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Time Integration (time + integration)
Terms modified by Time Integration Selected AbstractsNovel coupling Rosenbrock-based algorithms for real-time dynamic substructure testingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2008O. S. Bursi Abstract Real-time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile method for analysing the general case of linear and non-linear semi-discretized equations of motion. In this paper we propose for substructure testing, L-stable real-time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real-time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero-stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge,Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real-time substructure tests are used to demonstrate the favourable properties of the proposed algorithms. Copyright © 2007 John Wiley & Sons, Ltd. [source] A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001Victoria Dolean Abstract We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Interactive animation of cloth-like objects in virtual realityCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 1 2001Mark Meyer Abstract Modeling and animation of cloth have experienced important developments in recent years. As a consequence, complex textile models can be used to realistically drape objects or human characters in a fairly efficient way. However, real-time realistic simulation remains a major challenge, even if applications are numerous, from rapid prototyping to e-commerce. In this paper, we present a stable, real-time algorithm for animating cloth-like materials. Using a hybrid explicit/implicit algorithm, we perform fast and stable time integration of a physically based model with rapid collision detection and response, as well as wind or liquid drag effects to enhance realism. We demonstrate our approach through a series of examples in virtual reality environments, proving that real-time animation of cloth, even on low-end computers, is now achievable. Copyright © 2001 John Wiley & Sons, Ltd. [source] Novel coupling Rosenbrock-based algorithms for real-time dynamic substructure testingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2008O. S. Bursi Abstract Real-time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile method for analysing the general case of linear and non-linear semi-discretized equations of motion. In this paper we propose for substructure testing, L-stable real-time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real-time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero-stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge,Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real-time substructure tests are used to demonstrate the favourable properties of the proposed algorithms. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time-domain approach to linearized rotational response of a three-dimensional viscoelastic earth model induced by glacial-isostatic adjustment: I. Inertia-tensor perturbationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2005k Martinec SUMMARY For a spherically symmetric viscoelastic earth model, the movement of the rotation vector due to surface and internal mass redistribution during the Pleistocene glaciation cycle has conventionally been computed in the Laplace-transform domain. The method involves multiplication of the Laplace transforms of the second-degree surface-load and tidal-load Love numbers with the time evolution of the surface load followed by inverse Laplace transformation into the time domain. The recently developed spectral finite-element method solves the field equations governing glacial-isostatic adjustment (GIA) directly in the time domain and, thus, eliminates the need of applying the Laplace-domain method. The new method offers the possibility to model the GIA-induced rotational response of the Earth by time integration of the linearized Liouville equation. The theory presented here derives the temporal perturbation of the inertia tensor, required to be specified in the Liouville equation, from time variations of the second-degree gravitational-potential coefficients by the MacCullagh's formulae. This extends the conventional approach based on the second-degree load Love numbers to general 3-D viscoelastic earth models. The verification of the theory of the GIA-induced rotational response of the Earth is performed by using two alternative approaches of computing the perturbation of the inertia tensor: a direct numerical integration and the Laplace-domain method. The time-domain solution of both the GIA and the induced rotational response of the Earth is readily combined with a time-domain solution of the sea level equation with a time-varying shoreline geometry. In a follow-up paper, we derive the theory for the case when GIA-induced perturbations in the centrifugal force affect not only the distribution of sea water, but also deformations and gravitational-potential perturbations of the Earth. [source] Finite element analyses of layered visco-elastic system under vertical circular loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2008Q. Xu Abstract Analyses for the response of a linear visco-elastic system subjected to axi-symmetric vertical circular loading are presented. Hankel transforms with respect to the radial spatial coordinate are used to reduce the three-dimensional problem to that involving only a single spatial dimension, which is then discretized using the finite element method. Three techniques are employed to handle the time factor in the visco-elastic material: (i) direct time integration; (ii) Fourier transforms; and (iii) Laplace transforms. These methods are compared and evaluated through their numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] A meshless Total Lagrangian explicit dynamics algorithm for surgical simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2010Ashley Horton Abstract A method is presented for computing deformation of very soft tissue. The method is motivated by the need for simple, automatic model creation for real-time simulation. The method is meshless in the sense that deformation is calculated at nodes that are not part of an element mesh. Node placement is almost arbitrary. Fully geometrically nonlinear Total Lagrangian formulation is used. Geometric integration is performed over a regular background grid that does not conform to the simulation geometry. Explicit time integration is used via the central difference method. As an example the simple but fully nonlinear Neo-Hookean material model is employed. The results are compared with a finite element simulation to verify the usefulness of the method. Copyright © 2010 John Wiley & Sons, Ltd. [source] A unified starting procedure for the Houbolt methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Aram Soroushian Abstract The method proposed by J.C. Houbolt in 1950 is one of the pioneering methods of time integration. Nevertheless, especially due to its multi-step fashion and not having a well-defined starting procedure, the method has not met considerable acceptance. The conversion of the Houbolt method to a one-step method is reported in the literature. However, the resulting method still lacks an appropriate starting procedure for all practical cases. In this paper, a parameter-less unified starting procedure is proposed for time integration with the Houbolt method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Harmonic balance method for FEM analysis of fluid flow in a vibrating pipeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2006M. Ragulskis Abstract A numerical procedure for the analysis of non-Newtonian fluid flow in a longitudinally vibrating tube is developed. The formulation of the problem is presented in differential equation form and finite element model is developed leading to the first-order matrix differential equation. A special modification of the harmonic balance procedure is proposed for this non-linear problem. Numerical validation of the harmonic balance procedure was performed by comparison of the average mass flow rate with the results of direct time integration. Copyright © 2005 John Wiley & Sons, Ltd. [source] An objective incremental formulation for the solution of anisotropic elastoplastic problems at finite strainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2001S. Chatti Abstract This paper presents an objective formulation for the anisotropic elastic,plastic problems at large strain plasticity. The constitutive equations are written in a rotating frame. The multiplicative decomposition of the deformation gradient is adopted and the formulation is hyperelastic based. Since no stress rates are present and the incremental constitutive law was formulated in a rotating frame, the formulation is numerically objective in the time integration. Explicit algorithm was proposed and has been optimized with regard to stability and accuracy. The incremental law was integrated in fast Lagrangian analysis of continua (FLAC) method to model anisotropic elastic,plastic problems at finite strain. Structural tests are carried out for isotropic and orthotropic materials. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009A. Zolochevsky Abstract A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under plane stress conditions. The variational approach of establishing the basic equations of the plane stress problem under consideration has been introduced. For the solution of two-dimensional creep problems, the fourth-order Runge,Kutta,Merson's method of time integration, combined with the Ritz method and R-functions theory, has been used. Numerical solutions to various problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension,compression asymmetry on the stress,strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd. [source] Asynchronous multi-domain variational integrators for non-linear problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Mark Gates Abstract We develop an asynchronous time integration and coupling method with domain decomposition for linear and non-linear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce continuity at the domain interfaces. The asynchronous integrator lets each domain step with its own time step, using a smaller time step where required by stability and accuracy constraints and a larger time step where allowed. We show that in practice the time step is limited by accuracy requirements rather than by stability requirements. Copyright © 2008 John Wiley & Sons, Ltd. [source] Adaptive superposition of finite element meshes in non-linear transient solid mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007Z. Yue Abstract An s-adaptive finite element procedure is developed for the transient analysis of 2-D solid mechanics problems with material non-linearity due to progressive damage. The resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user-specified tolerances. The spatial error is quantified by the Zienkiewicz,Zhu error estimator and computed via superconvergent patch recovery, while the estimation of temporal error is based on the assumption of a linearly varying third-order time derivatives of the displacement field in conjunction with direct numerical time integration. The distinguishing characteristic of the s-adaptive procedure is the use of finite element mesh superposition (s-refinement) to provide spatial adaptivity. Mesh superposition proves to be particularly advantageous in computationally demanding non-linear transient problems since it is faster, simpler and more efficient than traditional h-refinement schemes. Numerical examples are provided to demonstrate the performance characteristics of the s-adaptive method for quasi-static and transient problems with material non-linearity. Copyright © 2007 John Wiley & Sons, Ltd. [source] A methodology for the formulation of error estimators for time integration in linear solid and structural dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006I. Romero Abstract In this article, we present a novel methodology for the formulation of a posteriori error estimators applicable to time-stepping algorithms of the type commonly employed in solid and structural mechanics. The estimators constructed with the presented methodology are accurate and can be implemented very efficiently. More importantly, they provide reliable error estimations even in non-smooth problems where many standard estimators fail to capture the order of magnitude of the error. The proposed methodology is applied, as an illustrative example, to construct an error estimator for the Newmark method. Numerical examples of its performance and comparison with existing error estimators are presented. These examples verify the good accuracy and robustness predicted by the analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] State-space time integration with energy control and fourth-order accuracy for linear dynamic systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Steen Krenk Abstract A fourth-order accurate time integration algorithm with exact energy conservation for linear structural dynamics is presented. It is derived by integrating the phase-space representation and evaluating the resulting displacement and velocity integrals via integration by parts, substituting the time derivatives from the original differential equations. The resulting algorithm has an exact energy equation, in which the change of energy is equal to the work of the external forces minus a quadratic form of the damping matrix. This implies unconditional stability of the algorithm, and the relative phase error is of fourth-order. An optional high-frequency algorithmic damping is constructed by optimal combination of three different damping matrices, each proportional to either the mass or the stiffness matrix. This leads to a modified form of the undamped algorithm with scalar weights on some of the matrices introducing damping of fourth-order in the frequency. Thus, the low-frequency response is virtually undamped, and the algorithm remains third-order accurate even when algorithmic damping is included. The accuracy of the algorithm is illustrated by an application to pulse propagation in an elastic medium, where the algorithmic damping is used to reduce dispersion due to the spatial discretization, leading to a smooth solution with a clearly defined wave front. Copyright © 2005 John Wiley & Sons, Ltd. [source] A finite element model for thermomechanical analysis of sheet metal formingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004G. Bergman Abstract A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin-walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature-dependent elastic,plastic model with a non-linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one-sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd. [source] A hybrid Padé ADI scheme of higher-order for convection,diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2010Samir KaraaArticle first published online: 8 SEP 200 Abstract A high-order Padé alternating direction implicit (ADI) scheme is proposed for solving unsteady convection,diffusion problems. The scheme employs standard high-order Padé approximations for spatial first and second derivatives in the convection-diffusion equation. Linear multistep (LM) methods combined with the approximate factorization introduced by Beam and Warming (J. Comput. Phys. 1976; 22: 87,110) are applied for the time integration. The approximate factorization imposes a second-order temporal accuracy limitation on the ADI scheme independent of the accuracy of the LM method chosen for the time integration. To achieve a higher-order temporal accuracy, we introduce a correction term that reduces the splitting error. The resulting scheme is carried out by repeatedly solving a series of pentadiagonal linear systems producing a computationally cost effective solver. The effects of the approximate factorization and the correction term on the stability of the scheme are examined. A modified wave number analysis is performed to examine the dispersive and dissipative properties of the scheme. In contrast to the HOC-based schemes in which the phase and amplitude characteristics of a solution are altered by the variation of cell Reynolds number, the present scheme retains the characteristics of the modified wave numbers for spatial derivatives regardless of the magnitude of cell Reynolds number. The superiority of the proposed scheme compared with other high-order ADI schemes for solving unsteady convection-diffusion problems is discussed. A comparison of different time discretizations based on LM methods is given. Copyright © 2009 John Wiley & Sons, Ltd. [source] FEM simulation of turbulent flow in a turbine blade passage with dynamical fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009Lixiang Zhang Abstract Results are described from a combined mathematical modeling and numerical iteration schemes of flow and vibration. We consider the coupling numerical simulations of both turbulent flow and structure vibration induced by flow. The methodology used is based on the stabilized finite element formulations with time integration. A fully coupled model of flow and flow-induced structure vibration was established using a hydride generalized variational principle of fluid and solid dynamics. The spatial discretization of this coupling model is based on the finite element interpolating formulations for the fluid and solid structure, while the different time integration schemes are respectively used for fluid and solid structure to obtain a stabilized algorithm. For fluid and solid dynamics, Hughes' predictor multi-corrector algorithm and the Newmark method are monolithically used to realize a monolithic solution of the fully coupled model. The numerical convergence is ensured for small deformation vibrating problems of the structure by using different time steps for fluid and solid, respectively. The established model and the associated numerical methodology developed in the paper were then applied to simulate two different flows. The first one is the lid-driven square cavity flow with different Reynolds numbers of 1000, 400 and 100 and the second is the turbulent flows in a 3-D turbine blade passage with dynamical fluid,structure interaction. Good agreement between numerical simulations and measurements of pressure and vibration acceleration indicates that the finite element method formulations developed in this paper are appropriate to deal with the flow under investigation. Copyright © 2009 John Wiley & Sons, Ltd. [source] High-order ENO and WENO schemes for unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2007W. R. Wolf Abstract This work describes the implementation and analysis of high-order accurate schemes applied to high-speed flows on unstructured grids. The class of essentially non-oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of third- and fourth-order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2-D Euler equations in a cell centred finite volume context. High-order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge,Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high-order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high-speed flow simulations are presented with the objective of assessing the implemented capability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Microfluidics simulation using adaptive unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2004Jacob Waltz Abstract A methodology for microfluidics simulation is presented. The methodology solves the three-dimensional incompressible Navier,Stokes equations with an adaptive unstructured Finite Element method. A semi-implicit Fractional Step procedure is used for time integration. The entire methodology has been parallelized for shared-memory architectures via an algebraic domain decomposition. Results from both verification problems and prototypical applications are included. Copyright © 2004 John Wiley & Sons, Ltd. [source] Non-oscillatory relaxation methods for the shallow-water equations in one and two space dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2004Mohammed Seaïd Abstract In this paper, a new family of high-order relaxation methods is constructed. These methods combine general higher-order reconstruction for spatial discretization and higher order implicit-explicit schemes or TVD Runge,Kutta schemes for time integration of relaxing systems. The new methods retain all the attractive features of classical relaxation schemes such as neither Riemann solvers nor characteristic decomposition are needed. Numerical experiments with the shallow-water equations in both one and two space dimensions on flat and non-flat topography demonstrate the high resolution and the ability of our relaxation schemes to better resolve the solution in the presence of shocks and dry areas without using either Riemann solvers or front tracking techniques. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004Alexander Yu. Abstract The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time-dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd. [source] A Petrov,Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001Seung-Buhm Woo Abstract A new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov,Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C2 -continuity. For the time integration an implicit predictor,corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model. Copyright © 2001 John Wiley & Sons, Ltd. [source] A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001E. Gadoin Abstract This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier,Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Linking movement behaviour, dispersal and population processes: is individual variation a key?JOURNAL OF ANIMAL ECOLOGY, Issue 5 2009Colin Hawkes Summary 1Movement behaviour has become increasingly important in dispersal ecology and dispersal is central to the development of spatially explicit population ecology. The ways in which the elements have been brought together are reviewed with particular emphasis on dispersal distance distributions and the value of mechanistic models. 2There is a continuous range of movement behaviours and in some species, dispersal is a clearly delineated event but not in others. The biological complexities restrict conclusions to high-level generalizations but there may be principles that are common to dispersal and other movements. 3Random walk and diffusion models when appropriately elaborated can provide an understanding of dispersal distance relationships on spatial and temporal scales relevant to dispersal. Leptokurtosis in the relationships may be the result of a combination of factors including population heterogeneity, correlation, landscape features, time integration and density dependence. The inclusion in diffusion models of individual variation appears to be a useful elaboration. The limitations of the negative exponential and other phenomenological models are discussed. 4The dynamics of metapopulation models are sensitive to what appears to be small differences in the assumptions about dispersal. In order to represent dispersal realistically in population models, it is suggested that phenomenological models should be replaced by those based on movement behaviour incorporating individual variation. 5The conclusions are presented as a set of candidate principles for evaluation. The main features of the principles are that uncorrelated or correlated random walk, not linear movement, is expected where the directions of habitat patches are unpredictable and more complex behaviour when organisms have the ability to orientate or navigate. Individuals within populations vary in their movement behaviour and dispersal; part of this variation is a product of random elements in movement behaviour and some of it is heritable. Local and metapopulation dynamics are influenced by population heterogeneity in dispersal characteristics and heritable changes in dispersal propensity occur on time-scales short enough to impact population dynamics. [source] Energy consistent time integration of planar multibody systemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Stefan Uhlar The planar motion of rigid bodies and multibody systems can be easily described by coordinates belonging to a linear vector space. This is due to the fact that in the planar case finite rotations commute. Accordingly, using this type of generalized coordinates can be considered as canonical description of planar multibody systems. However, the extension to the three-dimensional case is not straightforward. In contrast to that, employing the elements of the direction cosine matrix as redundant coordinates makes possible a straightforward treatment of both planar and three-dimensional multibody systems. This alternative approach leads in general to differential-algebraic equations (DAEs) governing the dynamics of rigid body systems. The main purpose of the present paper is to present a comparison of the two alternative descriptions. In both cases energy-consistent time integration schemes are applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Seismic response of slopes subjected to incident SV wave by an improved boundary element approachINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2007Behrouz Gatmiri Abstract In this paper, an improved boundary element approach for 2D elastodynamics in time-domain is presented. This approach consists in the truncation of time integrations, based on the rapid decrease of the fundamental solutions with time. It is shown that an important reduction of the computation time as well as the storage requirement can be achieved. Moreover, for half-plane problems, the size of boundary element (BE) meshes and the computation time can be significantly reduced. The proposed approach is used to study the seismic response of slopes subjected to incident SV waves. It is found that large amplifications take place on the upper surface close to the slope, while attenuations are produced on the lower surface. The results also show that surface motions become very complex when the incident wavelength is comparable with the size of the slope or when the slope is steep. Copyright © 2006 John Wiley & Sons, Ltd. [source] | |||||||||||||