CMES-Vol. 7, No. 2, 2005

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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 >

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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 >

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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 >

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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 >

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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 >

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Computation of Incompressible Navier-Stokes Equations by Local RBF-based Differential Quadrature Method
C. Shu^1,2, H. Ding², K.S. Yeo²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195
Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric More >

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Using radial basis functions in a ''finite difference mode''
A.I.Tolstykh, D.A. Shirobokov¹
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 207-222, 2005, DOI:10.3970/cmes.2005.007.207
Abstract A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good$h$-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered. More >

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Method of Fundamental Solutions for Scattering Problems of Electromagnetic Waves
D.L. Young^1,2, J.W. Ruan²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 223-232, 2005, DOI:10.3970/cmes.2005.007.223
Abstract The applications of the method of fundamental solutions (MFS) for modeling the scattering of time-harmonic electromagnetic fields, which are governed by vector Helmholtz equations with coupled boundary conditions, are described. Various perfectly electric conductors are considered as the scatterers to investigate the accuracy of the numerical performance of the proposed procedure by comparing with the available analytical solutions. It is also the intention of this study to reveal the characteristics of the algorithms by comparisons with other numerical methods. The model is first validated to the exact solutions of the electromagnetic wave propagation problems for More >

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