Lagrangian-Eulerian Finite Element Method Research Articles

3-D Sloshing Analysis by an Arbitrary Lagrangian-Eulerian Finite Element Method

This paper presents a new Arbitrary Lagrangiae-Eulerian (ALE) finite element method for the analysis of three-dimensional large-amplitude sloshing problems. The present method is composed of three phases, i.e., Phase 1: Purely Lagrangian calculation. Phase 2: Remeshing procedure and Phase 3: Rezoning procedure. By applying these procedures, the present method has succeeded in overcoming the main difficulty of computation in the large-amplitude sloshing analysis. In the Lagrengian calculation, a new fractional step method that satisfies the free-surface boundary condition has been applied, and treatment of the free surface on the multi-sloped wall boundary has been advanced. In the remeshing procedure, a method based on boundary-fitted coordinates is introduced. Numerical results are compared with experimental results, and it is shown that this method is sufficiently accurate to calculate the three-dimensional sloshing. Furthermore, a numerical example of large-amplitude sloshing in a tank with roofs and chamfers illustrates the validity of the method for the computation of large-amplitude sloshing waves whose free surface configuration is a double-valued function.

2-D Fluid-Structure Interaction Problems by an Arbitrary Lagrangian-Eulerian Finite Element Method

This paper presents a finite element analysis of a fluid-structure interaction problem by the Arbitrary Lagrangian-Eulerian (ALE) method. For the analysis of the Navier-Stokes equation, a fractional step method is used based the linear interpolation functions for both velocity and pressure. For a numerical example, the present method is applied to the flow analysis around an oscillating rectangular cylinder. The total calculation domain is divided into several sub-domains to improve the computational efficiency. In the inner domain, the mesh moves based on the ALE description. The outmost domain is the Eulerian domain. The intermediate domain is located as a transition.

SPLASH program for three dimensional fluid dynamics with free surface boundaries

This paper describes a three dimensional computer program SPLASH that solves Navier-Stokes equations based on the Arbitrary Lagrangian Eulerian (ALE) finite element method. SPLASH has been developed for application to the fluid dynamics problems including the moving boundary of a liquid metal cooled Fast Breeder Reactor (FBR). To apply SPLASH code to the free surface behavior analysis, a capillary model using a cubic Spline function has been developed. Several sample problems, e.g., free surface oscillation, vortex shedding development, and capillary tube phenomena, are solved to verify the computer program. In the analyses, the numerical results are in good agreement with the theoretical value or experimental observance. Also SPLASH code has been applied to an analysis of a free surface sloshing experiment coupled with forced circulation flow in a rectangular tank. This is a simplified situation of the flow field in a reactor vessel of the FBR. The computational simulation well predicts the general behavior of the fluid flow inside and the free surface behavior. Analytical capability of the SPLASH code has been verified in this study and the application to more practical problems such as FBR design and safety analysis is under way.

Ale finite element analysis of the opening and closing process of the artificial mechanical valve

Employing arbitrary Lagrangian-Eulerian (ALE) finite element method, this paper studies the opening and closing process of a St. Jude medical valve through a two-dimensional model of the mechanical valve—blood interaction in which the valve is regarded as a rigid body rotating around a fixed point, and the blood is simplified as viscous incompressible Newtonian fluid. The numerical analysis of the opening and closing behaviour of as St. Jude valve suggested that: 1. The whole opening and closing process of an artificial mechanical valve is consisted of four phases: (1)Opening phase; (2) Opening maintenance phase; (3) Closing phase; (4) Closing maintenance phase. 2. The St. Jude medical valve closes with prominent regurgitat which results in water-hammer effect. 3. During the opening and closing process of the St. Jude valve, high shear stresses occur in the middle region of the two leaflets and on the valve ring. The present model has made a breakthrough on the coupling computational analysis considering the interactive movement of the valve and blood.

A PARTICLE TRACKING TECHNIQUE FOR THE LAGRANGIAN-EULERIAN FINITE ELEMENT METHOD IN MULTI-DIMENSIONS

This paper presents a multi-dimensional particle tracking technique for applying the Lagrangian–Eulerian finite element method to solve transport equations in transient-state simulations. In the Lagrangian– Eulerian approach, the advection term is handled in the Lagrangian step so that the associated numerical errors can be considerably reduced. It is important to have an adequate particle tracking technique for computing advection accurately in the Lagrangian step. The particle tracking technique presented here is designed to trace fictitious particles in the real-world flow field where the flow velocity is either measured or computed at a limited number of locations. The technique, named ‘in-element’ particle tracking, traces fictitious particles on an element-by-element basis. Given a velocity field, a fictitious particle is traced one element by one element until either a boundary is encountered or the available time is completely consumed. For the tracking within an element, the element is divided into a desired number of subelements with the interpolated velocity computed at all nodes of the subelements. A fictitious particle, thus, is traced one subelement by one subelement within the element. The desired number of subelements can be determined based on the complexity of the flow field being considered. The more complicated the flow field is, the more subelements are needed to achieve accurate particle tracking results. A single-velocity approach can be used to efficiently perform particle tracking in a smooth flow field, while an average-velocity approach can be employed to increase the tracking accuracy for more complex flow fields.

A comparative study of the opening and closing process of two types of mechanical heart valves using ALE finite element method

Using arbitrary Lagrangian-Eulerian (ALE) finite element method, this paper made a comparative study of the opening and closing behaviour of a downstream directional valve (DDM) and a St. Jude medical valve (SJM) through a two dimensional model of mechanical valve-blood interaction in which the valve is considered as a rigid body rotating around a fixed point, and the blood is simplified as viscous incompressible fluid. It's concluded that: (1) Compared with SJM valve, DDM valve opens faster and closes the more gently. (2) The peak back-flow of DDM is smaller than that of SJM. The present investigation shows that being a better analogue of natural valve, DDM has a brighter potential on its durability than SJM.

Analysis and Design of Industrial Hot Extrusion Process through Square Dies for Manufacturing Complicated Al Alloy Profiles

In the analysis and design of hot square die extrusion processes, non-steady state analysis together with temperature analysis is recommended. In the present work, non-steady state analysis are carried out for hot square die extrusion of some typical industrial profiles by using the rigid-viscoplastic arbitrary Lagrangian-Eulerian(ALE) finite element method. Since flow guide and die lands play important roles in controlling the metal flow in the industrial practice, the related analyses are carried out and the effects of die land and flow guide are discussed. In order to estimate the variation of die land length, a scheme has been developed. The scheme is applied to extrusion of L-section without any axis of symmetry. The calculated configuration of die land is compared with the industrial design. As an effective tool for prediction of die wear, a wear map in introduced and demonstrated through the examples.

R-adapted arbitrary lagrangian-eulerian finite-element method in metal-forming simulation

In this article, mesh adaptation techniques have been used with the arbitrary Lagrangian-Eulerian finite-element method for analysis of metal-forming problems. The r-method of node relocation has been found suitable for this purpose and is driven by errors based on effective plastic strain. Two forming simulations for elastic-viscoplastic materials have been executed under plane-strain conditions, and the effect of mesh adaptation has been studied.

ALE finite element formulation for ring rolling analysis

AbstractIn this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring–roll interface as well as the distribution of effective stresses in the formed ring, are also presented.

An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body

A computational procedure is developed to solve the problems of coupled motion of a rigid body and a viscous incompressible fluid; the former is mounted on elastic springs, and the latter is surrounding the rigid body. The arbitrary Lagrangian-Eulerian method is employed to incorporate the interface conditions between the body and the fluid. The streamline upwind/Petrov-Galerkin finite element method is used for the spatial discretization of the fluid domain, and the predictor-corrector method is used for the time integration. The method is applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a circular cylinder induced by vortex sheddings.

TWO-DIMENSIONAL SLOSHING ANALYSIS BY THE ARBITRARY LAGRANGIAN-EULERIAN FINITE ELEMENT METHOD

This paper presents a new Arbitrary Lagrangian-Eulerian (ALE) finite element method for the calculation of a large amplitude sloshing wave in a tank with roofs and/or chamfers. For the analytical procedure, a new fractional step method to satisfy the free surface boundary condition has been applied, and the treatment of a free surface flow on the multi-sloped wall boundary has been advanced. Compared to experimental results, this method has proved to be sufficiently accurate to follow the free surface position and to obtain the velocity and pressure distributions. Furthermore, numerical examples show the validity to calculate large amplitude sloshing waves whose configuration of the free surface is double-valued function.

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids

Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.

Viscous Flow Structure Interaction

Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches are formulated within the framework of finite elements, and the majority of work deals with inviscid fluids. However, there has been little work done in the area of fluid-structure interaction problems accounting for flow separation and nonlinear phenomenon of steady streaming. In this paper, the Arbitrary Lagrangian Eulerian (ALE) finite element method is extended to address the flow separation and nonlinear phenomenon of steady streaming for arbitrarily shaped bodies undergoing large periodic motion in a viscous fluid. The results are designed to evaluate the fluid force acting on the body; thus, the coupled rigid body-viscous flow problem can be simplified to a standard structural problem using the concept of added mass and added damping. Formulas for these two constants are given for the particular case of a cylinder immersed in an infinite viscous fluid. The finite element modeling is based on a pressure-velocity mixed formulation and a streamline upwind Petrov/Galerkin technique. All computations are performed using a personal computer.

An arbitrary lagrangian-eulerian finite element method for path-dependent materials

The conservation laws, the constitutive equations, and the equation of state for path-dependent materials are formulated for an arbitrary Lagrangian-Eulerian finite element method. Both the geometrical and material nonlinearities are included in this setting. Computer implementations are presented and an elastic-plastic wave propagation problem is used to examine some features of the proposed method.

Adaptive Eulerian–Lagrangian finite element method for advection–dispersion

AbstractA new adaptive finite element method is proposed for the advection–dispersion equation using an Eulerian–Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single‐step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of one‐ and two‐dimensional dispersion in a uniform steady‐state velocity field suggest that the proposed adaptive method can handle the entire range of Péclet numbers from 0 to ∞, with Courant numbers well in excess of 1.

Response of fast-reactor core subassemblies to pressure transients

An Arbitrary Lagrangian-Eulerian (ALE) finite element method for analyzing the transient, nonlinear fluid-structure interaction in fast-reactor core subassemblies is presented. The method combines the basic attributes of the finite element technique — namely, ease in modeling complex geometries and in mixing fluid elements with structural elements — and the flexibility in moving the fluid mesh offered by the ALE description. The result of this combination is a very versatile modeling technique which permits accommodation of large fluid and structure displacements and logically simple, but accurate fluid-structure coupling. Numerical results are presented to illustrate the effectiveness of the proposed method. These include the response of a single hexagonal duct to internal, static or dynamic, pressure loading for which numerical predictions are compared to experimental data, and applications to clustered hexcans.