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  • Open Access

    ARTICLE

    A Radial Basis Function Collocation Approach in Computational Fluid Dynamics

    B. Šarler1

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 185-194, 2005, DOI:10.3970/cmes.2005.007.185

    Abstract This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady More >

  • Open Access

    ARTICLE

    On the use of a wave based prediction technique for steady-state structural-acoustic radiation analysis

    B. Pluymers1, W. Desmet1, D. Vandepitte1, P. Sas1

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 173-184, 2005, DOI:10.3970/cmes.2005.007.173

    Abstract Conventional element based methods for modelling structural-acoustic radiation problems are limited to low-frequency applications. Recently, a novel prediction technique has been developed based on the indirect Trefftz approach. This new wave based method is computationally more efficient than the element based methods and, as a consequence, can tackle problems also at higher frequencies. This paper discusses the basic principles of the new method and illustrates its performance for the two-dimensional radiation analysis of a bass-reflex loudspeaker. More >

  • Open Access

    ARTICLE

    A Meshless IRBFN-based Method for Transient Problems

    L. Mai-Cao1, T. Tran-Cong2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

    Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some More >

  • Open Access

    ARTICLE

    Two-Phase Flow Simulation by AMMoC, an Adaptive Meshfree Method of Characteristics

    Armin Iske1, Martin Käser2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 133-148, 2005, DOI:10.3970/cmes.2005.007.133

    Abstract Petroleum reservoir modelling requires effective multiscale methods for the numerical simulation of two-phase flow in porous media. This paper proposes the application of a novel meshfree particle method to the Buckley-Leverett model. The utilized meshfree advection scheme, called AMMoC, is essentially a method of characteristics, which combines an adaptive semi-Lagrangian method with local meshfree interpolation by polyharmonic splines. The method AMMoC is applied to the five-spot problem, a well-established model problem in petroleum reservoir simulation. The numerical results and subsequent numerical comparisons with two leading commercial reservoir simulators, ECLIPSE and FrontSim, show the good performance of More >

  • Open Access

    ARTICLE

    The method of fundamental solution for solving multidimensional inverse heat conduction problems

    Y.C. Hon1, T. Wei2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 119-132, 2005, DOI:10.3970/cmes.2005.007.119

    Abstract We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply the Tikhonov regularization method based on the generalized cross-validation criterion for choosing the regularization parameter to obtain a stable approximation to the solution. The effectiveness of the algorithm is illustrated by several numerical two- and More >

  • Open Access

    ARTICLE

    Predicting Wave Run-Up using Full ALE Finite Element Approach considering Moving Boundary

    Shahin Zohouri1, Moharram D. Pirooz2, Asad Esmaeily3

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 107-118, 2005, DOI:10.3970/cmes.2005.007.107

    Abstract A numerical scheme is developed to predict the wave run-up of an unsteady, incompressible viscous flow with free surface by the author$^1$. The method involves a two dimensional finite element with moving boundaries. The governing equations were the Navier-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation. A mapping algorithm was developed to solve highly deformed free surface problems, common in wave propagation. This algorithm transforms the run up model from the physical domain to a computational domain. A new Arbitrary Lagrangian-Eulerian (ALE) finite element More >

  • Open Access

    ARTICLE

    Investigation on the Normal Derivative Equation of Helmholtz Integral Equation in Acoustics

    Zai You Yan1,2, Fang Sen Cui2, Kin Chew Hung2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 97-106, 2005, DOI:10.3970/cmes.2005.007.097

    Abstract Taking the normal derivative of solid angles on the surface into account, a modified Burton and Miller's formulation is derived. From which, a more reasonable expression of the hypersingular operator is obtained. To overcome the hypersingular integral, the regularization scheme developed recently is employed. Plane acoustic wave scattering from a rigid sphere is computed to show the correctness of the modified formulation with the regularization scheme. In the computation, eight-nodded isoparametric element is applied. More >

  • Open Access

    ARTICLE

    A New Fast Multipole Boundary Element Method for Large Scale Analysis of Mechanical Properties in 3D Particle-Reinforced Composites

    Haitao Wang1, Zhenhan Yao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 85-96, 2005, DOI:10.3970/cmes.2005.007.085

    Abstract This paper addresses a new boundary element method (BEM) for the numerical analysis of mechanical properties in 3D particle-reinforced composites. The BEM is accelerated by a new version fast multipole method (FMM) in order to perform large scale simulation of a representative volume element (RVE) containing up to several hundred randomly distributed elastic spherical particles on only one personal computer. The maximum number of degrees of freedom (DOF) reaches more than 300,000. Efficiency of the developed new version fast multipole BEM code is evaluated compared with other conventional solutions for BEM. The effects of micro-structural More >

  • Open Access

    ARTICLE

    Local Integral Equations and two Meshless Polynomial Interpolations with Application to Potential Problems in Non-homogeneous Media

    V. Sladek1, J. Sladek1, M. Tanaka2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 69-84, 2005, DOI:10.3970/cmes.2005.007.069

    Abstract An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material coefficients. The method is based on the local integral equations (utilizing a fundamental solution) and meshfree approximation of field variable. A lot of numerical experiments are carried out in order to study the numerical stability, accuracy, convergence and efficiency of several approaches utilizing various interpolations. More >

  • Open Access

    ARTICLE

    A Tangent Stiffness MLPG Method for Atom/Continuum Multiscale Simulation

    Shengping Shen1, S. N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 49-68, 2005, DOI:10.3970/cmes.2005.007.049

    Abstract The main objective of this paper is to develop a multiscale method for the static analysis of a nano-system, based on a combination of molecular mechanics and MLPG methods. The tangent-stiffness formulations are given for this multiscale method, as well as a pure molecular mechanics method. This method is also shown to naturally link the continuum local balance equation with molecular mechanics, directly, based on the stress or force. Numerical results show that this multiscale method quite accurate. The tangent-stiffness MLPG method is very effective and stable in multiscale simulations. This multiscale method dramatically reduces More >

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