Xiao Zhao¹, Haitian Yang^1,2, Qiang Gao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.2, pp. 139-160, 2011, DOI:10.3970/cmes.2011.074.139

Abstract A piecewised adaptive algorithm in the time domain is presented to solve the transient convection-diffusion heat transfer problem. By expanding all variables at a time interval, an initial and boundary value problem is decoupled into a series of recursive boundary value problems which can be solved by FEM or other well developed numerical schemes to deal with boundary value problems. A steady computing accuracy can be adaptively maintained via the power increase of the expansion, particularly when the step size varies in the whole computing process. Additionally for the nonlinear cases, there is no requirement of iteration and additional assumption… More >

R. Djebali¹, M. El Ganaoui²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 179-202, 2011, DOI:10.3970/cmes.2011.071.179

Abstract The Lattice Boltzmann method (LBM) became, today, a powerful tool for simulating fluid flows. Its improvements for different applications and configurations offers more flexibility and results in several schemes such as in presence of external/internal forcing term. However, we look for the suitable model that gives correct informations, matches the hydrodynamic equations and preserves some features like coding easily, preserving computational cost, stability and accuracy. In the present work, high order incompressible models and equilibrium distribution functions for the advection-diffusion equations are analyzed. Boundary conditions, acceleration, stability and preconditioning with initial fields are underlined which permit to rigorously selecting two… More >

Han-Taw Chen¹, Li-Shie Liu¹, Shin-Ku Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 155-178, 2010, DOI:10.3970/cmes.2010.065.155

Abstract The finite difference method in conjunction with the least-squares scheme and experimental measured temperatures is proposed to solve a two-dimensional steady-state inverse heat conduction problem in order to predict the natural-convection heat transfer coefficient under the isothermal situation h^−iso from a three fin array mounted on a horizontal plate and fin efficiency η_f for various values of the fin spacing and fin height. The measured fin temperatures and ambient temperature are obtained from the present experimental apparatus conducted in a small wind tunnel. The heat transfer coefficient on a fin is non-uniform for the present problem, and its functional… More >

Hao-Chueh Mai¹, Kuen-Hau Lin¹, Cheng-Hsiu Yang¹, Chao-An Lin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 45-62, 2010, DOI:10.3970/cmes.2010.061.045

Abstract A thermal BGK lattice Boltzmann model for flows with viscous heat dissipation is proposed. In this model, the temperature is solved by a separate thermal distribution function, where the equilibrium distribution function is similar to its hydrodynamic counterpart, except that the leading quantity is temperature. The viscous dissipation rate is obtained by computing the second-order moments of non-equilibrium distribution function, which avoids the discretization of the complex gradient term, and can be easily implemented. The proposed thermal lattice Boltzmann model is scrutinized by computing two-dimensional thermal Poiseuille flow, thermal Couette flow, natural convection in a square cavity, and three-dimensional thermal… More >

Han Taw Chen¹, Shao Lun Sun¹, Hui Chen Huang¹, Sen Yung Lee^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 107-126, 2010, DOI:10.3970/cmes.2010.059.107

Abstract A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for the one term approximation solution… More >

Dan Gordon¹, Rachel Gordon²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 23-46, 2009, DOI:10.3970/cmes.2009.053.023

Abstract Linear systems with very large off-diagonal elements and discontinuous coefficients (LODC systems) arise in some modeling cases, such as those involving heterogeneous media. Such problems are usually solved by domain decomposition methods, but these can be difficult to implement on unstructured grids or when the boundaries between subdomains have a complicated geometry. Gordon and Gordon have shown that Björck and Elfving's (sequential) CGMN algorithm and their own block-parallel CARP-CG are very robust and efficient on strongly convection dominated cases (but without discontinuous coefficients). They have also shown that scaling the equations by dividing each equation by the L2-norm of its… More >

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 Ra_c and the critical wave… More >

Gerardo Anguiano-Orozco^1,2, Rubén Avila³

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.3, pp. 217-254, 2009, DOI:10.3970/cmes.2009.049.217

Abstract A numerical investigation of the transient, three dimensional, laminar natural convection of a fluid confined in a spherical container is carried out. Initially the fluid is quiescent with a uniform temperature T_i equal to the temperature of the wall of the container. At time t=0, the temperature of the wall is suddenly lowered to a uniform temperature T_w=0. The natural convection, that conducts to a vortex ring formation within the sphere, is driven by a terrestrial gravity force (laboratory gravity) and by the step change in the temperature of the wall. A scaling analysis of a simplified transient, two dimensional… More >

Alfredo Nicolás¹, Blanca Bermúdez², Elsa Báez³

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 83-106, 2009, DOI:10.3970/cmes.2009.048.083

Abstract Numerical results of natural convection flows in two-dimensional cavities, filled with air, are presented to study the effects on the characteristics of the flows as some parameters vary: the Rayleigh number Ra and the aspect ratio A of the cavity. This kind of thermal flows may be modeled by the unsteady Boussinesq approximation in stream function-vorticity variables. The results are obtained with a simple numerical scheme, previously reported for isothermal/mixed convection flows, based mainly on a fixed point iterative process applied to the non-linear elliptic system that results after time discretization. The evolution of the flows, mainly flows converging to… More >

Gang Lin¹, Yinghua Liu^1,2, Zhihai Xiang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.3, pp. 217-252, 2009, DOI:10.3970/cmes.2009.047.217

Abstract Deterioration of reinforced concrete (RC) structures due to chloride ingress followed by reinforcement corrosion is a serious problem all over the world, therefore prediction of chloride profiles is a key element in evaluating durability and integrity of RC structures exposed to chloride environment. In the present paper, an integrated finite element-based computational framework is developed for predicting service life of RC structures exposed to chloride environment, which takes environment temperature and humidity fluctuations, diffusion and convection, chloride binding, as well as the decay of durability of structures caused by coupled deterioration processes into account. The decay of RC structures due… More >