Peter Lucas¹, Alexander H. van Zuijlen¹, Hester Bijl¹

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 79-106, 2010, DOI:10.3970/cmes.2010.059.079

Abstract Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.
In previous work [Lucas, P.,Bijl, H., and Zuijlen, A.H. van(2010)], we have shown that a Jacobian-free Newton-Krylov (JFNK) algorithm, preconditioned with an approximate factorization of the Jacobian which approximately matches the target residual operator, enables a speed up of a factor of 10 compared to nonlinear multigrid (NMG) for two-dimensional, large Reynolds number, unsteady flow computations. Furthermore, in [Lucas, P., Zuijlen, A.H. van, and Bijl, H. (2010)] we show that this algorithm also greatly… More >

K. Han¹, Y. T. Feng¹, D. R. J. Owen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 1-30, 2010, DOI:10.3970/cmes.2010.059.001

Abstract A computational framework is established for effective modelling of fluid-thermal-particle interactions. The numerical procedures comprise the Discrete Element Method for simulating particle dynamics; the Lattice Boltzmann Method for modelling the mass and velocity field of the fluid flow; and the Discrete Thermal Element Method and the Thermal Lattice Boltzmann Method for solving the temperature field. The coupling of the three fields is realised through hydrodynamic interaction force terms. Selected numerical examples are provided to illustrate the applicability of the proposed approach. More >

A. Frangi¹, M. Bonnet²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 271-296, 2010, DOI:10.3970/cmes.2010.058.271

Abstract This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number N of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For β ≥ 1 it More >

J. Tausch¹, J. Xiao²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.058.221

Abstract A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is discretized by a Nyström method and is evaluated efficiently using a sequence of FFTs. The potential due to the local part is approximated by a truncated series in the mollification parameter. The smooth approximation of the kernel is obtained by multiplication of its Fourier transform with a filter. We will show that for a rational More >

A. Papacharalampopoulos², G. F. Karlis², A. Charalambopoulos³, D. Polyzos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 45-74, 2010, DOI:10.3970/cmes.2010.058.045

Abstract A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain More >

Lorenzo Codecasa¹, Francesco Trevisan²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 15-44, 2010, DOI:10.3970/cmes.2010.058.015

Abstract This paper starts from the spatial discretization of an electromagnetic problem over pairs of oriented grids, one dual of the other, according to the so called Discrete Geometric Approach(DGA) to computational electromagnetism; the Cell Method or the Finite Integration Technique are examples of such an approach. The core of the work is providing for the first time a convergence analysis when the discrete counter-parts of constitutive relations are computed by means of an energetic framework. More >

E. J. Sellountos¹, A. Sequeira¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.2, pp. 109-136, 2010, DOI:10.3970/cmes.2010.057.109

Abstract A new Local Boundary Integral Equation (LBIE) method is proposed for the solution of plane elastostatic problems. Non-uniformly distributed points taken from a Finite Element Method (FEM) mesh cover the analyzed domain and form background cells with more than four points each. The FEM mesh determines the position of the points without imposing any connectivity requirement. The key-point of the proposed methodology is that the support domain of each point is divided into parts according to the background cells. An efficient Radial Basis Functions (RBF) interpolation scheme is exploited for the representation of displacements in More >

M. Kashtalyan^1,2, Y.A. Zhuk³

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 1-30, 2010, DOI:10.3970/cmes.2010.057.001

Abstract The paper investigates propagation of stationary plane longitudinal and transverse waves along the layers in adhesively bonded multilayered structures for MEMS applications in the presence of residual stresses. The multilayered structure is assumed to consist of the infinite amount of the periodically recurring layers made of two different materials possessing significantly dissimilar properties: conductive metal layer and insulating adhesive layer. It is assumed that the mechanical behaviour of both materials is nonlinear elastic and can be described with the help of the elastic Murnaghan potential depending on the three invariants of strain tensor. The problem More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 85-112, 2010, DOI:10.3970/cmes.2010.056.085

Abstract We propose a novel technique, transforming the generalized SturmLiouville problem: w'' + q(x,λ)w = 0, a₁(λ)w(0) + a₂(λ)w'(0) = 0, b₁(λ)w(1) + b₂(λ)w'(1) = 0 into a canonical one: y'' = f, y(0) = y(1) = c(λ). Then we can construct a very effective Lie-group shooting method (LGSM) to compute eigenvalues and eigenfunctions, since both the left-boundary conditions y(0) = c(λ) and y'(0) = A(λ) can be expressed explicitly in terms of the eigen-parameter λ. Hence, the eigenvalues and eigenfunctions can be easily calculated with better accuracy, by a finer adjusting of λ to match the right-boundary condition y(1) = c(λ). Numerical examples More >

S. Hartmann¹, R. Weyler², J. Oliver¹, J.C. Cante², J.A. Hernández¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 211-270, 2010, DOI:10.3970/cmes.2010.055.211

Abstract This work describes a three-dimensional contact domain method for large deformation frictionless contact problems. Theoretical basis and numerical aspects of this specific contact method are given in [Oliver, Hartmann, Cante, Weyler and Hernández (2009)] and [Hartmann, Oliver, Weyler, Cante and Hernández (2009)] for two-dimensional, large deformation frictional contact problems. In this method, in contrast to many other contact formulations, the necessary contact constraints are formulated on a so-called contact domain, which can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. This contact domain has the same dimension More >