabrikant system we also demonstrate the robustness of this method to the presence of noise c 1999 elsevier science b v all rights reserved

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

accuracy analysis of explicit runge kutta methods applied to the incompressible navier stokes equations this paper investigates the temporal accuracy of the velocity and pressure when explicit runge kutta methods are applied to the incompressible navier stokes equations it is shown that at least up to and including fourth order the velocity attains the classical order of accuracy without further constraints however in case of a time dependent gradient operator which can appear in case of time varying meshes additional order conditions need to be satisfied to ensure the correct order of accuracy furthermore the pressure is only first order accurate unless additional order conditions are satisfied two new methods that lead to a second order accurate pressure are proposed which are applicable to a certain class of three and four stage methods a special case appears when the boundary conditions for the continuity equation are independent of time since in that case the pressure can be computed to the same accuracy as the velocity field without additional cost relevant computations of decaying vortices and of an actuator disk in a time dependent inflow support the analysis and the proposed methods

unified lagrangian formulation for solid and fluid mechanics and fsi problems abstract we present a lagrangian monolithic strategy for solving fluid structure interaction fsi problems the formulation is called unified because fluids and solids are solved using the same solution scheme and unknown variables the method is based on a mixed velocity pressure formulation each time step increment is solved via an iterative partitioned two step procedure the particle finite element method pfem is used for solving the fluid parts of the domain while for the solid ones the finite element method fem is employed both velocity and pressure fields are interpolated using linear shape functions for quasi incompressible materials the solution scheme is stabilized via the finite calculus fic method the stabilized elements for quasi incompressible hypoelastic solids and newtonian fluids are called vps s element and vps f element respectively other two non stabilized elements are derived for hypoelastic solids one is based on a velocity formulation v element and the other on a mixed velocity pressure scheme vp element the algorithms for coupling the solid elements with the vps f fluid element are explained in detail the unified formulation is validated by solving benchmark fsi problems and by comparing the numerical solution to the ones published in the literature

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

the analysis of chaotic time series data this paper presents a brief survey of time series analysis methods that are applicable to processes whose behavior can be described as low dimensional chaos the goal of these methods is to allow experimentalists to obtain local estimates of the dynamics directly from a set of data these estimates are often sufficiently accurate to attempt noise reduction prediction and control

the analytic formulas of the ripple free tracking problem abstract the forward pulse transfer function of the controlled system always contains at least one zero at infinity two formulas can be found which define the order of the unspecified polynomial in the design of ripple free digital control systems some fundamental concepts are introduced in this paper and a new method which has been widely applied to teaching and research is developed

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

simultaneous deadbeat tracking controller synthesis abstract a direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented this novel approach is based on polynomial algebra and the principle of system realizability without solving linear polynomial diophantine equations the proposed procedure consists of solving a set of linear equations depending on system dynamics and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals since all solutions are described in a parametric form some performance criteria can be easily incorporated as well examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

estimating the embedding dimension abstract well reconstructed dynamics should be described as a mapping we propose to search for the lowest embedding dimension for which the property of a continuous mapping is satisfied the images of close points are close we demonstrate the effectiveness of the approach by finding the lowest embedding dimension of several chaotic systems embedded by the method of delays

an accurate second order approximation factorization method for time dependent incompressible navier stokes equations in spherical polar coordinates a finite difference method for solving three dimensional time dependent incompressible navier stokes equations in spherical polar coordinates is presented in detail a new algorithm which is second order accurate in time and space is considered and decoupling between the velocity and the pressure is achieved by this algorithm further the numerical method is tested by computing the spherical couette flow between two concentric spheres with the inner one rotating a comparison of the numerical solutions with available numerical results and experimental measurements is made it is demonstrated that the numerical code is valid for solving three dimensional unsteady incompressible navier stokes equations in spherical polar coordinates

1d wave propagation in saturated viscous geomaterials improvement and validation of a fractional step taylor galerkin finite element algorithm abstract this paper tackles the numerical simulation of 1d wave propagation in saturated viscous porous media and especially in soil like geomaterials for this purpose an improved fractional step taylor galerkin algorithm is first formulated and then validated on the basis of a new analytical solution the algorithm based on a stress velocity pressure formulation of the hydro mechanical problem combines an explicit taylor galerkin method with a fractional time stepping while an accurate runge kutta type integrator is introduced to treat the viscosity of the porous skeleton the overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables even when the so called undrained incompressible limit is approached the accuracy and stability of the method are verified with reference to a 1d benchmark problem concerning the propagation of p waves along a saturated viscoelastic soil stratum for this problem a frequency domain analytical solution is derived assuming incompressible interstitial fluid and soil grains the assumption of maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem while the same rheology of a more realistic elasto viscoplastic non linear behaviour is maintained the performance of the fractional step taylor galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic impulsive and seismic input excitations in particular parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses as well as in dealing with weakly viscous materials

fast fluid structure interaction simulations using a displacement based finite element model equipped with an explicit streamline integration prediction abstract we propose here a displacement based updated lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements the novelty of the model consists in the use of the explicit streamline integration for predicting the end of step configuration of the fluid domain it is shown that this prediction considerably alleviates the time step size restrictions faced by the former lagrangian models due to the possibility of an element inversion within one time step the method is validated and compared with conventional approaches using three numerical examples time step size and corresponding courant numbers leading to optimal behavior in terms of computational efficiency are identified

stabilized mixed continuous enriched galerkin formulations for locally mass conservative poromechanics abstract local element wise mass conservation is often highly desired for numerical solutions to coupled poromechanical problems as an efficient numerical method featuring this property mixed continuous galerkin cg enriched galerkin eg finite elements have recently been proposed in which piecewise constant functions are enriched to the pore pressure interpolation functions of the conventional mixed cg cg elements while this enrichment of the pressure space provides local mass conservation it unavoidably alters the stability condition for mixed finite elements because no stabilization method has been available for the new stability condition high order displacement interpolation has been required for mixed cg eg elements if undrained condition is expected to circumvent this requirement here we develop stabilized formulations for the mixed cg eg elements that permit equal order interpolation functions even in the undrained limit we begin by identifying the inf sup condition for mixed cg eg elements by phrasing an enriched poromechanical problem as a twofold saddle point problem we then derive two types of stabilized formulations one based on the polynomial pressure projection ppp method and the other based on the fluid pressure laplacian fpl method a key finding of this work is that both methods lead to stabilization terms that should be augmented only to the cg part of the pore pressure field not to the enrichment part the two stabilized formulations are verified and investigated through numerical examples that involve various conditions spanning 1d to 3d isotropy to anisotropy and homogeneous to heterogeneous domains the methodology presented in this work may also help stabilize other types of mixed finite elements in which the constraint field is enriched by additional functions

state space reconstruction parameters in the analysis of chaotic time series the role of the time window length abstract the most common state space reconstruction method in the analysis of chaotic time series is the method of delays mod many techniques have been suggested to estimate the parameters of mod i e the time delay and the embedding dimension m we discuss the applicability of these techniques with a critical view as to their validity and point out the necessity of determining the overall time window length w for successful embedding emphasis is put on the relation between w and the dynamics of the underlying chaotic system and we suggest to set w p the mean orbital period p is approximated from the oscillations of the time series the procedure is assessed using the correlation dimension for both synthetic and real data for clean synthetic data values of w larger than p always give good results given enough data and thus p can be considered as a lower limit w p for noisy synthetic data and real data an upper limit is reached for w which approaches p for increasing noise amplitude

an efficient staggered time marching procedure for porodynamics the present work proposes a novel time marching procedure which is designed for the dynamic simulation of the coupled two phase biot equations considering the displacement pressure u p formulation the new approach provides unconditional stability and excellent efficiency due to the staggered character of the temporal discretization where equilibrium is established at time t for the u group of governing equations and at time t t for the p group of governing equations the resulting systems of equations have an improved format and can be factorized solved at significantly less computational effort when compared to standard approaches such as the generalized newmark scheme in addition the resulting new systems of equations are characterized by considerably lower condition numbers reducing correlated numerical issues unconditional stability is achieved by a consistent manipulation of the mass and compressibility matrix of the model which causes virtually no computational overhead as a byproduct of the altered compressibility matrix the method is capable of simulating incompressible and impermeable phenomena without the need for any further feats the newly developed time marching technique is implemented and tested considering different benchmark problems for comparison the commonly used newmark scheme is also applied and both direct lu decomposition and iterative gmres linear solvers are employed in order to assess the efficiency of the new technique

an ale pfem method for the numerical simulation of two phase mixture flow abstract a new finite element method is proposed to simulate two phase mixture problems with free surfaces and or large moving boundaries the two phases are treated as interpenetrating continua within a two fluid model in contrast to the conventional two fluid model formulations in which the governing equations are written in the eulerian eulerian description the modified two fluid model has the governing equations of one fluid phase written in the lagrangian description while the respective equations of the other phase is formulated in the arbitrary lagrangian eulerian ale description with relative velocities defined with respect to the moving mesh associated with the first fluid phase the finite element method fem together with stabilization techniques the characteristic based split cbs and the algebraic flux correction afc method is employed to solve the equations numerically in space and time the nodes of the computational mesh are updated together with the flow of the phase described in the lagrangian description the computational mesh is updated by applying techniques used in the so called particle finite element method pfem characterized by regenerating the mesh in each computational step according to the updated nodal positions while the current boundary of the domain is identified using shape method the performance of the method is demonstrated by means of three 2d and 3d examples including a mixing process of two fluids in a stirred tank a free surface flow a 3d two phase channel flow a phase separation problem and the flow of two immiscible fluids

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

stable element free galerkin solution procedures for the coupled soil pore fluid problem it is always difficult to solve the coupled soil pore fluid problem when the soil is saturated and impermeable because this situation often results in intensive oscillations of the solutions this topic has been discussed widely in the field of the finite element method but rarely by meshless methods the element free galerkin efg method has outstanding advantages of solving this problem based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain in this study an efg numerical model together with a stabilization technique is proposed to obtain stable solutions especially for the saturated and impermeable soil close agreement between computational results and analytical solutions for one and two dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil furthermore the influences of the hydraulic anisotropy a typical property of two dimensional problems on the proposed stabilization technique are discussed it is suggested that the optimal distribution of the nodes of essential variables can be designed according to the relative importance of the permeability in different directions copyright c 2010 john wiley sons ltd

comparison of monolithic and splitting solution schemes for dynamic porous media problems 5 summary proceeding from the governing equations describing a saturated poroelastic material with intrinsically 7 incompressible solid and fluid constituents we compare the monolithic and splitting solution of the different multi field formulations feasible in porous media dynamics because of the inherent solid fluid momentum 9 interactions one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the momentum equations and the algebraic incompressibility constraint here the 11 resulting set of differential algebraic equations dae is solved by the finite element method fem following two different strategies 1 an implicit monolithic approach where the equations are first 13 discretized in space using stable mixed finite elements and second in time using stiffly accurate implicit time integrators 2 a semi explicit implicit splitting scheme in the sense of a fractional step method 15 where the dae are first discretized in time split using intermediate variables and then discretized in space using linear equal order approximations for all primary unknowns finally a one and a two dimensional 17 wave propagation example serve to reveal the pros and cons in regard to accuracy and stability of both solution strategies therefore several test cases differing in the used multi field formulation the 19 monolithic time stepping method and the approximation order of the individual unknowns are analyzed for varying degrees of coupling controlled by the permeability parameter in the end we provide a 21 reliable recommendation which of the presented strategies and formulations is the most suitable for which particular dynamic porous media problem copyright q 2009 john wiley sons ltd 23

a fast immersed boundary method for external incompressible viscous flows using lattice green s functions a new parallel computationally efficient immersed boundary method for solving three dimensional viscous incompressible flows on unbounded domains is presented immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original peskin s immersed boundary method unlike peskin s method boundary forces are regarded as lagrange multipliers that are used to satisfy the no slip condition the incompressible navier stokes equations are discretized on an unbounded staggered cartesian grid and are solved in a finite number of operations using lattice green s function techniques these techniques are used to automatically enforce the natural free space boundary conditions and to implement a novel block wise adaptive grid that significantly reduces the run time cost of solutions by limiting operations to grid cells in the immediate vicinity and near wake region of the immersed surface these techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half explicit runge kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation incompressibility constraint and no slip constraint linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation free nested projection technique the algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems e g discrete poisson problems that are compatible with recent parallel fast multipole methods for difference equations numerical experiments on low aspect ratio flat plates and spheres at reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation

high order direct stokes solvers with or without temporal splitting numerical investigations of their comparative properties a recently proposed direct stokes solver which decouples the velocity and pressure operators without calling for a temporal scheme is numerically analyzed in comparison first with the splitting scheme proposed by g karniadakis m israeli and s orszag in j comput phys 97 1991 pp 414 443 and with the unique grid bbb p n bbb p n 2 uzawa approach for the space accuracy and computational costs the chebyshev collocation approximation is used to analyze the spectra of the continuous temporal evolution operators and their discrete time versions from the first to the fourth order an explicit boundary condition is also involved in the proposed stokes solver and it is numerically shown that the trace of bf delta bf u on the boundary must be evaluated through its bf nabla times bf nabla times contribution only otherwise the ellipticity is lost before proceeding to the time discretization the explicit evaluation of the rotational boundary term does not prevent the first and second order in time schemes from being unconditionally stable while the schemes built at the next two higher orders are limited by the usual explicit cal o n 4 stability criterion on the time step the proposed bf u p decoupling gives this limitation a less restrictive coefficient and supplies the expected temporal orders on the whole explored range of time step sizes the effective accuracy obtained for the navier stokes 2d solutions has been measured for the re 1000 lid driven cavity problem and has been found equivalent to what is supplied by the much more expensive uzawa decoupling method

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

adaptive coupled arbitrary lagrangian eulerian finite element and meshfree method for injection molding process this paper presents an adaptive method that couples the finite element fe method and the meshfree mf method in the arbitrary lagrangian eulerian ale description for numerical simulation of injection molding processes the ale feature is used to accurately capture moving free surfaces of flow problems and meanwhile to alleviate mesh distortion and its influence on the accuracy and robustness of numerical solutions based on the continuous blending method originally presented for properly imposing the essential boundary conditions in mf methods the coupled ale fe and mf method is developed to exploit the respective advantages of both fe and mf methods but to avoid their respective weak points the method features self adaptivity in view of the fact that moving free surfaces in an injection molding process are continuously advanced the pressure stabilized fractional step algorithm in which the modified version of the finite increment calculus process is extended to the coupled ale fe and mf method is used to solve incompressible navier stokes equations governing the injected polymer flow so that equal low order u p interpolations that violate the lbb condition can be effectively used numerical experiments demonstrate the significance and ability of the proposed method for numerical simulation of injection molding processes copyright 2007 john wiley sons ltd

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

iterative dynamic analysis of linear and nonlinear fully saturated porous media considering edge based smoothed meshfree techniques abstract in this work smoothed meshfree methods are firstly applied to numerically analyze nonlinear pore dynamic models a weakened weak formulation based on the edges of triangular cells obtained by a delaunay triangulation is considered here framing the so called edge based smoothed domains the meshfree shape functions are computed by the radial point interpolation method considering the t6 scheme for the shape function support domains enhanced procedures to compute the mass compressibility and coupling matrices of the pore dynamic model are discussed which are consistent with the computation of the stiffness and permeability matrices as well as internal force vectors in case of nonlinear analyses of the edge based smoothed domain formulation and that consider finer local integration techniques at lower computational costs rendering more accurate and efficient procedures two numerical formulations are considered here to analyze the time domain nonlinear coupled system of equations that arises once the spatial discretization is accomplished the standard newmark newton raphson method and an alternative iterative coupling approach in this iterative approach each phase of the coupled problem is treated separately uncoupling the governing equations of the model thus smaller and better conditioned systems of equations are obtained rendering more attractive techniques a relaxation parameter is introduced in order to improve the efficiency of the iterative coupling procedure and an expression to compute optimal values for the relaxation parameter is discussed at the end of the paper numerical examples are presented illustrating the effectiveness and potentialities of the proposed methodologies

efficient algorithm on a nonstaggered mesh for simulating rayleigh benard convection in a box an efficient semi implicit second order accurate finite difference method is described for studying incompressible rayleigh benard convection in a box with sidewalls that are periodic thermally insulated or thermally conducting operator splitting and a projection method reduce the algorithm at each time step to the solution of four helmholtz equations and one poisson equation and these are are solved by fast direct methods the method is numeri cally stable even though all field values are placed on a single non staggered mesh commensurate with the boundaries the efficiency and accuracy of the method are characterized for several representative convection problems

a lagrangian nodal integration method for free surface fluid flows abstract we present a lagrangian nodal integration method for the simulation of newtonian and non newtonian free surface fluid flows the proposed nodal lagrangian method uses a finite element mesh to discretize the computational domain and to define the linear shape functions for the unknown nodal variables as in the standard particle finite element method pfem in this approach however the integrals are performed over nodal patches and not over elements and strains stresses are defined at nodes and not at gauss points this allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental pfem several numerical tests in 2d and in 3d are presented to validate the proposed nodal pfem in all cases the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature a thorough comparison between nodal and elemental pfems is also presented focusing on crucial issues such as solution accuracy convergence mass conservation and sensitivity to mesh distortion

an eulerian mixed formulation for viscoplastic materials abstract this paper presents an eulerian mixed formulation for viscoplastic materials the algorithm is formulated in terms of deviatoric stress velocity and hydrostatic pressure using a fractional step algorithm that allows the use of equal order of interpolation for the three variables the constitutive law is based on the viscoplasticity theory of perzyna with the von mises yield criterion the jaumann rate of cauchy stress tensor is used to ensure the objectivity of the constitutive law a splitting scheme based on a two step taylor galerkin algorithm for the advective terms plus a fourth order runge kutta scheme for the sources has been used to improve the accuracy of the method

extremely simple nonlinear noise reduction method a very simple method to reduce noise in experimental data with nonlinear time evolution is presented locally constant fits are used to obtain a less noisy trajectory consistent with the dynamics as well as with the measured data neighborhoods are defined by coordinates both from the past and from the future the method is applied to the h enon map and to a discretized form of the mackey glass equation

ripple free tracking problem in the deadbeat control of discrete plants originating from continuous ones it is important to have exact tracking not only at the sampling instants but also in between the instants this paper investigates such a problem in the general case of a reference signal that can vary within a pre specified class the design procedure proposed here is based on a polynomial algebra approach an internally stable closed loop system is derived by means of an algorithm where the transfer function of the controller originates from the solution of a set of linear equations algebraic conditions are given to determine the minimum time control scheme numerical examples are reported to show the feasibility of the method and the simplicity of including other specific requirements into the control law

a petrov galerkin formulation for the incompressible navier stokes equations using equal order interpolation for velocity and pressure a new petrov galerkin method for the incompressible navier stokes equations is presented the use of the so called optimal upwind parameter in multidimensions is justified by a time scale analysis of the relevant physical processes the resulting procedure circumvents the babuska brezzi condition and allows equal order interpolation for velocity and pressure to be used

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series we propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series the suggested plot defines a time dependent exponent and a plus exponent based on their changes with the embedding dimension and delay time a criterion for estimating simultaneously the minimal acceptable embedding dimension the proper delay time and the largest lyapunov exponent has been obtained when redefining the time dependent exponent lambda k curves on a series of shells we have found that whether a linear envelope to the lambda k curves exists can serve as a direct dynamical method of distinguishing chaos from noise

fdm solutions to linear dynamics of porous media efficiency stability and parallel solution strategy summary this paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation the method is named parallel lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations as a result the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved the other advantage of the scheme is the fulfilment of the inf sup stability condition the scheme is developed to solve porous media formulations derived from the theory of porous media both the u p and u v p formulations are considered u displacement of solid p pressure of liquid and v velocity of liquid several simulations are performed to demonstrate the capabilities of the method

nonlinear transient phenomena in saturated porous media abstract in this report the transient static and dynamic response of saturated porous medium is analyzed the saturated porous medium viewed as a two phase system whose state is described by the stresses displacements velocities and accelerations within each phase the coupled field and constitutive equations based on mixture s theories are presented and solved numerically by the use of the finite element method time integration is achieved by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers the procedure allows for a convenient selection of implicit and explicit elements and for an implicit explicit split of the various operators appearing in the differential equations accuracy and versatility of the proposed procedure are demonstrated by applying it to obtain solution to various dynamic and pseudo static one and two dimensional initial value problems

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

improved accuracy in algebraic splitting methods for navier stokes equations this paper studies a new alteration of yosida algebraic splitting methods for the navier stokes equations by applying the usual or pressure corrected yosida splitting techniques to discretizations written in terms of velocity and pressure updates u n 1 u n p n 1 p n we show that the accuracy is increased by one full order in delta t without any additional cost in the respective methods proofs of the convergence results are given both in linear algebraic and finite element frameworks several numerical tests are given which reveal the sometimes dramatic improvement in accuracy offered by the proposed fix

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

wave propagation and localization problems in saturated viscoplastic geomaterials this paper presents an improved algorithm to deal with wave propagation and localization problems in saturated viscoplastic geomaterials it consists of a mixed formulation in terms of effective stress velocity and pore pressure that uses a fractional step algorithm allowing the use of equal order of interpolation for the three variables and the simplest element such as the linear triangle the viscoplastic model used is of modified cam clay type viscoplasticity results in a strong source term that deteriorates the accuracy of the two step taylor galerkin algorithm therefore a runge kutta splitting scheme has been used to deal with the source terms resulting in a better accuracy of the method copyright 2006 john wiley sons ltd

on the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids the purpose of this paper is to study the effect of the bulk modulus on the iterative solution of free surface quasi incompressible fluids using a mixed partitioned scheme a practical rule to set up the value of a pseudo bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given the efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field the convergence rate and the computational speed of the analyses the technique has been tested on a finite calculus particle finite element method lagrangian formulation but it can be easily extended to other quasi incompressible stabilized finite element formulations copyright c 2014 john wiley sons ltd

filtered noise can mimic low dimensional chaotic attractors this contribution presents four results first calculations indicate that when examined by the grassberger procaccia algorithm alone filtered noise can mimic low dimensional chaotic attractors given the ubiquity of signal filtering in experimental investigations this is potentially important second a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor third it is shown that a criterion derived by eckmann and ruelle physica d 56 185 1992 to estimate the minimum number of data points required in a grassberger procaccia calculation can be used to provide a further check on these dimension estimates fourth it is shown that surrogate data techniques recently published by theiler and his colleagues in nonlinear modeling and forecasting edited by m casdagli and s eubanks addison wesley reading ma 1992 can successfully distinguish between linearly correlated noise and nonlinear structure these results and most particularly the first indicate that grassberger procaccia results must be interpreted with far greater circumspection than has previously been the case and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data when filtered signals are examined by this algorithm alone a finite noninteger value of mathit d 2 is consistent with low dimensional chaotic behavior but it is certainly not a definitive diagnostic of chaos

min max kalman filtering abstract the problem of h optimal state estimation of linear continuous time systems that are measured with an additive white noise is addressed the relevant cost function is the expected value of the standard h performance index with respect to the measurement noise statistics the solution is obtained by applying the matrix version of the maximum principle to the solution of the min max problem in which the estimator tries to minimize the mean square estimation error and the exogenous disturbance tries to maximize it while being penalized for its energy the solution is given in terms of two coupled riccati difference equations from which the filter gains are derived in the case where an infinite penalty is imposed on the energy of the exogenous disturbance the celebrated kalman filter is recovered in the stationary case where all the signals are stationary an upper bound on the solutions of the coupled riccati equations is obtained via a solution of coupled linear matrix inequalities the resulting filter then guarantees a bound on the estimation error covariance matrix an illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the position

improving mass conservation in simulation of incompressible flows summary we propose a technique for improving mass conservation features of fractional step schemes applied to incompressible flows the method is illustrated by using a lagrangian fluid formulation where the mass loss effects are particularly apparent however the methodology is general and could be used for fixed grid approaches the idea consists in reflecting the incompressibility condition already in the intermediate velocity this is achieved by predicting the end of step pressure and using this prediction in the fractional momentum equation the resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme in turn the predicted pressure can be used as the boundary condition necessary for the solution of the pressure poisson equation in case a continuous laplacian matrix is employed using this approximation of the end of step incompressible pressure as the essential boundary condition considerably improves the conservation of mass specially for the free surface flows of fluids with low viscosity the pressure prediction does not require the resolution of any additional equations system the efficiency of the method is shown in two examples the first one shows the performance of the method with respect to mass conservation the second one tests the method in a challenging fluid structure interaction benchmark which can be naturally resolved by using the presented approach copyright 2012 john wiley sons ltd

numerical solution of the incompressible navier stokes equations with coriolis forces based on the discretization of the total time derivative in this paper we present a numerical formulation to solve the incompressible navier stokes equations written in a rotating frame of reference the method is based on a finite difference discretization in time and a finite element discretization in space when the viscosity is very small numerical oscillations may appear due both to the high reynolds number and to the presence of the coriolis forces to overcome these oscillations a special discretization in time is proposed the idea is to discretize the total time derivative in an inertial basis rather than only the partial time derivative in the rotating reference system after this is done a further high order approximation is introduced leading to a problem posed in the rotating frame of reference and in spatial coordinates in contrast with the straightforward discretization of the original equations some additional terms appear that enhance the stability of the numerical scheme in the absence of coriolis forces the method is a generalization of the characteristic galerkin technique for convection dominated flows

implicit dynamic three dimensional finite element analysis of an inelastic biphasic mixture at finite strain part 1 application to a simple geomaterial abstract based on the mixture theory formulation for a fluid saturated inelastic pressure sensitive porous solid subjected to dynamic large strain deformation a 3d finite element implementation with implicit time integration is presented a recently published 2d implementation li et al 2004 cmame v193 p3837 70 is extended to 3d porosity dependent permeability and pressure sensitive inelastic solid skeleton response at finite strain the clausius duhem inequality provides the form of the constitutive equations for the solid and fluid phases as well as the dissipation function a non associative drucker prager cap plasticity model at finite strain is formulated based on a multiplicative decomposition of the deformation gradient and numerically integrated semi implicitly in the intermediate configuration to avoid questions of incremental objectivity the elastic implementation is verified with available 1d analytical and 2d benchmark problems new numerical solutions for 3d large strain dynamic behavior of saturated inelastic porous media are presented the computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

non gaussian noise models in signal processing for telecommunications new methods an results for class a and class b noise models the subject here is generalized i e non gaussian noise models and specifically their first order probability density functions pdfs attention is focused primarily on the author s canonical statistical physical class a and class b models in particular class a noise describes the type of electromagnetic interference emi often encountered in telecommunication applications where this ambient noise is largely due to other intelligent telecommunication operations on the other hand ambient class b noise usually represents man made or natural nonintelligent i e nonmessage bearing noise and is highly impulsive class a noise is not an spl alpha stable process nor is it reducible to such except in the limiting gaussian cases of high density noise by the central limit theorem class b noise is also asymptotically normal before model approximation under rather broad conditions principally governed by the source propagation and distribution scenarios the pdf of class b noise alone no gaussian component can usually be approximated by 1 a symmetric gaussian spl alpha stable s spl alpha s model in the case of narrowband reception or when the pdf spl omega sub 1 spl alpha of the amplitude is symmetric and 2 a nonsymmetric spl alpha stable ns spl alpha s model no gaussian component can be constructed in broadband regimes new results here include i counting functional methods for constructing the general qth order characteristic functions cfs of class a and class b noise from which all moments and in principle the pdfs follow ii the first order cfs pdfs and cumulative probabilities apds of nonsymmetric broadband class b noise extended to include additive gauss noise agn iii proof of the existence of all moments in the basic class a and class b models iv the key physical role of agn and the fact that agn removes spl alpha stability v the explicit roles of the propagation and distribution scenarios and vi extension to noise fields although telecommunication applications are emphasized class a and class b noise models apply selectively but equally well to other physical regimes e g underwater acoustics and em radar optics etc supportive empirical data are included

an extension of the immersed boundary method based on the distributed lagrange multiplier approach an extended formulation of the immersed boundary method which facilitates simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for linear stability analysis of the flows is presented the lagrangian forces and heat sources are distributed on the fluid structure interface the method treats pressure the lagrangian forces and heat sources as distributed lagrange multipliers thereby implicitly providing the kinematic constraints of no slip and the corresponding thermal boundary conditions for immersed surfaces extensive verification of the developed method for both isothermal and natural convection 2d flows is provided strategies for adapting the developed approach to realistic 3d configurations are discussed

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

parameterization of all multivariable ripple free deadbeat tracking controllers this paper presents an explicit parameterization of all ripple free deadbeat tracking controllers for multi input multi output mimo sampled data control systems the advantages over the previous results are the following first a useful necessary and sufficient condition to obtain a ripple free deadbeat tracking response for mimo sampled data control systems is presented second not only all ripple free mimo deadbeat tracking controllers but also all achievable deadbeat sequences and all control input ones are characterized by completely free parameters in an explicit form third the design method is simple and straightforward the computation consists of simple polynomial matrix equations without involving troublesome calculation such as the reduction to smith mcmillan form fourth the class of the reference inputs for which ripple free deadbeat tracking responses are achieved is generalized finally a numerical example demonstrates that the proposed parameterization makes it easy to clarify the r

an ale based iterative cbs algorithm for non isothermal non newtonian flow with adaptive coupled finite element and meshfree method this paper presents a generalized scheme of the fractional step algorithm using characteristic based split cbs in ale framework for the numerical simulation of incompressible non isothermal non newtonian fluid flows and applies it combined with the adaptive coupled finite element and meshfree method for spatial discretizations to the polymer injection molding process based on the idea to discretize the material time derivative instead of the spatial time derivative the characteristic galerkin method is derived in a more general way and is used to discretize the non newtonian momentum and the energy conservation equations an iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain numerical experiments with the power law fluid model demonstrate and validate the performance and the capability of the proposed scheme

a consistent direct discretization scheme on cartesian grids for convective and conjugate heat transfer a new discretization scheme on cartesian grids namely a consistent direct discretization scheme is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object the navier stokes and the pressure poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face velocity and the pressure gradient from verifications in fundamental flow problems the present method is found to significantly improve the accuracy of the velocity and the wall shear stress it is also confirmed that the numerical results are less sensitive to the courant number owing to the consistency between the velocity and pressure fields the concept of the consistent direct discretization scheme is also explored for the thermal field the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface it takes different forms depending on the thermal boundary conditions dirichlet isothermal and neumann adiabatic iso heat flux boundary conditions for convective heat transfer and a fluid solid thermal interaction for conjugate heat transfer the validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions and it is confirmed that the present schemes also show high accuracy for the thermal field a significant improvement for the conjugate heat transfer problems is that the second order spatial accuracy and numerical stability are maintained even under severe conditions of near practical physical properties for the fluid and solid phases

uncoupled temporally second order accurate implicit solver of incompressible navier stokes equations an efficient method with temporal second order accuracy for solving the incompressible navier stokes equations in generalized coordinate systems is developed efficiency is obtained by extending an existing fractional step semi implicit solver into an implicit one with implicit approximation of the convection terms a novel three level linearization scheme is proposed to decouple the momentum equations from one another in addition to the fractional step approach that decouples the continuity equation from the momentum equations consequently all of the governing equations are uncoupled without degrading temporal accuracy or stability and without the need for iterations to solve the nonlinear system of equations at each time level the proposed decoupling technique can be used for other systems of nonlinear and time dependent partial differential equations moreover only minor modifications are required to apply the method to existing two level schemes several test cases confirm that the proposed decoupled scheme has temporal second order accuracy and allows the use of large time steps

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

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

evidence of chaotic behavior in noise from industrial process usually in dealing with the dynamical behavior of noise from an industrial process nfip random or even white noise is assumed to describe it however since white noise is just an ideal model in mathematics and can hardly exist in an industrial process this assumption seriously hinders the successful application of classical control theory in practice for this reason nonlinear time series analysis is used to analyze nfip in an attempt to capture the signature of chaos the chaotic behavior is apparent in nfip due to the presence of finite and non integer correlation dimension and the minimum number of macroscopic variables required to model nfip dynamics is obtained these results indicate that nfip is deterministic and high dimensional chaos but not random or white noise and in the future might lead the way towards the direct solution of prediction and modeling of nfip and a series of changes to the traditional algorithms in the control field may appear

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

unified lagrangian formulation for elastic solids and incompressible fluids application to fluid structure interaction problems via the pfem abstract we present a general lagrangian formulation for treating elastic solids and quasi fully incompressible fluids in a unified form the formulation allows to treat solid and fluid subdomains in a unified manner in fluid structure interaction fsi situations in our work the fsi problem is solved via the particle finite element method pfem the pfem is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows accounting for splashing of waves large motions of the bodies and frictional contact conditions applications of the unified lagrangian formulation to a number of fsi problems are given

3d regularized μ i rheology for granular flows simulation abstract this paper proposes two regularized models of the i rheology and shows their application to the numerical simulation of 3d dense granular flows the proposed regularizations are inspired by the papanastasiou and bercovier engleman methods typically used to approximate the bingham law the key idea is to keep limited the value of the apparent viscosity for low shear rates without introducing a fixed cutoff the proposed techniques are introduced into the particle finite element method pfem framework to deal with the large deformations expected in free surface granular flows after showing the numerical drawbacks associated to the standard i rheology the two regularization strategies are derived and discussed the regularized i rheology is then applied to the simulation of the collapse of 2d and 3d granular columns the numerical results show that the regularization techniques improve substantially the conditioning of the linear system without affecting the solution accuracy a good agreement with the experimental tests and other numerical methods is obtained in all the analyzed problems

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

filtering with a small non linear term in the signal abstract the filtering problem when the signal and observation processes are linear and have gaussian noise has an explicit finite dimensional solution the kalman filter in a recent paper picard considered the situation where there is in addition a small non linear term in the signal process using a girsanov transformation on the signal and using homogeneous chaos expansions he estimated the error when related linearizations are considered in this paper the non linearity is approximated by considering stochastic flows for the signal and a girsanov transformation for the observation the result can be expressed in terms of gaussian densities

a lagrangian finite element approach for the analysis of fluid structure interaction problems a lagrangian finite element method for the analysis of incompressible newtonian fluid flows based on a continuous re triangulation of the domain in the spirit of the so called particle finite element method is here revisited and applied to the analysis of the fluid phase in fluid structure interaction problems a new approach for the tracking of the interfaces between fluids and structures is proposed special attention is devoted to the mass conservation problem it is shown that despite its lagrangian nature the proposed combined finite element particle method is well suited for large deformation fluid structure interaction problems with evolving free surfaces and breaking waves the method is validated against the available analytical and numerical benchmarks copyright 2010 john wiley sons ltd