Open Access
ARTICLE
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 >
Open Access
ARTICLE
P.D.Gosling1,2, L. Zhang2
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 203-252, 2011, DOI:10.3970/cmes.2011.071.203
Abstract The analysis of a continuum membrane by means of a discrete network of cables or bars is an efficient and readily tractable approach to the solution of a complex mechanics problem. However, is so doing, compromises are made in the quality of the approximation of the strain field. It is shown in this paper that the original form of the cable-analogy continuum triangle formulation is degraded by an inherent assumption of small strains in the underlying equations, in which the term ßmall" is shown to be "negligibly small". A revised version of this formulation is proposed in which a modification… More >
Open Access
ARTICLE
B. Ren1,2, J. Qian1, X. Zeng1, A. K. Jha3, S. Xiao4, S. Li1,5
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 253-278, 2011, DOI:10.3970/cmes.2011.071.253
Abstract Ductile failure is a complex multi-scale phenomenon evolved from the micro-voids to macro-crack. There are three main failure mechanisms behinds a ductile failure: adiabatic shear band (ASB), spall fracture, and crack. Since this type of thermo-mechanical phenomena involves large deformation and large scale plastic yielding, a meshfree method has intrinsic advantages in solving this kind of problems over the conventional finite element method. In this paper, the numerical methodologies including multi-physics approach for ASB, parametric visibility condition for crack propagation, and multi-scale approach to determine spall strength in simulating ductile failure have been reviewed. A thermo-mechanical coupling algorithm is proposed… More >
Open Access
ARTICLE
Chein-Shan Liu1, Satya N. Atluri2
CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 279-304, 2011, DOI:10.3970/cmes.2011.071.279
Abstract For solving a system of nonlinear algebraic equations (NAEs) of the type: F(x)=0, or Fi(xj) = 0, i,j = 1,...,n, a Newton-like algorithm has several drawbacks such as local convergence, being sensitive to the initial guess of solution, and the time-penalty involved in finding the inversion of the Jacobian matrix ∂Fi/∂xj. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we can derive a gradient-flow system of nonlinear ordinary differential equations (ODEs) governing the evolution of x with a fictitious time-like variable t as an independent variable. We can prove… More >
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