Data-parallel computation of EBE finite element method for air/water/soil coupled system

The authors developed a method to adequately compute the fluid-structure interactions to analyze a coupled phenomena for gas, liquid and solid. With the implementation of VOF method, the new methodology may handle the moving boundaries as well. The present technique is based on the predecessing approach for analyzing the incompressible viscous fluid for large scale problems [3]. The characteristic of this method is that by implementing the matrix-storage free formulation [1], which is based on the one-point quadrature scheme, the amount of necessary storage and the number of operations for calculating the integration are considerably. Moreover, the data-parallel coding is implemented taking advantage of the element-by-element structure of the program. We selected two problems in order to examine the effectiveness of this newly developed program:flow inside a subway station and water scour around a bridge pier.     

Parallel performance and scalability for block preconditioned finite element (p) solution of viscous flow

A two-dimensional p-type finite element scheme for distributed parallel computation of viscous flows is developed. The approach is based on an element-by-element implementation of the Biconjugate Gradient Stabilized 2 iterative method coupled with a recently developed class of block preconditioners. Critical to the overall parallel performance is the parallel solution of the imbedded bilinear preconditioner. Performance results are presented for the 2-D driven cavity incompressible viscous flow problem solved using incremental continuation in the Reynolds number on the Intel Touchstone Delta. These results are used to validate a run-time model. The run-time model is then used to examine the scaling properties of the method over a range of p and h.     

A parallel element-by-element solution scheme

A parallel element-by-element scheme is developed for finite-element solution of elliptic boundary-value problems. It is shown that, for a broad class of computational grids, the solution algorithm is totally parallelizable. Moreover, the conversion of an existing serial EBE code to a parallel code is seen to be quite simple. The method is implemented on the Alliant FX/8 and Sequent Balance parallel computers and ‘speedup’ performance studies are conducted for a representative elliptic PDE in two dimensions. The present procedure can be applied quite generally to other finite-element applications, and the associated programs can be modified in a straightforward way to implement the method.     

Parallel computation for acoustic radiation in a subsonic nonuniform flow with a coupled FEM/BEM formulation

This paper presents a parallel implementation of the coupled finite element method/boundary element method formulation for sound radiation in a subsonic nonuniform flow. The parallelization is based on a cost analysis of the sequential algorithm and is implemented on a heterogeneous computer system using the Parallel Virtual Machine software. A dynamically distributed parallel computation scheme (DDPCS) is developed to improve efficiency and reliability. Our test cases demonstrate that it is possible to get high parallel efficiency and reliability on a virtual parallel machine, although greater heterogeneity decreases efficiency.     

Parallel point interpolation method for three-dimensional metal forming simulations

Parallel point interpolation method (PIM) is developed for metal forming with large deformation analysis of three-dimensional (3-D) solids, based on the Galerkin weak form formulation using 3-D meshless shape functions constructed using radial basis functions (RBFs). As the radial PIM (RPIM) shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite element method (FEM). The kinematics and the explicit integration scheme for PIM meshless method are given. The OpenMP parallelization toolkit is used to parallelize our meshless code, and the parallelization of the PIM meshless code has been conducted for a shared memory system using OpenMP. Some examples are then presented to demonstrate the efficiency and accuracy of the proposed implementations concerning the accuracy and efficiency of the code. It is demonstrated that the present parallel 3-D PIM meshless program is robust, stable, reliable and efficiency for metal forming analysis of 3-D problems.     

An efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids

This paper presents the development and validation of a parallel unstructured‐grid fluid–structure interaction (FSI) solver for the simulation of unsteady incompressible viscous flow with long elastic moving and compliant boundaries. The Navier–Stokes solver on unstructured moving grid using the arbitrary Lagrangian Eulerian formulation is based on the artificial compressibility approach and a high‐order characteristics‐based finite‐volume scheme. Both unsteady flow and FSI are calculated with a matrix‐free implicit dual time‐stepping scheme. A membrane model has been formulated to study fluid flow in a channel with an elastic membrane wall and their interactions. This model can be employed to calculate arbitrary wall movement and variable tension along the membrane, together with a dynamic mesh method for large deformation of the flow field. The parallelization of the fluid–structure solver is achieved using the single program multiple data programming paradigm and message passing interface for communication of data. The parallel solver is used to simulate fluid flow in a two‐dimensional channel with and without moving membrane for validation and performance evaluation purposes. The speedups and parallel efficiencies obtained by this method are excellent, using up to 16 processors on a SGI Origin 2000 parallel computer. A maximum speedup of 23.14 could be achieved on 16 processors taking advantage of an improved handling of the membrane solver. The parallel results obtained are compared with those using serial code and they are found to be identical. Copyright © 2005 John Wiley & Sons, Ltd.     

Computation of stresses in axisymmetric elastostatical problems using BEM

The application of the conjugate residual method to the indefinite system resulting from the finite element approximation of the incompressible Navier-Stokes equations is studied. The possibility to use an element-by-element preconditioner for the acceleration of the convergence is also discussed. With this scheme, one can achieve significant savings in storage without ever forming the large total matrix. Furthermore, the hybrid finite element mesh, a mixture of the structured and unstructured mesh subdivisions, is employed to minimize the storage requirement. The numerical simulations of the Karman vortex street, a driven cavity flow and the flow in a safety valve are presented to demonstrate the applicability of the proposed strategies.     

三维有限元并行EBE方法

采用Jacobi预处理,推导了基于EBE方法的预处理共轭梯度算法,给出了有限元EBE方法在分布存储并行机上的计算过程,可以实现整个三维有限元计算过程的并行化。编制了三维有限元求解的PFEM(ParallelFiniteElementMethod)程序,并在网络机群系统上实现。采用矩形截面悬臂梁的算例,对PFEM程序进行了数值测试,对串行计算和并行计算的效率进行了分析,最后将PFEM程序应用于二滩拱坝-地基系统的三维有限元数值计算中。结果表明,三维有限元EBE算法在求解过程中不需要集成整体刚度矩阵,有效地减少了对内存的需求,具有很好的并行性,可以有效地进行三维复杂结构的大规模数值分析。     

基于EBE策略实现结构动力响应的并行计算

基于EBE(Element by Element)策略的并行算法不用形成总体刚度矩阵,而且无需进行三维模型的区域分解,从而提高并行计算的速度和效率,是实现结构动力响应快速分析的有效途径。采用Newmark法,结合EBE并行算法和Jacobi预处理技术实现结构动力方程的并行计算。在此基础上,利用虚拟激励方法实现结构随机振动的并行计算。最后在网络集群环境下,综合运用多种编程语言和分析工具,应用该并行算法对三维零件的冲击响应以及随机振动进行仿真计算,并与Ansys、精细时程积分法的相比较。结果表明,该并行算法的计算误差小,并行效率较高,适用于工程计算。     

A domain decomposition implementation of the SIMPLE method with PVM

A parallel implementation of a finite volume method for the solution of the Navier-Stokes equations on a distributed computing environment through Parallel Virtual Machine (PVM) is reported. The numerical method is implicit and is based on the SIMPLE algorithm in which the system of equations is discretised using a hybrid scheme. An Alternative Direction Implicit (ADI) scheme, and the Thomas tri-diagonal solver are used to solve the algebraic equations. The parallelization of the program is implemented by a domain decomposition strategy on MIMD parallel architectures using PVM platform. The program was tested for laminar flow in a cavity. The parallelisation strategy and performance are discussed. It is concluded that the efficiency is strongly dependent on the grid size, block numbers and the number of processors. Different strategies to improve the computational efficiency are proposed.     

Adaptive error analysis in seepage problems

Numerical experiments in adapting variations of a computationally simple error estimator (the Zienkiewicz-Zhu estimator) to an existing finite element code are shown. The error estimator used allows both overall and local errors to be estimated. From the local estimates of error, refinements of the mesh are calculated to reach a prescribed error tolerance. These calculated refinements are used by a mesh refiner to produce a modified mesh which lowers the overall error to the prescribed value while keeping the mesh as crude as possible. The physical example on which these numerical experiments are performed is that of free surface flow through an earth dam with a toe drain. It is also shown how the problem formulation affects the error analysis and how the choice of computational scheme affects the mesh adaptation.     

A PARALLEL COMPUTING SOLUTION OF HEAT AND MOISTURE TRANSFER IN UNSATURATED SOIL

New parallel software for the analysis of coupled heat and moisture transfer in unsaturated soil is developed. The model, written in a two-dimensional polar co-ordinate formulation, is based on a finite difference self-implicit method. The code is programmed in FORTRAN with message passing libraries PARMACS and executed on a ‘Paramid’ parallel supercomputer. The validity of the parallel code by comparison of simulation results with experimentally measured values obtained from a laboratory heating experiment is examined. An assessment of the algorithm's performance on a large network of processors is also explored. It was found that the simulation results compared very well with the experimental measurements. The efficiency of the parallel code was also revealed leading to the conclusion that the algorithm was highly efficient in nature. The new parallel code was also found to be more efficient when dealing with larger problems requiring more finite difference nodal points, on a larger network of processors.     

Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation

A parallel edge-based solution of three dimensional viscoplastic flows governed by the steady Navier–Stokes equations is presented. The governing partial differential equations are discretized using the SUPG/PSPG stabilized finite element method on unstructured grids. The highly nonlinear algebraic system arising from the convective and material effects is solved by an inexact Newton-Krylov method. The locally linear Newton equations are solved by GMRES with nodal block diagonal preconditioner. Matrix-vector products within GMRES are computed edge-by-edge (EDE), diminishing flop counts and memory requirements. A comparison between EDE and element-by-element data structures is presented. The parallel computations were based in a message passing interface standard. Performance tests were carried out in representative three dimensional problems, the sudden expansion for power-law fluids and the flow of Bingham fluids in a lid-driven cavity. Results have shown that edge based schemes requires less CPU time and memory than element-based solutions.     

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

A Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed methods.     

Development of a scalable finite element solution to the Navier–Stokes equations

A scalable numerical model to solve the unsteady incompressible Navier–Stokes equations is developed using the Galerkin finite element method. The coupled equations are decoupled by the fractional-step method and the systems of equations are inverted by the Krylov subspace iterations. The data structure makes use of a domain decomposition of which each processor stores the parameters in its subdomain, while the linear equations solvers and matrices constructions are parallelized by a data parallel approach. The accuracy of the model is tested by modeling laminar flow inside a two-dimensional square lid-driven cavity for Reynolds numbers at 1,000 as well as three-dimensional turbulent plane and wavy Couette flow and heat transfer at high Reynolds numbers. The parallel performance of the code is assessed by measuring the CPU time taken on an IBM SP2 supercomputer. The speed up factor and parallel efficiency show a satisfactory computational performance.The authors wish to acknowledge Mr. W. K. Kwan of The University of Hong Kong for his help in using the IBM SP2 supercomputer.     

Parallel programming of a peridynamics code coupled with finite element method

Using OpenMP (the Open Multi- Processing application programming interface), dynamic peridynamics code coupled with a finite element method is parallelized. The parallel implementation improves run-time efficiency and makes the realistic simulation of crack coalescence possible. To assess the accuracy and efficiency of the parallel code, we investigate its speedup and scalability. In addition, to validate the parallel code, experimental results for crack coalescence development sequences are compared. It is noted that this parallelized code markedly reduces computation time along with the coupling scheme. Moreover, the coupling approach used in this parallel code enables a more realistic and feasible numerical prediction of coalescing fractures. With the parallel implementation, two main types of crack coalescences between two flaws, formed by two short shear cracks and by a short central tensile segment and subsequent shear cracks are in detail discussed in terms of their development sequences. Consequently, this proposed coupled peridynamics code can be used to efficiently solve actual coalescence development sequences, thereby providing a numerical solution for fracture mechanics.     

Fast Computation of Stationary Inviscid Flow Around an Airfoil

The parallel performance of an implicit solver for the Euler equations on a structured grid is discussed. The flow studied is a two-dimensional transonic flow around an airfoil. The spatial discretization involves the MUSCL scheme, a higher-order Total Variation Diminishing scheme. The solver described in this paper is an implicit solver that is based on quasi Newton iteration and approximate factorization to solve the linear system of equations resulting from the Euler Backward scheme. It is shown that the implicit time-stepping method can be used as a smoother to obtain an efficient and stable multigrid process. Also, the solver has good properties for parallelization comparable with explicit time-stepping schemes. To preserve data locality domain decomposition is applied to obtain a parallelizable code. Although the domain decomposition slightly affects the efficiency of the approximate factorization method with respect to the number of time steps required to attain the stationary solution, the results show that this hardly affects the performance for practical purposes. The accuracy with which the linear system of equations is solved is found to be an important parameter. Because the method is equally applicable for the Navier-Stokes equations and in three-dimensions, the presented combination of efficient parallel execution and implicit time-integration provides an interesting perspective for time-dependent problems in computational fluid dynamics.     

Parallel simulation of unsteady hovering rotor wakes

Numerical simulation using low diffusion schemes, for example free‐vortex or vorticity transport methods, and theoretical stability analyses have shown the wakes of rotors in hover to be unsteady. This has also been observed in experiments, although the instabilities are not always repeatable. Hovering rotor wake stability is considered here using a finite‐volume compressible CFD code. An implicit unsteady, multiblock, multigrid, upwind solver, and structured multiblock grid generator are presented, and applied to lifting rotors in hover. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed, and parallel performance using upto 1024 CPUs is presented. A four‐bladed rotor is considered, and it is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then performed, and also shows an unsteady wake. Detailed analysis of the time‐accurate wake history shows that three dominant unsteady modes are captured, for this four‐bladed case, with frequencies of one, four, and eight times the rotational frequency. A comparison with theoretical stability analysis is also presented. Copyright © 2006 John Wiley & Sons, Ltd.     

An U-ALE formulation of 3-D unsteady viscoelastic flow

The Arbitrary-Lagrange-Euler (ALE) formulation is applied to the analysis of unsteady viscoelastic flow of an Upper-Convected-Maxwell (UCM) medium. It is shown how the requirement of incremental objectivity affects the stress updating scheme. The current implementation of the ALE formulation uses the Time-Discontinuous/Galerkin-Least-Squares (TD/GLS) method to handle the advective parts of the equations. Further, the ALE formulation is compared with an Updated-ALE formulation that is shown to give comparable results but is much more cost effective. The technique presented is particularly effective for free surface flows. Three applications are given.     

基于 Pro/E 和 MasterCAM 的饮料瓶模具设计与数控加工

目的研究基于Pro/E和MasterCAM的包装容器模具设计及数控加工。方法以饮料瓶模具为例,利用Pro/E软件进行零件造型及模具结构设计,将图形文件转换到MasterCAM软件,详细分析了饮料瓶模具的加工工艺,确定了加工方案,分别对型腔粗加工、半精加工、精加工及清角加工设置了加工参数。结果通过几何建模、确定刀具路径、仿真加工和后置处理等,实现了对饮料瓶模具进行数控自动编程与仿真加工,得到了NC代码加工程序。结论将Pro/E和Mastercam结合使用,发挥各自优势功能,可以提高包装容器模具设计及其数控加工的质量和效率。