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Arbitrary Lagrangian (arbitrary + lagrangian)

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Selected Abstracts

Arbitrary Lagrangian,Eulerian method for large-strain consolidation problems

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008
Majidreza Nazem
Abstract In this paper, an arbitrary Lagrangian,Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore-water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated-Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. [source]

PC cluster parallel finite element analysis of sloshing problem by earthquake using different network environments

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002
Kazuo Kashiyama
Abstract This paper presents a parallel finite element method for the analysis of the sloshing problem caused by earthquakes. The incompressible Navier,Stokes equation based on Arbitrary Lagrangian,Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed to improve the numerical stability and the accuracy. Parallel implementation of the unstructured grid based formulation was carried out on a PC cluster. The present method was applied to analyse the sloshing problem of a rectangular tank and an actual reservoir. The effect of parallelization on the efficiency of the computations was examined using a number of different network environments. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Generation of Arbitrary Lagrangian,Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
B. V. Wells
Abstract A moving mesh method is outlined based on the use of monitor functions. The method is developed from a weak conservation principle. From this principle a conservation law for the mesh position is derived. Using the Helmholtz decomposition theorem, this conservation law can be converted into an elliptic equation for a mesh velocity potential. The moving mesh method is discretized using standard finite elements. Once the mesh velocities are obtained an arbitrary Lagrangian,Eulerian (ALE) (Journal of Computational Physics 1974; 14:227) fluid solver is used to update the solution on the adaptive mesh. Results are shown for the compressible Euler equations of gas dynamics in one and two spatial dimensions. Two monitor functions are used, the fluid density (which corresponds to a Lagrangian description), and a function which includes the density gradient. A variety of test problems are considered. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Injection/suction boundary conditions for fluid,structure interaction simulations in incompressible flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2002
G. Medic
Abstract This paper presents the analysis of injection/suction boundary conditions in the context of the fluid,structure interactions simulation of the incompressible turbulent flow. First, the equations used in the modelling of the fluid and the structure are presented, as well as the numerical methods used in the corresponding solvers. Injection/suction boundary conditions are then presented with details of different implementation alternatives. Arbitrary Lagrangian,Eulerian (ALE) approach was also implemented in order to test the injection/suction boundary conditions. Numerical tests are performed where injection/suction boundary conditions are compared to ALE simulations. These tests include forced movement of the structure and two-degrees-of-freedom structure model simulations. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Arbitrary Lagrangian,Eulerian method for large-strain consolidation problems

An operator-split ALE model for large deformation analysis of geomaterials

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2007
Y. Di
Abstract Analysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian,Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid,fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Simulation technique for wave generation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003
S. Aliabadi
Abstract In this paper, we present a new finite element technique for simulation of water waves impacting on floating structures. The emphasis will be on the numerical methods for water wave generation and propagation. In our approach, the governing equations are the Navier,Stokes equations written for two incompressible fluids. An interface function with two distinct values serves as a marker identifying the location of the free-surface. This function is transported throughout the computational domain with a time-dependent advection equation. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian,Eulerian domain. This allows us to handle the motion of the physical boundaries, such as the wave generator surface by moving the computational nodes. In the mesh-moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The numerical examples include 3D wave generation and wave breaking as they approach the coast, and the waves impacting on near-shore support columns. Copyright © 2003 John Wiley & Sons, Ltd. [source]

ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008
Julio Garcia-Espinosa
Abstract This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233,267) and arbitrary Lagrangian,Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235,249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier,Stokes equations are solved using an iterative monolithic predictor,corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Prediction of the non-ideal detonation performance of commercial explosives using the DeNE and JWL++ codes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005
S. Esen
Abstract The non-ideal detonation performance of two commercial explosives is determined using the DeNE and JWL++ codes. These two codes differ in that DeNE is based on a pseudo-one-dimensional theory which is valid on the central stream-tube and capable of predicting the non-ideal detonation characteristics of commercial explosives as a function of the explosive type, rock properties and blasthole diameter. On the other hand, JWL++ is a hydrocode running in a 2-D arbitrary Lagrangian,Eulerian code with CALE-like properties and can determine the flow properties in all stream lines within the reaction zone. The key flow properties (detonation velocity, pressure, specific volume, extent of reaction and reaction zone length) at the sonic locus on the charge axis have been compared. In general, it is shown that the flow parameters determined using both codes agree well. The pressure contours determined using the JWL++ are analysed in detail for two explosives at 165 mm blastholes confined in limestone and kimberlite with a view to further investigate the explosive/rock interface. The DeNE and JWL++ codes have been validated using the measured in-hole detonation velocity data. Copyright © 2005 John Wiley & Sons, Ltd. [source]

An arbitrary Lagrangian,Eulerian finite element method for finite strain plasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
Francisco Armero
Abstract This paper presents a new arbitrary Lagrangian,Eulerian (ALE) finite element formulation for finite strain plasticity in non-linear solid mechanics. We consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part (F = FeFp), with the stresses given by a hyperelastic relation. In contrast with more classical ALE approaches based on plastic models of the hypoelastic type, the ALE formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh. This aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables. In fact, this advection is carried out exactly through a particle tracking in the reference mesh, a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh. A staggered scheme defined by three steps (the smoothing, the advection and the Lagrangian steps) leads to an efficient method for the solution of the resulting equations. We present several representative numerical simulations that illustrate the performance of the newly proposed methods. Both quasi-static and dynamic conditions are considered in these model examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Flow-induced vibrations of non-linear cables.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002
Part 1: Models, algorithms
Abstract In this paper, we develop governing equations for non-linear cables as well as a formulation for the coupled flow-structure problem. The structure is discretized with second-order accuracy while the flow is discretized using spectral/hp elements in the context of the arbitrary Lagrangian,Eulerian formulation (ALE). Several benchmark problems are considered and the computational implementation is detailed. In the second part of this work large-scale simulation examples are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source]

An arbitrary Lagrangian,Eulerian method based on the adaptive Riemann solvers for general equations of state

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009
Baolin Tian
Abstract Approximate or exact Riemann solvers play a key role in Godunov-type methods. In this paper, three approximate Riemann solvers, the MFCAV, DKWZ and weak wave approximation method schemes, are investigated through numerical experiments, and their numerical features, such as the resolution for shock and contact waves, are analyzed and compared. Based on the analysis, two new adaptive Riemann solvers for general equations of state are proposed, which can resolve both shock and contact waves well. As a result, an ALE method based on the adaptive Riemann solvers is formulated. A number of numerical experiments show good performance of the adaptive solvers in resolving both shock waves and contact discontinuities. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Sigma transformation and ALE formulation for three-dimensional free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
A. Decoene
Abstract In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian,Eulerian (ALE) approach. For that purpose we introduce the ALE-sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
Martin Engel
Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Generation of Arbitrary Lagrangian,Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations

An implicit edge-based ALE method for the incompressible Navier,Stokes equations,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Richard W. Smith
Abstract A new finite volume method for the incompressible Navier,Stokes equations, expressed in arbitrary Lagrangian,Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is first evaluated using several well-known unsteady incompressible Navier,Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in 2003 by John Wiley & Sons, Ltd. [source]