D.-A. An-Vo¹, C.-D. Tran¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.4, pp. 303-359, 2012, DOI:10.3970/cmes.2012.089.303

Abstract Many important engineering problems have multiple-scale solutions. Thermal conductivity of composite materials, flow in porous media, and turbulent transport in high Reynolds number flows are examples of this type. Direct numerical simulations for these problems typically require extremely large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we develop a high order computational method, based on multiscale basis function approach and integrated radialbasis- function (IRBF) approximant, for the solution of multiscale elliptic problems with reduced computational cost. Unlike other methods based on multiscale basis function approach, sets… More >

S. Turrin¹, M. Hanss¹, A.P.S. Selvadurai²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.3, pp. 237-258, 2009, DOI:10.3970/cmes.2009.052.237

Abstract Despite the continuing advances in rockfall analysis, the mathematical modeling and simulation of rockfall phenomena continues to be significantly influenced by a large amount of aleatory and epistemic uncertainty on significant number of model parameters. This paper focuses on the representation and quantification of epistemic uncertainties in rockfall modeling and simulation by fuzzy numbers. The propagation of the epistemic uncertainties considered is then calculated by the transformation method as a practical implementation of fuzzy arithmetic. Epistemic uncertainties on the material properties, on the boulder geometry and dimensions, on the kinematics of the impact and on the contact response between boulder… More >

Chan T.L.^1,2, Xie M.L.^1,3, Cheung C.S.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 191-212, 2009, DOI:10.3970/cmes.2009.051.191

Abstract An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It satisfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is much simpler than the method… More >

Z. Aksamija^1,2, U. Ravaioli³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.1, pp. 45-64, 2008, DOI:10.3970/cmes.2008.037.045

Abstract Finding the scalar potential from the Poisson equation is a common, yet challenging problem in semiconductor modeling. One of the central problems in traditional mesh-based methods is the assignment of charge to the regular mesh imposed for the discretisation. In order to avoid this problem, we create a mesh-free algorithm which starts by assigning each mesh point to each particle present in the problem. This algorithm is based on a Fourier series expansion coupled with point matching. An efficient algorithm for repeatedly solving the Poisson problem for moving charge distributions is presented. We demonstate that this approach is accurate and… More >

G.J.A. Loeven^1,2, H. Bijl³

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.3, pp. 193-212, 2008, DOI:10.3970/cmes.2008.036.193

Abstract In this paper a Two-Step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters. Both steps are performed using the Probabilistic Collocation method. The first step consists of a sensitivity analysis to identify the most important parameters of the problem. The sensitivity derivatives are obtained using a first or second order Probabilistic Collocation approximation. For the most important parameters the probability distribution functions are propagated using the Probabilistic Collocation method using higher order approximations. The Two-Step approach is demonstrated for flow around a NACA0012 airfoil with eight uncertain parameters in the free stream conditions and geometry.… More >

B. Yang², V. K. Tewary³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 165-178, 2006, DOI:10.3970/cmes.2006.015.165

Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has been developed previously for efficient… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 69-86, 2006, DOI:10.3970/cmes.2006.015.069

Abstract In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at t=0 and t=T in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(u₀,u_T) and the establishment of a mid-point Lie group element G(r). Then, by imposing G(u₀,u_T) = G(r) we can search the missing initial conditions through an iterative solution of the weighting factor r ∈ (0,1). Numerical examples were examined to convince that the new approach… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 77-90, 2006, DOI:10.3970/cmes.2006.014.077

Abstract In this paper we derive the first-order and second-order one-step GPS applied to the estimation of thermophysical properties. Solving the resultant algebraic equations, which usually converges within ten iterations, it is not difficult to estimate the unknown temperature-dependent thermal conductivity and heat capacity simultaneously, if some supplemented data of measured temperature at a time T is provided. When the measured temperature in the conducting slab is contaminated by noise, our estimated results are also good. The new method does not require any prior information on the functional forms of thermal conductivity and heat capacity. Numerical examples are examined to show… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 55-66, 2006, DOI:10.3970/cmes.2006.012.055

Abstract In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserving scheme (BGPS) for the semi-discretization of Burgers equation. The one-step BGPS is very effectively to calculate the solution at an initial time t = 0 from a given final data at t = T, which with a time stepsize equal to T and with a suitable grid length produces a highly accurate solution never seen before. Under noisy final data the BGPS is also robust to against the disturbance. When the solution appears steep gradient, several steps… More >

Wanil Byun¹, Seung Jo Kim²

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.6, pp. 551-576, 2012, DOI:10.3970/cmes.2012.086.551

Abstract A structural eigensolver for large-scale finite element analysis is developed. The algorithms and data structures implemented in this paper are well suited for a distributed memory environment. As an eigenvalue extracting algorithm, the well-known M orthogonal block Lanczos iteration incorporated with a parallel multifrontal solver (PMFS) was chosen. Basically, for the better performance of this algorithm in parallel computation, Lanczos vector allocation, mass matrix multiplication, and M inner product procedures were efficiently implemented. And the PMFS for a linear equation which is the most time-consuming part during Lanczos iterations was improved. The idea was to optimize network topologies of parallel… More >