a higher order time integration algorithm for the simulation of nonlinear fluid structure interaction abstract in this paper higher order time integration schemes are applied to nonlinear fluid structure interaction fsi simulations for a given accuracy we investigate the efficiency of higher order time integration schemes compared to lower order methods in the partitioned fsi simulations on a one dimensional piston problem a mixed implicit explicit imex time integration scheme is employed the implicit scheme is used to integrate the fluid and structural dynamics whereas an explicit runge kutta scheme integrates the coupling terms the resulting imex scheme retains the order of the implicit and explicit schemes in the imex scheme considered the implicit scheme consists of an explicit first stage singly diagonally implicit runge kutta esdirk scheme which is a multi stage l stable scheme

subword conditions and subword histories this paper introduces the notion of a subword condition and investigates languages defined by them the special case where the language reduces to one word concerns the inference of a sequence from its subsequences we obtain various characterization and decidability results for languages defined by subword conditions the results contribute to the theory of parikh matrices and arithmetizing the study of words an important notion from early automata theory that of a quasi uniform event plays a central role in our characterization

independence of certain quantities indicating subword occurrences when words are characterized in terms of numerical quantities awkward considerations due to the noncommutativity of words are avoided the numerical quantity investigated in this paper is w u the number of occurrences of a word u as a scattered subword of a word w parikh matrices recently introduced have these quantities as their entries according to the main result in this paper no entry in a parikh matrix no matter how high the dimension can be computed in terms of the other entries consequences concerning various inference problems between numbers w u themselves as well as of the word w from these numbers are obtained

connections between subwords and certain matrix mappings parikh matrices recently introduced have turned out to be a powerful tool in the arithmetizing of the theory of words in particular many inequalities between scattered subword occurrences have been obtained as consequences of the properties of the matrices this paper continues the investigation of parikh matrices and subword occurrences in particular we study certain inequalities as well as information about subword occurrences sufficient to determine the whole word uniquely some algebraic considerations facts about forbidden subwords as well as some open problems are also included

subword histories and associated matrices the basic numerical quantity investigated in this paper is w u the number of occurrences of a word u as a scattered subword of a word w arithmetical combinations of such quantities yield a so called subword history we investigate the information content of subword histories reducing subword histories to linear ones as well as the recently introduced parikh matrices will be important tools simple polynomial formulas for computing the value of a subword history for arbitrary powers of a word are obtained

on fuzzy pseudo normed vector spaces abstract we provide a method for introducing fuzzy pseudo metric topologies on sets and fuzzy pseudo normed topologies on vector spaces over r or c which will be fuzzy linear topologies we define fuzzy pseudo metrics for pairs of crisp points and fuzzy pseudo norms for crisp points as fuzzy real numbers 0 as defined by hutton we define the associated fuzzy open balls with crisp points for their centres and fuzzy real numbers 0 for their radii these form a basis for the associated fuzzy pseudo metric topology the axioms governing fuzzy pseudo metric and fuzzy pseudo norm are straightforward extensions for the corresponding axioms in the crisp case the formulation conforms with zadeh s extension principle we show that katsaras concept of fuzzy seminorm fuzzy sets and systems 12 1984 143 154 is equivalent to ours in the sense that both concepts will result in same fuzzy linear topologies

numerical model of unsteady subsonic aeroelastic behavior a method for predicting unsteady subsonic aeroelastic responses was developed the technique accounts for aerodynamic nonlinearities associated with angles of attack vortex dominated flow static deformations and unsteady behavior the fluid and the wing together are treated as a single dynamical system and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain the method employs an iterative scheme based on a predictor corrector technique the aerodynamic loads are computed by the general unsteady vortex lattice method and are determined simultaneously with the motion of the wing because the unsteady vortex lattice method predicts the wake as part of the solution the history of the motion is taken into account hysteresis is predicted two models are used to demonstrate the technique a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting the method can be readily extended to account for structural nonlinearities and or substitute aerodynamic load models the time domain solution coupled with the unsteady vortex lattice method provides the capability of graphically depicting wing and wake motion

convergence analysis of a projection semi implicit coupling scheme for fluid structure interaction problems in this paper we provide a convergence analysis of a projection semi implicit scheme for the simulation of fluid structure systems involving an incompressible viscous fluid the error analysis is performed on a fully discretized linear coupled problem a finite element approximation and a semi implicit time stepping strategy are respectively used for space and time discretization the fluid is described by the stokes equations the structure by the classical linear elastodynamics equations linearized elasticity plate or shell models and all changes of geometry are neglected we derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least sqrt delta t finally some numerical experiments that confirm the theoretical analysis are presented

a partitioned strongly coupled fluid structure interaction method to model heart valve dynamics a new method for the calculation of fluid structure interaction fsi of highly flexible bodies is presented this innovative algorithm demonstrates the strong coupling of a commercial computational fluid dynamics code with an in house coded structural solver the strong response of the pressure distribution to the displacement can be approximated by a reduced order model for the fluid solver the jacobian of this reduced order model is then used in the structural solver to obtain a stable and full implicit iteration scheme the method is demonstrated on a 2d model of a flexible aortic valve during the cardiac cycle furthermore the model is able to calculate shear stresses on the leaflet

control fluid interaction in air conditioned aircraft cabins to study the temperature control in aircraft cabins a computational fluid dynamics cfd program is coupled to a controller model in a time accurate way in the present paper two common coupling algorithms are considered stability and accuracy of these algorithms have been analysed a priori by replacing the cfd program by an analytical model based on heat conservation numerical experiments corroborate that this simple analysis is suitable to predict the time step sizes that are required for stability and accuracy for both coupling schemes the time step restrictions imposed by accuracy requirements are shown to be dominant

fuzzy metric neighbourhood spaces abstract hohle founded the first coherent topological study of menger s probabilistic metric spaces by endowing them with fuzzy t uniformities we continue hohle s work in the special case when the triangular norm t used is min that is when the resulting probabilistic metric uniformities are lowen fuzzy uniformities in this case we call the induced fuzzy topological spaces fuzzy pseudo metric neighbourhood spaces we introduce axioms of n regularity and n normality which are satisfied in fuzzy pseudo metric neighbourhood spaces we introduced a lowen fuzzy uniform topology on the fuzzy real line ri called the n euclidean topology by means of a fuzzy probabilistic metric on r i called the axiom of n complete regularity which characterizes the lowen fuzzy uniform topologies

a two step two field hybrid method for the static and dynamic analysis of substructure problems with conforming and non conforming interfaces abstract the need for assembling independent finite element substructure solutions arises in several engineering and scientific problems including the design and analysis of complex structural systems component mode synthesis global local analysis adaptive refinement and parallel processing in this paper we discuss the solution of such problems by a two field hybrid method where the substructures are jointed with low order polynomial or piece wise polynomial lagrange multipliers and present a rayleigh ritz based smoothing procedure for improving the accuracy of the computed coupled solution in the presence of various substructure heterogeneities we consider both conforming and nonconforming substructure meshes and demonstrate the benefits of the proposed two step solution method with several examples from structural mechanics

a computational strategy for thermo poroelastic structures with a time space interface coupling this paper deals with a computational strategy suitable for the simulation of multiphysics problems based on the large time increment latin method the simulation of such problems must encounter the possible different time and space scales which usually arise with the different physics herein we focus on using different time and space discretizations for each physics by introducing an interface with its own discretization the feasibility of both a time and space couplings is exemplified on a nonlinear 3 physics strongly coupled problem the thermal fluid structure interaction in a thermo poroelastic structure

computation of strongly coupled multifield interaction in particle fluid systems the present work develops a flexible and robust solution strategy to resolve coupled systems comprised of large numbers of flowing particles embedded within a fluid a model problem consisting of particles which may undergo inelastic collisions in the presence of near field forces is considered the particles are surrounded by a continuous interstitial fluid which is assumed to obey the compressible navier stokes equations thermal effects are also considered such particle fluid systems are strongly coupled due to the mechanical forces and heat transfer induced by the fluid onto the particles and vice versa because the coupling of the various particle and fluid fields can dramatically change over the course of a flow process a primary focus of this work is the development of a recursive staggering solution scheme whereby the time steps are adaptively adjusted to control the error associated with the incomplete resolution of the coupled interaction between the various solid particulate and continuum fluid fields a central feature of the approach is the ability to account for the presence of particles within the fluid in a straightforward manner that can be easily incorporated within any standard computational fluid mechanics code based on finite difference finite element or finite volume type discretization a three dimensional example is provided to illustrate the overall approach 2007 elsevier b v all rights reserved

treatment of acoustic fluid structure interaction by localized lagrange multipliers formulation a new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure the coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure and using node collocated lagrange multipliers to connect the frame to each subsystem the time domain response analysis is performed by a partitioned analysis procedure the main advantages of this localized lagrange multiplier llm primal dual coupling method are complete localization of the structure and fluid subsystems elimination of the conventional predictor in the partitioned time integration method and the ability to accommodate non matching meshes the standard newmark time integrator is used on both the fluid and structure models it is shown that if the integrator is a stable and second order accurate for a monolithic treatment it retains those properties for both mortar and llm partitioned solution procedures infinite and finite piston problems are used to explain and verify the methodology a sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation

words and special factors in this paper we consider sets of factors of a given finite word over a finite alphabet which permit us to reconstruct the entire word this analysis is based on the notion of special factor a factor u of a finite word w is called right resp left special if there exist two distinct letters x and y such that ux uy resp xu yu are factors of w a factor is bispecial if it is right and left special a proper box of w is any factor of w of the kind asb with a b letters and s a bispecial factor of w the initial resp terminal box of w is the shortest prefix resp suffix of w which is an unrepeated factor a box is called maximal if it is not a proper factor of another box the main result of the paper is the following theorem maximal box theorem any finite word w is uniquely determined by the initial box the terminal box and the set of maximal boxes a consequence is that a finite word w is uniquely determined by the knowledge of its factors up to the length n max rw kw 1 where kw is the length of the terminal box and rw is the minimal natural number for which there is no right special factor of length rw some structural properties of boxes are studied another important combinatorial notion is that of superbox a superbox is any factor of w of the kind asb with a b letters and such that s is a repeated factor whereas as and sb are unrepeated factors a theorem for superboxes similar to the maximal box theorem is proved some algorithms allowing us to construct boxes and superboxes and conversely to reconstruct the word are given in this combinatorial frame we give an upper and a lower bound to the number of states of a minimal deterministic automaton recognizing the set of the factors of w these bounds are sharper than the known bounds

linear fuzzy neighborhood spaces some of the properties of linear fuzzy neighborhood spaces are studied a special class of these spaces is the family of all fuzzy linear spaces whose topology is given by probabilistic seminorms as in the classical case it is shown that a linear fuzzy neighborhood space is probabilistic normable iff it is hausdorff and it has an n bounded convex fuzzy neighborhood of zero

fixed point convergence of modular steady state heat transfer models coupling multiple scales and phenomena for melt crystal growth a block gauss seidel iteration procedure is employed to couple two independent heat transfer codes representing different scales and phenomena in a melt crystal growth system via shared domain boundaries in general such strategies are attractive because of their simplicity for solving problems that may be represented by linking via shared boundary conditions existing codes using a modular design however these approaches often meet with limited success due to convergence difficulties associated with the overall model the mathematical framework of fixed point iterations is employed to assess convergence behaviour for steady state non linear heat transfer models analytical forms describe the convergence of one dimensional problems and provide insight to the behaviour of more complicated two dimensional models certain implementations that are physically reasonable result in algorithms that will never converge demonstrating that notions based on physical intuition may not be useful for predicting algorithm performance a mixing of flux and temperature information along the shared model boundary leads to successful iterative strategies under many conditions

extending parikh matrices we introduce the notion of parikh matrix induced by a word a natural extension to the notion of parikh matrix and prove a set of properties for this kind of matrices we also study the relation between these two notions we show that combining properties from both we obtain a more powerful tool for proving algebraic properties of words

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

criteria for the matrix equivalence of words this paper investigates the criteria for deciding whether two words are matrix equivalent certain upper diagonal matrices generally referred to as the parikh matrices have been widely investigated because of their usefulness in computing the numbers of subword occurrences and thereby characterizing words by numbers however apart from the binary alphabet not much is known about the properties of the matrix equivalent words that is words possessing the same matrix the paper investigates both the general criteria as well as the criteria valid in natural special cases an exhaustive solution is obtained for ternary alphabets

stability analysis of finite difference schemes revisited a study of decoupled solution strategies for coupled multifield problems summary many problems in engineering physics or other disciplines require an integrated treatment of coupled heterogeneous fields the mathematical models of such problems commonly consist of a coupled pde system considerable progress has been made in the development of schemes to solve such systems resulting in a wide spectrum of monolithic and decoupled numerical solution approaches in particular the flexibility offered by the decoupled strategies in choosing appropriate solution methods and adjustable time step sizes has motivated the elaboration of these schemes however the way of decoupling can influence the stability of the resulting solution algorithm and hence urges a comprehensive stability analysis the purpose of this contribution is to elucidate the salient points in the stability analysis of the numerical solution schemes to this end we introduce a general framework for the stability analysis of solution strategies and provide an easy to use procedure to find the necessary stability condition the procedure is tested against decoupled solution strategies for volume and surface coupled problems namely thermoelastodynamics porous media dynamics and fluid and structure structure interaction in this context the influence of explicit and implicit predictors and the sequence of the time integration on the stability condition is carefully examined copyright 2013 john wiley sons ltd

fixed grid fluid structure interaction in two dimensions based on a partitioned lattice boltzmann and p fem approach over the last decade the lattice boltzmann method which was derived from the kinetic gas theory has matured as an efficient approach for solving navier stokes equations the p fem approach has proved to be highly efficient for a variety of problems in the field of structural mechanics our goal is to investigate the validity and efficiency of coupling the two approaches to simulate transient bidirectional fluid structure interaction problems with geometrically non linear structural deflections a benchmark configuration of self induced large oscillations for a flag attached to a cylinder can be accurately and efficiently reproduced within this setting we describe in detail the force evaluation techniques displacement transfers and the algorithm used to couple these completely different solvers as well as the results and compare them with a benchmark reference solution computed by a monolithic finite element approach copyright 2009 john wiley sons ltd

a fuzzy r 1 separation axiom abstract we introduce a new r 1 separation axiom for fuzzy topological spaces we identify from the literature which lower fuzzy separation axioms are compatible with our r 1 axiom we provide alternative descriptions for this r 1 axiom in the special setting of fuzzy neighborhood spaces this special case has standard higher fuzzy separation axioms in it we establish aspects of compatibility of our r 1 axiom with those higher separation axioms as well as with fuzzy compactness

generalized possibility measures we define a generalized possibility measure gpm on a set x to be a function from the power set of x to the unit interval i 0 1 whereby the measure of a finite union of subsets of x equals the maximum of their measures we characterize gpms as the infima of downward directed families of possibility measures this helps to confer an intuitive meaning on gpms we discuss all directed families of possibility measures or equivalently of possibility distributions which generate a given gpm and we identify the largest such family we introduce extensions of gpms to real functions on ix obtained through a continuous triangular norm we provide characterizations and alternative descriptions for those extensions

errata complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines abstract we construct a fuzzy multiplication for the case l a chain in the l fuzzy real line r l which is jointly fuzzy continuous and which is the unique piecewise consistent extension of ordinary multiplication to r l distributing over the fuzzy addition constructed by the author in 47 we also specify the fuzzy integers and give an extensive analysis of fuzzy contractions and expansions these results the constructions of this paper and the results of 47 are used to prove r l and the stratified r c l are nontopologically isomorphic complete fuzzy topological hyperfields if l is a chain with l 3 we can now completely answer for l a chain the following question of 27 in the affirmative can a set of fuzzy numbers its fuzzy topology and its fuzzy addition and multiplication be defined such that these operations are jointly fuzzy continuous extensions of the usual addition and multiplication of r and can we specify the fuzzy integers these results in combination with recent papers of several authors would seem to answer in the affirmative the following philosophical question cf 34 does fuzzy topology have deep specific canonical examples

continuity of fuzzy multiplication in the n euclidean space abstract the n euclidean space m i is a fuzzy normed vector space whose underlying set is the smallest real vector space including all nonnegative fuzzy real numbers the fuzzy multiplication on the fuzzy real line easily extends to a multiplication on m i we show that under that multiplication m i is a fuzzy normed algebra in consequence fuzzy multiplication is shown to be continuous in the n euclidean topology on m i

extending substructure based iterative solvers to multiple load and repeated analyses direct solvers currently dominate commercial finite element structural software but do not scale well in the fine granularity regime targeted by emerging parallel processors substructure based iterative solvers often called also domain decomposition algorithms lend themselves better to parallel processing but must overcome several obstacles before earning their place in general purpose structural analysis programs one such obstacle is the solution of systems with many or repeated right hand sides such systems arise for example in multiple load static analyses and in implicit linear dynamics computations direct solvers are well suited for these problems because after the system matrix has been factored the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions on the other hand iterative solvers in general are ill suited for these problems because they often must restart from scratch for every different right hand side in this paper we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides basically we formulate the overall problem as a series of minimization problems over k orthogonal and supplementary subspaces and tailor the preconditioned conjugate gradient algorithm to solve them efficiently the resulting solution method is scalable whereas direct factorization schemes and forward and backward substitution algorithms are not we illustrate the proposed methodology with the solution of static and dynamic structural problems and highlight its potential to outperform forward and backward substitutions on parallel computers as an example we show that for a linear structural dynamics problem with 11640 degrees of freedom every time step beyond time step 15 is solved in a single iteration and consumes 1 0 second on a 32 processor ipsc 860 system for the same problem and the same parallel processor a pair of forward backward substitutions at each step consumes 15 0 seconds

truncation error and energy conservation for fluid structure interactions abstract this paper describes the numerical analysis of low speed large displacements fluid structure interaction problems after reviewing the basic conservation principles and kinematic interface conditions governing the problem under study it concentrates on truncation error and kinetic energy conservation such properties are indeed crucial for checking both the stability and convergence of the numerical scheme and the physical stability of the mechanical system under study we observe that classical time integration schemes which are dissipative unconditionally stable and accurate for fluids flowing inside fixed domains may loose their long term stability properties when used on moving domains we also produce new estimates proving that high order schemes using a partially nonconservative formulation associated to the variable j u properly conserve the kinetic energy and that the same schemes used on different formulations only conserve this energy approximately with an error which depends on the smoothness of the grid deformations and on the truncation error in the equation of mass conservation numerical results finally illustrate the approach

a feti based domain decomposition technique for time dependent first order systems based on a dae approach we present a novel partitioned coupling algorithm to solve first order time dependent non linear problems e g transient heat conduction the spatial domain is partitioned into a set of totally disconnected subdomains the continuity conditions at the interface are modeled using a dual schur formulation where the lagrange multipliers represent the interface fluxes or the reaction forces that are required to maintain the continuity conditions the interface equations along with the subdomain equations lead to a system of differential algebraic equations daes for the resulting equations a numerical algorithm is developed which includes choosing appropriate constraint stabilization techniques the algorithm first solves for the interface lagrange multipliers which are subsequently used to advance the solution in the subdomains the proposed coupling algorithm enables arbitrary numeric schemes to be coupled with different time steps i e it allows subcycling in each subdomain this implies that existing software and numerical techniques can be used to solve each subdomain separately the coupling algorithm can also be applied to multiple subdomains and is suitable for parallel computers we present examples showing the feasibility of the proposed coupling algorithm copyright 2008 john wiley sons ltd

fuzzy inner product spaces in this paper we show that all results obtained recently on fuzzy inner product spaces are obvious to achieve this goal we modify the definition of the fuzzy inner product space and then we mention and prove some monotonicity and orthogonality properties of the new fuzzy inner product space finally we describe fuzzy inner products in terms of families of crisp inner products namely any fuzzy inner product corresponds to a family of crisp inner products and vice versa

stability of multi time step partitioned integrators for first order finite element systems abstract mixed time integration procedures are those in which different time steps and different integrators are used in different parts of the mesh a rigorous stability analysis is provided for the first time for this type of time integration for first order semidiscretizations such as arise in diffusion problems the stability analysis is verified by some numerical examples

compact probabilistic metrics on bounded closed intervals of distribution functions a menger space a special type of probabilistic metric spaces is said to be compact if its strong uniformity is compact we construct in a natural way menger t metrics on the set of distribution functions one for each copula t a special type of continuous t norms we show that on each bounded closed interval of distribution functions the strong uniformities of all our spaces are induced by the modified levy metric hence they are compact we establish an alternative description and a number of good properties of our menger spaces which may render them well behaved examples for workers in the field

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

fuzzy inner product spaces abstract the n euclidean space m i is a fuzzy pseudo normed algebra whose underlying set is the smallest real vector space including all nonnegative fuzzy real numbers we introduce axioms for a fuzzy inner product on a unitary m i module with values in m i we establish the fuzzy schwarz inequality for fuzzy inner products we introduce the cartesian product of fuzzy inner product spaces and investigate the relations between their underlying topologies we conclude the research by supplying two interesting examples of fuzzy inner product spaces

completeness of the standard fuzzy real line for fns abstract we consider a special class of fuzzy metric neighbourhood spaces where the fuzzy distance is induced by a fuzzy pseudo norm this class is contained in lowen s well known category fns of fuzzy neighbourhood spaces we define the fuzzy limit of a sequence a fuzzy cauchy sequence and fuzzy convergence in fuzzy metric neighbourhood spaces we prove that the set of all nonnegative fuzzy real numbers r i under the n euclidean metric the standard fuzzy real line for fns is complete but that the smallest fuzzy neighbourhood real algebra m i including r i is not complete we also characterize the fuzzy cauchy sequences in m i in terms of their corresponding real sequences of cuts

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

laser induced heating of dynamic particulate depositions in additive manufacturing abstract many applications in additive manufacturing involve the dynamic deposition of powders and the in flight heating of such material by a laser in order to characterize such systems the discrete element method dem is employed specifically this paper focuses on the initial stages of this process by developing a modular discrete element type multiphysics simulation method for the particle dynamics and heating by a laser and detailed thermal behavior the objective is to provide researchers with a framework to construct computational tools for this growing industry in order to achieve this from a simulation standpoint the overall particle mixture system is constructed by coupling submodels for each primary physical process dynamics and heating together an iterative staggering scheme is developed whereby within every time step each individual particle is solved freezing the state of the remaining multiparticle system the state of the particle is then updated and the algorithm moves to the next particle in the system and the process is repeated the overall process sweeps through the entire system repeatedly until convergence is achieved in an appropriate norm as the system evolves an error estimate dictates the time step size that is needed to induce convergence to below an appropriate error level thus the process can be considered as an implicit time stepping scheme which is combined with an internal iterative staggering process in order to control rates of convergence within a time step the algorithm adjusts the time step size if the iterative process does not converge within a desired number of iterations below an error tolerance the time step is reduced the degree of time step reduction is determined by utilizing an estimate of the spectral radius of the coupled system since the construction of model and solution process is modular one can easily replace physical submodels with other choices making it easy to numerically experiment with a variety of models qualitative and quantitative analyses are provided as well as three dimensional numerical examples this paper addresses the first of two overall macrostages of a complex manufacturing process with dem the first stage addressed in this paper concentrates on dry powder materials which are of a discrete particulate character using dem to characterize the deposition and in flight particle heating other papers of the author zohdi 2010 2013 2014 2015 81 82 2008 have addressed stage two namely phase transformations curing cooling and stress analysis using more appropriate continuum and hybrid dem continuum approaches

bounded linear transformations between probabilistic normed vector spaces we denote by r i the set of all nonnegative fuzzy real numbers that is functions n from r 0 to the unit interval i which are left continuous and nonascending and satisfy 0 1 and 0 this set r i canonically includes r in the obvious way it is ordered by the usual pointwise order of real functions

a linearized method for the frequency analysis of three dimensional fluid structure interaction problems in all flow regimes abstract we present a computational fluid dynamics cfd based linearized method for the frequency analysis of three dimensional fluid structure interaction problems this method is valid in the subsonic transonic and supersonic flow regimes and is insensitive to the frequency or damping level of the sought after coupled eigenmodes it is based on the solution by an orthogonal iteration procedure of a complex eigenvalue problem derived from the linearization of a three field fluid structure moving mesh formulation the key computational features of the proposed method include the reuse of existing unsteady flow solvers a second order approximation of the flux jacobian matrix and a parallel domain decomposition based iterative solver for the solution of large scale systems of discretized fluid structure equations while the frequency analysis method proposed here is primarily targeted at the extraction of the eigenpairs of a wet structure we validate it with the flutter analysis of the agard wing 445 6 for which experimental data is available

an enhanced fiver method for multi material flow problems with second order convergence rate abstract the finite volume fv method with exact two material riemann problems fiver is an eulerian computational method for the solution of multi material flow problems it is robust in the presence of large density jumps at the fluid fluid interfaces and the presence of large structural motions deformations and even topological changes at the fluid structure interfaces to achieve simplicity in implementation it approximates each material interface by a surrogate surface which conforms to the control volume boundaries unfortunately this approximation introduces a first order error of the geometric type in the solution process in this paper it is first shown that this error causes the original version of fiver to be inconsistent in the neighborhood of material interfaces and degrades its global order of spatial accuracy then an enhanced version of fiver is presented to rectify this issue restore consistency and achieve for smooth problems the desired global convergence rate to this effect the original definition of a surrogate material interface is retained because of its attractive simplicity however the solution at this interface of a two material riemann problem is enhanced with a simple reconstruction procedure based on interpolation and extrapolation next the extrapolation component of this procedure is equipped with a limiter in order to achieve nonlinear stability for non smooth problems in the one dimensional inviscid setting the resulting fiver method is also shown to be total variation bounded focusing on the context of a second order fv semi discretization the nonlinear stability and second order global convergence rate of this enhanced fiver method are illustrated for several model multi fluid and fluid structure interaction problems the potential of this computational method for complex multi material flow problems is also demonstrated with the simulation of the collapse of an air bubble submerged in water and the comparison of the computed results with corresponding experimental data

energy conservation under incompatibility for fluid structure interaction problems concurrent numerical methods for fluid structure interaction problems are typically based on partitioned solution procedures however such partitioned methods are inherently non conservative in the present work we investigate the conservation properties of monolithic discretisations for fluid structure interaction problems we consider a prototypical fluid structure interaction problem viz the piston problem a variational formulation allows us to establish precisely the conservation properties of the continuum problem and its discretisation by the finite element method we show that the conservation of energy by monolithic discretisations is only trivially maintained under restrictive compatibility conditions on the approximation spaces in the fluid and the structure moreover we introduce a new discretisation based on coincidence conditions which ensures energy conservation under incompatibility numerical results which illustrate the effectiveness of the new discretisation are presented

the relevance of conservation for stability and accuracy of numerical methods for fluid structure interaction numerical simulation of fluid structure interactions has typically been done using partitioned solution methods however partitioned methods are inherently non conservative and generally numerically unstable the deficiencies of partitioned methods have motivated the investigation of monolithic solution methods conservation is possible for monolithic methods the conditions have recently been presented e h van brummelen s j hulshoff r de borst energy conservation under incompatibility for fluid structure interaction problems comput methods appl mech engrg 192 2003 2727 2748 in the present paper we investigate the relevance of maintaining conservation for a model fluid structure interaction problem viz the piston problem to distinguish the effect of the error induced by the interface coupling from the fluid and structure discretization errors we use fluid subcycling and an exact time integration method for the structure a comparison between conservative and non conservative monolithic methods as well as partitioned methods is made we show that maintaining conservation has considerable impact on the stability and accuracy of the numerical method these results also indicate that only for a conservative monolithic scheme the improvement in accuracy over partitioned methods warrants the computational cost associated with a monolithic solution moreover we illustrate the implications that particular combinations of fluid and structure discretizations can have on the conservation properties of the fluid structure interaction problem

error amplification analysis of subiteration preconditioned gmres for fluid structure interaction the customary subiteration method for solving fluid structure interaction problems exhibits several deficiencies viz only conditional stability potential convergence difficulties due to non normality induced divergence and the inability to reuse information from previously solved similar problems to overcome these deficiencies a novel solution method is considered in which subiteration is used as a preconditioner to gmres this paper treats the linear algebra aspects of the subiteration method and of the subiteration preconditioned gmres method on the basis of properties of the error amplification matrix for the aggregated fluid structure system an analysis of the error amplification matrix of subiteration establishes that subiteration condenses errors into a low dimensional subspace which can be associated with the interface degrees of freedom therefore the gmres acceleration of subiteration can be confined to the interface degrees of freedom the error amplification analysis provides a clear explanation of the relation between the local gmres acceleration i e on the interface degrees of freedom and the global error amplification properties i e for the aggregated system moreover we show that the subiteration iterates span a krylov space corresponding to a preconditioned aggregated system we then address the implications of the non normality of the subiteration preconditioner for the convergence of gmres the subiteration preconditioned gmres method enables the optional reuse of krylov vectors in subsequent invocations of gmres which can substantially enhance the efficiency of the method to assess the potential and the limitations of the reuse option we analyse the error amplification matrix of the gmres method with reuse furthermore we establish that the gmres acceleration on the interface degrees of freedom generates an approximation to the schur complement for the aggregated system the gmres acceleration and the reuse of krylov vectors are then assessed in terms of the approximation properties for the schur complement and in terms of the properties of the corresponding error amplification matrices numerical experiments on a model fluid structure interaction problem illustrate the developed theory in particular we analyse the convergence of the respective methods in terms of spectral radii matrix norms and sharp convergence upper bounds

fuzzy semi inner product of fuzzy points abstract in an earlier paper using the set of non negative fuzzy real numbers r i we constructed a fuzzy normed algebra c i in this paper the concept of fuzzy semi inner product of fuzzy points is introduced on a c i module x also some properties of fuzzy linear functionals on the fuzzy semi inner product space of fuzzy points are studied

subcycling first and second order generalizations of the trapezoidal rule subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first and second order systems of equations arising in finite element analysis as well as for integration using explicit implicit partitions of a model the author has recently extended this work to implicit implicit multi timestep partitions of both first and second order systems in this paper improved algorithms for multi timestep implicit integration are introduced that overcome some weaknesses of those proposed previously in particular in the second order case improved stability is obtained some of the energy conservation properties of the newmark family of algorithms are shown to be preserved in the new multi timestep extensions of the newmark method in the first order case the generalized trapezoidal rule is extended to multiple timesteps in a simple way that permits an implicit implicit partition explicit special cases of the present algorithms exist these are compared to algorithms proposed previously c 1998 john wiley sons ltd

multi level quasi newton coupling algorithms for the partitioned simulation of fluid structure interaction abstract in partitioned fluid structure interaction simulations the flow equations and the structural equations are solved separately coupling iterations between the flow calculation and the structural calculation can be used to enforce the equilibrium conditions on the fluid structure interface low wave number fourier modes of the difference between the correct interface displacement and the interface displacement during gauss seidel coupling iterations are typically unstable for strongly coupled problems with a dirichlet neumann decomposition using interface quasi newton iterations with an approximation for the inverse of the jacobian from a least squares model iqn ils these unstable modes are automatically detected and stabilized as the unstable modes have a low wave number and can hence be resolved on coarser grids the new multi level iqn ils ml iqn ils technique first constructs the approximation for the inverse of the jacobian on coarser grid levels and then uses it and improves it further on the original finest grid level this multi level approach reduces the number of coupling iterations on the finest grid level and can also be applied to the interface block quasi newton ibqn ls technique one dimensional and three dimensional numerical results demonstrate that this new class of multi level quasi newton coupling techniques can reduce the duration of a partitioned fluid structure interaction simulation

a monolithical fluid structure interaction algorithm applied to the piston problem abstract an investigation of time marching computational fluid structure interaction algorithms is presented the analysis is applied to the piston problem attention is focussed on the time integration properties of the coupling algorithms the staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor corrector fashion this algorithm suffers from a time lag between the integration of the fluid and structure the influence of the time lag is investigated by the comparison of different predictions for the structure a novel monolithical algorithm is then introduced in order to annihilate the time lag this algorithm integrates fluid structure and interaction as a single system by an implicit algorithm linear acoustic as well as nonlinear euler equations for gas dynamics are investigated the numerical results of the staggered scheme reveal a non physical deviation of the mean position of the piston at higher cfl numbers the deviation of the mean position is not present in the calculation with the monolithical scheme stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability this domain can be enlarged by an improvement of the structural prediction analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term the analyses lead to the formulation of the interaction consistency law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions

two level algorithms for partitioned fluid structure interaction computations abstract in this paper we use the multigrid algorithm commonly used to improve the efficiency of the flow solver to improve the efficiency of partitioned fluid structure interaction iterations coupling not only the structure with the fine flow mesh but also with the coarse flow mesh often present due to the multigrid scheme leads to a significant efficiency improvement as solution of the flow equations typically takes much longer than the structure solve and as multigrid is not standard in structure solvers we do not coarsen the structure or the interface as a result the two level method can be easily implemented into existing solvers two types of two level algorithms were implemented 1 coarse grid correction of the partitioning error and 2 coarse grid prediction or full multigrid to generate a better initial guess the resulting schemes are combined with a fourth order runge kutta implicit time integration scheme for the linear one dimensional piston problem with compressible flow the superior stability accuracy and efficiency of the two level algorithms is shown the parameters of the piston problem were chosen such that both a weak and a strong interaction case were obtained even the strong interaction case with a flexible structure could be solved with our new two level partitioned scheme with just one iteration on the fine grid this is a major accomplishment as most weakly coupled methods fail in this case of the two algorithms the coarse grid prediction or full multigrid method was found to perform best the resulting efficiency gain for our one dimensional problem is around a factor of ten for the coarse to intermediate time steps at which the high order time integration methods should be run for two and three dimensional problems the efficiency gain is expected to be even larger

on the nonnormality of subiteration for a fluid structure interaction problem subiteration forms the basic iterative method for solving the aggregated equations in fluid structure interaction problems in which the fluid and structure equations are solved alternatingly subject to complementary partitions of the interface conditions in the present work we establish for a prototypical model problem that the subiteration method can be characterized by recursion of a nonnormal operator this implies that the method typically converges nonmonotonously despite formal stability divergence can occur before asymptotic convergence sets in it is shown that the transient divergence can amplify the initial error by many orders of magnitude thus inducing a severe degradation in the robustness and efficiency of the subiteration method auxiliary results concern the dependence of the stability and convergence of the subiteration method on the physical parameters in the problem and on the computational time step

the urysohn lemma for fuzzy neighbourhood spaces abstract the framework fns of lowen s fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology it encompasses its own metrics uniformities and proximities among other interesting constructions this is a fresh and fast growing field of research it promises to develop quickly to a calculus which combines depth with applicability within this framework we establish the urysohn lemma for the mashhour morsi axiom of n normality the formulation employs the mashhour morsi n euclidean space as the suitable fuzzy analogue of the real line the proof makes use of the artico moresco fuzzy proximities the lowen fuzzy uniformities and the mashhour morsi axiom of n complete regularity

computation of unsteady viscous flows around moving bodies using the k e turbulence model on unstructured dynamic grids abstract we consider the numerical solution on unstructured dynamic meshes of the averaged navier stokes equations equipped with the k e turbulence model and a wall function we discuss discretization issues pertaining to conservation laws moving grids and numerical dissipation we also present a robust spring analogy method for constructing dynamic meshes we validate our implementation of this two equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder we also apply our solution methodology to the two dimensional aerodynamic stability analysis of the tacoma narrows bridge and report numerical results that are in good agreement with observed data

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

a partitioned fully explicit lagrangian finite element method for highly nonlinear fluid structure interaction problems summary in this work a fully explicit partitioned method for the simulation of fluid structure interaction fsi problems is presented the fluid domain is modelled with an explicit particle finite element method pfem based on the hypothesis of weak compressibility the lagrangian description of the fluid is particularly effective in the simulation of fsi problems with free surface flows and large structural displacements since the fluid boundaries are automatically defined by the position of the mesh nodes a distinctive feature of the proposed fsi strategy is that the solid domain is modelled using the explicit integration finite element method fem in a off the shelf commercial software abaqus explicit this allows to perform simulations with a complete and advanced description on the structural domain including advanced structural material models and contact the structure to fluid coupling algorithm is based on a technique derived from the domain decomposition methods namely the gravouil and combescure gc algorithm the method allows for arbitrarily large interface displacements using different time incrementation and non conforming meshes in the different domains which is an essential feature for the efficiency of an explicit solver involving different materials the resulting fully explicit and fully lagrangian finite element approach is particularly appealing for the possibility of its efficient application in a large variety of highly nonlinear engineering problems this article is protected by copyright all rights reserved

modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy in the present paper we propose another space discretization of the kinematic constraint for a single grid multi velocity formulation leading to a better approximation of the interface physics the paper is organized as follows in the next section we will briefly review the problem to solve and the single mesh multi velocity discretization strategy in section 3 we will then introduce our new cell based discretization of the normal velocity continuity constraint on the interface develop the proper velocity enrichment and analyse its stability a generic time discretization is next introduced in section 4 and adapted to the specific space discretization proposed herein the proposed methodology is finally validated on a few numerical examples

towards stable coupling methods for high order discretization of fluid structure interaction algorithms and observations weak coupling of an explicit spectral hp finite element ale fluid solver with a chebyshev collocation structural solver for fluid structure interaction problems is addressed when attempting to couple high order spatial discretizations of both fluid and structural phenomena we are required to consider first principles in order to answer two important questions 1 what information e g forces velocities displacements does one transfer and when and 2 how does one transfer information our goal is to address these questions by considering a non conventional transfer of velocities of the wet surface from the structure to the fluid and the usual transfer of pressures on the wet surface from the fluid to the structure a subsonic three dimensional compressible flow over an elastic non linear plate model is considered as a representative example problem and we explore the various function spaces in which data such as pressures velocities and displacements lie we provide arguments as to what projection algorithms to use in combination with a time staggering scheme to achieve stable and accurate results and at the same time to retain a temporal second order scheme we demonstrate the proposed algorithms by numerical examples considering long time integration

comparative study of coupling coefficients in dirichlet robin procedure for fluid structure aerothermal simulations this paper tests the performance of coupling coefficients of a dirichlet robin transmission procedure in the context of steady conjugate heat transfer cht particular emphasis is put on the optimal coefficients highlighted recently in a theoretical study based on a normal mode stability analysis this work can be seen as the logical continuation of that study in order to assess the relevance of the coefficients provided by the model problem in a realistic aerothermal computation first the numerical and physical cht modeling methodologies are presented then the optimal procedure applied to a dirichlet robin algorithm one coefficient method is briefly described in order to gauge the ability of this model to predict the stability and convergence properties of a realistic case it is compared on a heated cylinder in a flowfield test case a series of five coupling coefficients and three fourier numbers are considered these parameters are introduced into the model problem as data to compute the amplification factor and the stability limits the stability and convergence properties predicted by the model problem are then compared to those obtained in the cht computation this comparison shows an excellent overall agreement moreover for all the fourier numbers considered the numerical solution is stable and oscillation free when the optimal coefficient of the model problem is used this would suggest that the one dimensional normal mode analysis can provide relevant coefficients directly applicable to real cht problems

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism