Periodic tidal flow analysis by finite element perturbation method

The numerical analysis of periodic tidal flow is presented. The present paper investigates a numerical procedure based on the mixed approach of the finite element method and the perturbation method by postulating periodic motion. Several numerical studies are presented to examine the validity of the formulation.     

Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir

The development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital. A poor understanding of how the reservoir behaves during production may lead to inept, costly and inefficient development schemes. The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is hence presented. The present formulation, consisting of both the equilibrium and multiphase mass conservation equations, accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly non-linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.     

Computer simulation of a cold fluidized bed

The theory of two-phase flow provides a set of partial differential equations describing the dynamics of a fluidized bed. A code, developed by Systems, Science, and Software,¹ to solve this system of equations is used to simulate a facility at Alexandria, Virginia.³ Calculated values of pressure drop are compared with experiment.     

Application of a posteriori error estimation to finite element simulation of incompressible Navier-Stokes flow

The main goal of this paper is to study adaptive mesh techniques, using a posteriori error estimates, for the finite element solution of the Navier-Stokes equations modeling steady and unsteady flows of an incompressible viscous fluid. Among existing operator splitting techniques, the θ-scheme is used for time integration of the Navier-Stokes equations. Then, a posteriori error estimates, based on the solution of a local system for each triangular element, are presented in the framework of the generalized incompressible Stokes problem, followed by its practical application to the case of incompressible Navier-Stokes problem. Hierarchical mesh adaptive techniques are developed in response to the a posteriori error estimation. Numerical simulations of viscous flows associated with selected geometries are performed and discussed to demonstrate the accuracy and efficiency of our methodology.     

Application of a posteriori error estimation to finite element simulation of compressible Navier-Stokes flow

In this paper, we discuss how to improve the adaptive finite element simulation of compressible Navier-Stokes flow via a posteriori error estimate analysis. We use the moving space-time finite element method to globally discretize the time-dependent Navier-Stokes equations on a series of adapted meshes. The generalized compressible Stokes problem, which is the Stokes problem in its most generalized form, is presented and discussed. On the basis of the a posteriori error estimator for the generalized compressible Stokes problem, a numerical framework of a posteriori error estimation is established corresponding to the case of compressible Navier-Stokes equations. Guided by the a posteriori errors estimation, a combination of different mesh adaptive schemes involving simultaneous refinement/unrefinement and point-moving are applied to control the finite element mesh quality. Finally, a series of numerical experiments will be performed involving the compressible Stokes and Navier-Stokes flows around different aerodynamic shapes to prove the validity of our mesh adaptive algorithms.     

A fully 3D adaptive finite element simulation and prototype for gas flow in a porous media

This paper presents a three-dimensional (3D) adaptive finite element solution for gas flow in a porous media. The solution obtained is truly 3D and employs a dynamic h-adaptive refinement technique for efficiency. The adaptive procedure uses a new node-based storage mechanism [Wang GH, Tyler JM, Weltman JS, Callahan JD. Advances in Engineering Software including Computing Systems in Engineering 1999;30:31–41]. This node-based structure substantially reduces the memory necessary to store the finite element mesh. A prototype simulator, written in C++, has been implemented for Eugene Island block 305, a multi-well condensate reservoir off the coast of Louisiana to demonstrate the use of this adaptive procedure. Results, presented in this paper, show dramatic agreement with the actual production data. This prototype simulator uses Windows workstations to support a fully dynamic 3D mesh plus mesh generation.     

Computer modelling and finite element analysis of spiral triangular strands

In this paper a new mathematical geometric model of spiral triangular wire strands with a construction of (3 + 9) and (3 + 9 + 15) wires is proposed and an accurate computational two-layered triangular strand 3D solid modelling, which is used for a finite element analysis, is presented. The present geometric model fully considers the spatial configuration of individual wires in the strand. The three dimensional curve geometry of wires axes in the individual layers of the triangular strand consists of straight linear and helical segments. The derived mathematical representation of this curve is in the form of parametric equations with variable input parameters which facilitate the determination of the centreline of an arbitrary circular wire of the right and left hand lay triangular one and two-layered strands. Derived geometric equations were used for the generation of accurate 3D geometric and computational strand models. The correctness of the derived parametric equations and performance of the generated strand model are controlled by visualizations. The 3D computational model was used for a finite element behaviour analysis of the two-layered triangular strand subjected to tension loadings. Illustrative examples are presented to highlight the benefits of the proposed geometric parametric equations and computational modelling procedures by using the finite element method.     

人体头颈计算机模型的建立与有限元分析

本文首先阐述了人体头颈有限元计算模型的建立依然是有限元分析方法解决生物力学问题过程中面临的难题.然后利用CT扫描技术,Mimics软件的自动建模功能和计算机软件Geomagic逆向建模方法准确地、快速地建立了人体头颈部的几何模型.最后在有限的计算机硬件资源下利用有限元分析软件的前处理器建立了与人体头颈实际状态相近的有限元计算模型,并通过有限元分析软件ANSYS对所建的头颈有限元动力响应分析,得到与试验大致相符的头部位移响应曲线,验证了所建的人体头颈有限元计算机模型,同时得到了人体头部和颈部在受到冲击载荷下的任何时间变形和应力,为头颈部损伤的临床提供了重要的参考.     

Adaptive finite element simulation of ventricular fibrillation dynamics

The paper communicates simulation results (computations and visualizations) for the dynamics of ventricular fibrillation caused by irregular excitation in the frame of the monodomain model with an action potential model due to Aliev–Panfilov for a human 3D geometry. The numerical solution of this challenging multiscale reaction–diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library KARDOS). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle). Supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.     

Shot peening simulation using discrete and finite element methods

Modeling shot peening process is very complex as it involves the interaction of metallic surfaces with a large number of shots of very small diameter. Conventionally such problems are solved using the finite element software (such as ABAQUS) to predict the stresses and strains. However, the number of shots involved and the number of elements required in a real-life components for a 100% coverage that lasts a considerable duration of peening make such an approach impracticable. Ideally, a method that is suitable for obtaining residual compressive stresses (RCS) and the amount of plastic deformations with the least computational effort seems a dire need.In this paper, an attempt has been made to address this issue by using the discrete element method (DEM) in combination with the finite element method (FEM) to obtain reasonably accurate predictions of the residual stresses and plastic strains. In the proposed approach, the spatial information of force versus time from the DEM simulation is utilized in the FE Model to solve the shot peening problem as a transient problem. The results show that the RCS distribution obtained closely matches with that of the computationally intensive direct FEM simulation. It has also been established, in this paper, that this method works well even in the situations where the robust unit cell approaches are found to be difficult to handle.     

Collocation finite element solution of a compressible flow

In this paper, the subcritical compressible small disturbance equation is employed to simulate the nonlifting flow over a 6% thick circular arc. The governing nonlinear elliptic boundary value problem is solved numerically with the collocation finite element technique using the Hermite bicubic shape functions. The lack of quadrature calculations makes the overall simulation fast and accurate. The calculation results are compared with experimental measurements supporting their validity.     

On one type of finite element simulation in dynamic elasticity

The aim of the present paper is to generalize the finite element approximation for numerical simulation of special types of problems in the dynamic theory of elasticity, described by the two-dimensional mixed boundary value problems, and to demonstrate the property of their numerical solution. Physically the problems describe propagation of elastic waves, generated by a harmonic line source, in a nonhomogeneous anisotropic media. The existence and unicity of the weak solution as well as of the finite element approximation is proved. Convergence of the method is proved for any regular family of triangulations.     

Mathematical modelling and finite element simulation of smart tubular composites

This paper presents a mathematical modelling and numerical simulation method for three-dimensional smart tubular 1(0)-3 composites based on a representative composite volume (RCV) approach. For the problems we consider, numerical results show that the maximum mechanical displacement varies linearly with the applied electrical potential and grows nonlinearly with increasing the RCV height. Further, we observe that decreasing the distance between the inner and outer radii results in increasing the maximum displacement. This refers to composites with large Young’s modulus of the polymer phase, whereas for “soft” polymers (i.e. for Young’s modulus of the polymers of order less than GPa) no particular ‘rule’ is evident, in which case the Poisson’s ratio is the most important parameter.     

Computer simulation of a patient end tidal CO2 controller system

A computer model of the patient end tidal CO2 controller system has been developed and tested in simulation trials. It is intended to aid in finding the appropriate PI (proportional-integral) controller settings by means of computer simulation instead of real experiments with the system. The latter approach is costly, time consuming and sometimes impossible to perform. The simulator consists of two equations: the patient equation and the PI controller equation. The software has been written in the C language and can be run on an IBM-PC/XT. Some examples of the simulation trials, illustrating the choice of controller settings, are given.     

On the control of noise in finite element tidal computations: A semi-implicit approach

Numerical solution of the two-dimensional shallow water equations is achieved by coupling the finite element method in space with finite difference time stepping schemes. Solutions obtained with an efficient leapfrog model are found to contain severe short-wavelength oscillations in space when compared to analytic solutions. An alternative semi-implicit formulation in the time domain, which retains most of the economical advantages of the leapfrog scheme is developed and tested. A significant reduction in the mode-to-node oscillations and improved agreement with analytical solutions are obtained. Both linear triangles and quadratic isoparametric quadrilaterals are examined. Emphasis is on the numerical behavior of the schemes tested and a comparison with a field case is not attempted.     

Computer simulation of a material flow system

This paper presents a computer simulation model of a material flow system. The flow system is a conveyor fed system for sorting and packing different types of bundles of cigarettes. Several bundle-types of cigarettes are produced at different rates by different machines and then released onto a common belt conveyor. The conveyor transports the bundles to a marshalling area. Because of the nature of the flow system different types of bundles get mixed up in the conveyor and several workers are stationed in the marshalling area to sort the different bundle-types and then pack into different crates. The model is used to answer questions relating to assignment of workers to particular bundle-types, whether workers should help each other in picking up bundles, and manpower levels in the marshalling area.This paper illustrates the application of computer simulation to a real world problem in a small factory.     

Computer simulation of wind flow around buildings

This paper looks at the relationship between wind flow round a building and heat loss from it. The relative merits of numerical and wind tunnel models are discussed and various numerical techniques examined.     

Applications of finite element analysis in the rational design of track bed structures

Applications of finite element analysis in the study of the mechanical behaviour of track and track bed structures are presented.First are examined the conceptualization of the mesh and the effect of three-dimensional or bidimensional approaches. The appropriate constitutive law and the contact conditions between two layers are discussed afterwards.This method was used to predict stress and strain at the subgrade, sleeper and rail level, by taking into account:

• •• the form of the sleeper (wooden sleepers, prestresssed concrete sleepers, reinforced concrete sleepers)
• •• the thickness of the track bed structures
• •• the quality of the soil of the subgrade.

The flexibility of the various forms of sleepers was also studied. Practical use of the results obtained has been made in the rational design of track bed structures.     

Comparison of finite element and pendulum models for simulation of sloshing

The pendulum model is a cost effective tool for the simulation of sloshing. However, the accuracy and applicability of the model has not been well established. In this article, we compare the simulation results obtained from the pendulum model and a more complicated finite element model for sloshing of liquids in tanker trucks. In the pendulum model, we assume that the liquid in the tanker is a point mass oscillating like a frictionless pendulum subjected to an external acceleration. In the finite element model, we solve the full Navier-Stokes equations written for two fluids to obtain the location and motion of the free surface. Stabilized finite element formulations are used in these complex 3D simulations. These finite element formulations are implemented in parallel using the message-passing interface libraries. The numerical example includes the simulation of sloshing in tanker trucks during turning.