Open Access
ARTICLE
R. Zakhama1,2,3, M.M. Abdalla2, H. Smaoui1,3, Z. Gürdal2
CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.051.001
Abstract A multigrid accelerated cellular automata algorithm for two and three dimensional continuum topology optimization problems is presented. The topology optimization problem is regularized using the traditional SIMP approach. The analysis rules are derived from the principle of minimum total potential energy, and the design rules are derived based on continuous optimality criteria interpreted as local Kuhn-Tucker conditions. Three versions of the algorithm are implemented; a cellular automata based design algorithm, a baseline multigrid algorithm for analysis acceleration and a full multigrid integrated analysis and design algorithm. It is shown that the multigrid accelerated cellular automata scheme is a powerful tool… More >
Open Access
ARTICLE
Tae-Hyuk Ahn1, Layne T. Watson1,2, Yang Cao1,1, Clifford A. Shaffer1, William T. Baumann3
CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 27-52, 2009, DOI:10.3970/cmes.2009.051.027
Abstract For biochemical systems, where some chemical species are represented by small numbers of molecules, discrete and stochastic approaches are more appropriate than continuous and deterministic approaches. The continuous deterministic approach using ordinary differential equations is adequate for understanding the average behavior of cells, while the discrete stochastic approach accurately captures noisy events in the growth-division cycle. Since the emergence of the stochastic simulation algorithm (SSA) by Gillespie, alternative algorithms have been developed whose goal is to improve the computational efficiency of the SSA. This paper explains and empirically compares the performance of some of these SSA alternatives on a realistic… More >
Open Access
ARTICLE
G.S. Li1, D. Yao2, Y.Z. Wang3, H.Y. Jiang2
CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 53-72, 2009, DOI:10.3970/cmes.2009.051.053
Abstract In this paper, an undisturbed soil-column infiltrating experiment is investigated, and a mathematical model describing multi-components solutes transport behaviors in the column is put forward by combing hydro-chemical analysis with advection dispersion mechanisms, which is a group of advection-dispersion-reaction partial differential equations. Since the model involving six reaction coefficients which can not be obtained directly, an optimal perturbation regularization algorithm of determining these parameters is performed, and numerical simulations under different conditions are carried out. Furthermore, the inversion algorithm is applied to solve the real inverse problem by utilizing the measured breakthrough data. The reconstruction data basically coincide with the… More >
Open Access
ARTICLE
Rubén Avila1, Eduardo Ramos2, S. N. Atluri3
CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 73-92, 2009, DOI:10.3970/cmes.2009.051.073
Abstract A Chebyshev Tau numerical algorithm is presented to solve the perturbation equations that result from the linear stability analysis of the convective motion of a fluid layer that appears when an unconfined solid melts in the presence of gravity. The system of equations that describe the phenomenon constitute an eigenvalue problem whose accurate solution requires a robust method. We solve the equations with our method and briefly describe examples of the results. In the limit where the liquid-solid interface recedes at zero velocity the Rayleigh-Bénard solution is recovered. We show that the critical Rayleigh number Rac and the critical wave… More >
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