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Time Integration Schemes (time + integration_scheme)
Selected AbstractsNumerical solution for consolidation and desiccation of soft soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002Daniel T. C. Yao Abstract The consolidation and desiccation behaviour of soft soils can be described by two time-dependent non-linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi-implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. [source] Optimal time integration parameters for elastodynamic contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001A. Czekanski Abstract In this paper, we employ the generalized- , time integration scheme for treating elastodynamic contact problems. The criteria invoked for the selection of the four time integration parameters are motivated by our desire to ensure that the solution is unconditionally stable, second-order accurate, provides optimal high-frequency dissipation and preserves the energy and momentum transfer in dynamic rigid impact problems. New closed-form expressions for the time integration parameters are determined in terms of user-specified high-frequency spectral radius. The selected parameters help in avoiding the spurious high-frequency modes, which are present in the traditional Newmark method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heatINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Dong Qian Abstract This paper focuses on the non-linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo-elasto-viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit,implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd. [source] Modelling of wetting and drying of shallow water using artificial porosityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005B. van't Hof Abstract A new method for wetting and drying in two-dimensional shallow water flow models is proposed. The method is closely related to the artificial porosity method used by different authors in Boussinesq-type models, but is further extended for use in a semi-implicit (ADI-type) time integration scheme. The method is implemented in the simulation model WAQUA using general boundary fitted coordinates and is applied to realistic schematization for a portion of the river Meuse in the Netherlands. A large advantage of the artificial porosity method over traditionally used methods on the basis of ,screens' is a strongly reduced sensitivity of model results. Instead of blocking all water transport in grid points where the water level becomes small, as in screen-based methods, the flow is gradually closed off. Small changes in parameters such as the initial conditions or bottom topography therefore no longer lead to large changes in the model results. Copyright © 2005 John Wiley & Sons, Ltd. [source] An implementation of radiative transfer in the cosmological simulation code gadgetMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2009Margarita Petkova ABSTRACT We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget. It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe. [source] Modeling and numerical analysis of masonry structuresNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2007Mark Ainsworth Abstract We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone-blocks) in unilateral, frictional contact. The problem is formulated as a quasi-variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time-step, the quasi-variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal-dual active-set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch-ring made of bricks, deformed due to body forces and surface tractions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 798,816, 2007 [source] Spectral-element simulations of wave propagation in porous mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2008Christina Morency SUMMARY We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as ,type II' or ,Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral-element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach. We perform various benchmarks involving poroelastic wave propagation and acoustic,poroelastic and poroelastic,poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance. [source] Multi-time-step domain coupling method with energy controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010N. Mahjoubi Abstract A multi-time-step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state-space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time-integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state-space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces. Copyright © 2010 John Wiley & Sons, Ltd. [source] Analysis of the block Gauss,Seidel solution procedure for a strongly coupled model problem with reference to fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009M. M. Joosten Abstract 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. Copyright © 2008 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] A modification of the artificial compressibility algorithm with improved convergence characteristicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Frank Muldoon Abstract The artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven-cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward-facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the geometric conservation law in transient flow calculations on deforming domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Ch. Förster Abstract This note revisits the derivation of the ALE form of the incompressible Navier,Stokes equations in order to retain insight into the nature of geometric conservation. It is shown that the flow equations can be written such that time derivatives of integrals over moving domains are avoided prior to discretization. The geometric conservation law is introduced into the equations and the resulting formulation is discretized in time and space without loss of stability and accuracy compared to the fixed grid version. There is no need for temporal averaging remaining. The formulation applies equally to different time integration schemes within a finite element context. Copyright © 2005 John Wiley & Sons, Ltd. [source] Iterative solution techniques for unsteady flow computations using higher order time integration schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005H. Bijl Abstract In this paper iterative techniques for unsteady flow computations with implicit higher order time integration methods at large time steps are investigated. It is shown that with a minimal coding effort the standard non-linear multigrid method can be combined with a Newton,Krylov method leading to speed-ups in the order of 30%. Copyright © 2005 John Wiley & Sons, Ltd. [source] Higher order explicit time integration schemes for Maxwell's equationsINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5-6 2002Holger Spachmann Abstract The finite integration technique (FIT) is an efficient and universal method for solving a wide range of problems in computational electrodynamics. The conventional formulation in time-domain (FITD) has a second-order accuracy with respect to spatial and temporal discretization and is computationally equivalent with the well-known finite difference time-domain (FDTD) scheme. The dispersive character of the second-order spatial operators and temporal integration schemes limits the problem size to electrically small structures. In contrast higher-order approaches result not only in low-dispersive schemes with modified stability conditions but also higher computational costs. In this paper, a general framework of explicit Runge,Kutta and leap-frog integrators of arbitrary orders N is derived. The powerful root-locus method derived from general system theory forms the basis of the theoretical mainframe for analysing convergence, stability and dispersion characteristics of the proposed integrators. As it is clearly stated, the second- and fourth-order leap-frog scheme are highly preferable in comparison to any other higher order Runge,Kutta or leap-frog scheme concerning stability, efficiency and energy conservation. Copyright © 2002 John Wiley & Sons, Ltd. [source] A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Scott A. Sarra Abstract Differentiation matrices associated with radial basis function (RBF) collocation methods often have eigenvalues with positive real parts of significant magnitude. This prevents the use of the methods for time-dependent problems, particulary if explicit time integration schemes are employed. In this work, accuracy and eigenvalue stability of symmetric and asymmetric RBF collocation methods are numerically explored for some model hyperbolic initial boundary value problems in one and two dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [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] | ||||||||||