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  • Open Access


    On the Efficiency of the Parallel-in-Time Finite Volume Calculation of the Unsteady Navier-Stokes Equations

    J. M. F. Trindade1, J. C. F. Pereira2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 1-10, 2007, DOI:10.3970/cmes.2007.020.001

    Abstract In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model… More >

  • Open Access


    Fracture Analyses in Continuously Nonhomogeneous Piezoelectric Solids by the MLPG

    J. Sladek1, V. Sladek1, Ch. Zhang2, P. Solek3, L. Starek3

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 247-262, 2007, DOI:10.3970/cmes.2007.019.247

    Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals on the surfaces of subdomains.… More >

  • Open Access


    In Vivo/Ex Vivo MRI-Based 3D Non-Newtonian FSI Models for Human Atherosclerotic Plaques Compared with Fluid/Wall-Only Models

    Chun Yang1, Dalin Tang2, Chun Yuan3, Thomas S. Hatsukami4, Jie Zheng5, Pamela K. Woodard5

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 233-246, 2007, DOI:10.3970/cmes.2007.019.233

    Abstract It has been recognized that fluid-structure interactions (FSI) play an important role in cardiovascular disease initiation and development. However, in vivo MRI multi-component FSI models for human carotid atherosclerotic plaques with bifurcation and quantitative comparisons of FSI models with fluid-only or structure-only models are currently lacking in the literature. A 3D non-Newtonian multi-component FSI model based on in vivo/ex vivo MRI images for human atherosclerotic plaques was introduced to investigate flow and plaque stress/strain behaviors which may be related to plaque progression and rupture. Both artery wall and plaque components were assumed to be hyperelastic, isotropic, incompressible and homogeneous. Blood… More >

  • Open Access


    Improved Velocity Projection for the Material Point Method

    P. C. Wallstedt1, J. E. Guilkey1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 223-232, 2007, DOI:10.3970/cmes.2007.019.223

    Abstract The standard velocity projection scheme for the Material Point Method (MPM) and a typical form of the GIMP Method are examined. It is demonstrated that the fidelity of information transfer from a particle representation to the computational grid is strongly dependent on particle density and location. In addition, use of non-uniform grids and even non-uniform particle sizes are shown to introduce error. An enhancement to the projection operation is developed which makes use of already available velocity gradient information. This enhancement facilitates exact projection of linear functions and reduces the dependence of projection accuracy on particle location and density for… More >

  • Open Access


    A Modified Method of Fundamental Solutions with Source on the Boundary for Solving Laplace Equations with Circular and Arbitrary Domains

    D.L. Young1, K.H. Chen2, J.T. Chen3, J.H. Kao4

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 197-222, 2007, DOI:10.3970/cmes.2007.019.197

    Abstract A boundary-type method for solving the Laplace problems using the modified method of fundamental solutions (MMFS) is proposed. The present method (MMFS) implements the singular fundamental solutions to evaluate the solutions, and it can locate the source points on the real boundary as contrasted to the conventional MFS, where a fictitious boundary is needed to avoid the singularity of diagonal term of influence matrices. The diagonal term of influence matrices for arbitrary domain can be novelly determined by relating the MFS with the indirect BEM and are also solved for circular domain analytically by using separable kernels and circulants. The… More >

  • Open Access


    Mesoscopic Simulation of Binary Immiscible Fluids Flow in a Square Microchannel with Hydrophobic Surfaces

    S. Chen1,2, Y. Liu1,3, B.C. Khoo4, X.J. Fan5, J.T. Fan6

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 181-196, 2007, DOI:10.3970/cmes.2007.019.181

    Abstract The mesoscopic simulation for fluids flow in a square microchannel is investigated using dissipative particle dynamics. The velocity distribution for single fluid in a square channel is compared with the solutions of CFD solver, which is found to be in good agreement with each other. The no-slip boundary condition could be well held for the repulsive coefficient ranged from 9.68 to 18.0. For the same range of repulsive coefficient, various wettabilities could be obtained by changing the repulsive coefficient for binary immiscible fluids, in which the immiscible fluids are achieved by increasing the repulsive force between species. The typical motion… More >

  • Open Access


    On the Modelling of Rate-Dependent Domain Switching in Piezoelectric Materials under Superimposed Stresses

    A. Arockiarajan1, A. Menzel2

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 163-178, 2007, DOI:10.3970/cmes.2007.019.163

    Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic approach -- a purely phenomenologically… More >

  • Open Access


    A MRIEM for Solving the Laplace Equation in the Doubly-Connected Domain

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 145-162, 2007, DOI:10.3970/cmes.2007.019.145

    Abstract A new method is developed to solve the Dirichlet problems for the two-dimensional Laplace equation in the doubly-connected domains, namely the meshless regularized integral equations method (MRIEM), which consists of three portions: Fourier series expansion, the Fredholm integral equations, and linear equations to determine the unknown boundary conditions onartificial circles. The boundary integral equations on artificial circles are singular-free and the kernels are degenerate. When boundary-type methods are inefficient to treat the problems with complicated domains, the new method can be applicable for such problems. The new method by using the Fourier series and the Fourier coefficients can be adopted… More >

  • Open Access


    The Parallel Mechanism of Node-Based Seamless Finite Element Method

    Y.F. Nie1, S. Chang1, X.K. Fan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 135-144, 2007, DOI:10.3970/cmes.2007.019.135

    Abstract A new parallel mechanism for Node-based Seamless Finite Element Method was proposed in this paper, which possessed the following three prominent points: realizing the workload balance for the parallel processes naturally, achieving synchronization of all the schedules under complex parallel environment, and filling up the gap between pre-processing and main processing. To support the scheme, three specific solutions of the parallel mechanism were proposed in this paper, all of which achieved the highly efficient parallel seamless connection between the FEM mesh generation process and structure analysis process. Two of the three schemes, i.e. dynamic scheme and self-adaptive scheme, enabled both… More >

  • Open Access


    Molecular Mechanics Based Finite Element For Carbon Nanotube Modeling

    T.C. Theodosiou1, D.A. Saravanos2

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 121-134, 2007, DOI:10.3970/cmes.2007.019.121

    Abstract In this paper a new method is introduced for carbon nanotube modeling combining features of Molecular Mechanics and Finite Element Analysis. Repetitive atomic cells are treated as finite elements, whose internal energy is determined by the semi-empirical Brenner molecular potential model; internal forces and linearized stiffness matrices are formulated analytically in order to gain in speed and accuracy, and the resultant discrete system is formulated and solved using the Newton-Raphson method. The presented method is validated through comparisons to numerical and experimental results provided by other researchers. The bending and shearing of CNTs is also simulated. More >

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