CMES-Vol. 104, No. 1, 2015

Open Access

ARTICLE

Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large Noise
Chein-Shan Liu¹, Satya N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 1-39, 2015, DOI:10.3970/cmes.2015.104.001
Abstract A double optimal solution of an n-dimensional system of linear equations Ax = b has been derived in an affine m « n. We further develop a double optimal iterative algorithm (DOIA), with the descent direction z being solved from the residual equation Az = r₀ by using its double optimal solution, to solve ill-posed linear problem under large noise. The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||² = ||b - Ax||² being reduced by a positive quantity ||Az_k||² at each iteration step, which is found to be better than those algorithms based More >

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ARTICLE

Numerical Simulation of Bubble Formation at a Single Orifice in Gas-fluidized Beds with Smoothed Particle Hydrodynamics and Finite Volume Coupled Method
F.Z. Chen^1,2, H.F. Qiang¹, W.R. Gao¹
CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 41-68, 2015, DOI:10.3970/cmes.2015.104.041
Abstract A coupled method describing gas-solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds. Solid particles are traced with smoothed particle hydrodynamics, whereas gas phase is discretized by finite volume method. Drag force, gas pressure gradient, and volume fraction are used to couple the two methods. The effect of injection velocities, particle sizes, and particle densities on bubble growth is analyzed using the coupled method. The simulation results, obtained for two-dimensional geometries, include the shape and diameter size of a bubble as a function of time; More >

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Numerical Study for a Class of Variable Order Fractional Integral-differential Equation in Terms of Bernstein Polynomials
Jinsheng Wang¹, Liqing Liu², Yiming Chen², Lechun Liu², Dayan Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.1, pp. 69-85, 2015, DOI:10.3970/cmes.2015.104.069
Abstract The aim of this paper is to seek the numerical solution of a class of variable order fractional integral-differential equation in terms of Bernstein polynomials. The fractional derivative is described in the Caputo sense. Four kinds of operational matrixes of Bernstein polynomials are introduced and are utilized to reduce the initial equation to the solution of algebraic equations after dispersing the variable. By solving the algebraic equations, the numerical solutions are acquired. The method in general is easy to implement and yields good results. Numerical examples are provided to demonstrate the validity and applicability of More >

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