K. Le-Cao¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.3, pp. 265-294, 2010, DOI:10.3970/cmes.2010.067.265

Abstract In this paper, radial basis functions are utilised for numerical prediction of the bulk properties of particulate suspensions under simple shear conditions. The suspending fluid is Newtonian and the suspended particles are rigid. Results obtained are compared well with those based on finite elements in the literature. More >

Roland Martin¹, Carlos Couder-Castaneda¹

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.1, pp. 47-78, 2010, DOI:10.3970/cmes.2010.063.047

Abstract We develop an unsplit convolutional perfectly matched layer (CPML) technique to absorb efficiently compressible viscous flows and their related supersonic or subsonic regimes at the outer boundary of a distorted computational domain. More particularly subsonic outgoing flows or subsonic wall-boundary layers close to the PML are well absorbed, which is difficult to obtain without creating numerical instabilities over long time periods. This new PML (CPML) introduces the calculation of auxiliary memory variables at each time step and allows an unsplit formulation of the PML. Damping functions involving a high shift in the frequency domain allow… More >

L. Távara¹, V. Manticˇ ¹, E. Graciani¹, J. Cañas¹, F. París¹

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 247-270, 2010, DOI:10.3970/cmes.2010.058.247

Abstract The problem of a crack in a thin adhesive layer is considered. The adherents may have orthotropic elastic behavior which allows composite laminates to be modeled. In the present work a linear elastic-brittle constitutive law of the thin adhesive layer, called weak interface model, is adopted, allowing an easy modeling of crack propagation along it. In this law, the normal and tangential stresses across the undamaged interface are proportional to the relative normal and tangential displacements, respectively. Interface crack propagation is modeled by successive breaking of the springs used to discretize the weak interface. An… 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 >

Waipot Ngamsaad, Wannapong Triampo¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.2, pp. 49-50, 2009, DOI:10.3970/icces.2009.013.049

Abstract The Min-proteins oscillation in \emph {E. coli} has an essential role in controlling the accuracy placement of cell-division septum at the middle cell zone of the bacteria. This biochemical process has been successfully described by a set of reaction-diffusion equation at the macroscopic level [1]. Recently, a mesoscopic modeling by the lattice Boltzmann method (LBM) has been proposed to simulate the Min-proteins oscillation [2]. However, as pointed out by Zhang et al., the standard boundary conditions are not accuracy for a class of dispersion transport modeled by LBM [3]. In this present work, we investigated More >

Chih-Fung Ho¹, Cheng Chang¹, Kuen-Hau Lin¹, Chao-An Lin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 137-156, 2009, DOI:10.3970/cmes.2009.044.137

Abstract Consistent formulations of 2D and 3D pressure and velocity boundary conditions along both the stationary and non-stationary plane wall and corner for lattice Boltzmann simulations are proposed. The unknown distribution functions are made function of local known distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definitions of density and momentum. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. Discrete macroscopic equation is also derived for steady fully developed channel flow to assess the effect of the boundary condition… More >

D. L. Young^1,3, K. H. Chen², T. Y. Liu³, L. H. Shen³, C. S. Wu³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 225-270, 2009, DOI:10.3970/cmes.2009.040.225

Abstract In this article, a hypersingular meshless method (HMM) is extended to solve 3D potential problems for arbitrary domains after a 2D model was successfully developed (Young et al. 2005a). The solutions are represented by a distribution of the double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions (MFS). By using the desingularization technique to regularize the singularity and hypersingularity of the double layer potentials, the source points can be located exactly on the real boundary to avoid the sensitivity of locating fictitious boundary for putting… More >

R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 274-304, 2008, DOI:10.3970/cmes.2008.037.274

Abstract In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work… More >

Meiling Zhao¹, Yufeng Nie²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 97-112, 2008, DOI:10.3970/cmes.2008.037.097

Abstract Meshless local Petrov-Galerkin (MLPG) method is successfully applied for electromagnetic field computations. The moving least square technique is used to interpolate the trial and test functions. More attention is paid to imposing the essential boundary conditions of electromagnetic equations. A new coupled meshless local Petrov-Galerkin and finite element (MLPG-FE) method is presented to enforce the essential boundary conditions. Unlike the conventional coupled technique, this approach can ensure the smooth blending of the potential variables as well as their derivatives in the transition region between the meshless and finite element domains. Then the boundary singular weight More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 227-252, 2008, DOI:10.3970/cmes.2008.034.227

Abstract A new numerical technique for solving generalized Sturm--Liouville problem d²w/dx² + q(x, λ )w = 0, b_l[ λ ,w(a)] = b_r[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues. The same technique can be applied to a very wide class of More >