Table of Content

03 July 2013, Volume 34 Issue 7

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Articles

Fast precise integration method for hyperbolic heat conduction problems

Feng WU;Qiang GAO;Wan-xie ZHONG

2013, 34(7):  791-800.  doi:10.1007/s10483-013-1707-6

Abstract ( 703 )   PDF (384KB) ( 682 )  

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A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

Y. S. KIM;Li-qun CHEN

2013, 34(7):  801-810.  doi:10.1007/s10483-013-1708-9

Abstract ( 668 )   PDF (428KB) ( 732 )  

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One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition (EMD) method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrinsic mode functions (IMFs) through the filtering algorithm based on the wavelet packet decomposition (GIFWPD). In this paper, it is demonstrated that the GIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis (CEDA) and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

Ming CHEN;Guang-wei JIAO;Song-sheng DENG;Jian-hua WANG

2013, 34(7):  811-822.  doi:10.1007/s10483-013-1709-x

Abstract ( 784 )   PDF (548KB) ( 573 )  

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The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

T. HAYAT;S. A. SHEHZAD;A.ALSAEDI

2013, 34(7):  823-832.  doi:10.1007/s10483-013-1710-7

Abstract ( 704 )   PDF (292KB) ( 1211 )  

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This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM)

M. SHEIKHOLESLAMI;M. GORJI-BANDPY;G. DOMAIRRY

2013, 34(7):  833-846.  doi:10.1007/s10483-013-1711-9

Abstract ( 970 )   PDF (1955KB) ( 1854 )  

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The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles: TiO2, Ag, Cu, and Al2O3. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical methods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ = 2.5 when Ra = 106 while at λ = 1.5 for other Rayleigh numbers.

Propagation of P- and S-waves in initially stressed gravitating half space

S. GUPTA;S. K. VISHWAKARMA

2013, 34(7):  847-860.  doi:10.1007/s10483-013-1712-7

Abstract ( 720 )   PDF (736KB) ( 655 )  

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The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity
parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L² projection method

Dong-yang SHI;Li-fang PEI

2013, 34(7):  861-874.  doi:10.1007/s10483-013-1713-x

Abstract ( 702 )   PDF (220KB) ( 500 )  

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A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem

Li-meng WU;Ming-kang NI;Hai-bo LU

2013, 34(7):  875-888.  doi:10.1007/s10483-013-1714-8

Abstract ( 759 )   PDF (214KB) ( 566 )  

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The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.

Effect of magnetic field on poroelastic bone model for internal remodeling

A. M. ABD-ALLA;S. M. ABO-DAHAB

2013, 34(7):  889-906.  doi:10.1007/s10483-013-1715-6

Abstract ( 874 )   PDF (383KB) ( 628 )  

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This paper studies the effects of the magnetic field and the porosity on a poroelastic bone model for internal remodeling. The solution of the internal bone remodeling process induced by a magnetic field is presented. The bone is treated as a poroelastic material by Biot’s formulation. Based on the theory of small strain adaptive elasticity, a theoretical approach for the internal remodeling is proposed. The components of the stresses, the displacements, and the rate of internal remodeling are obtained in analytical forms, and the numerical results are represented graphically. The results indicate that the effects of the magnetic field and the porosity on the rate of internal remodeling in bone are very pronounced.

Numerical solutions to regularized long wave equation based on mixed covolume method

Zhi-chao FANG;Hong LI

2013, 34(7):  907-920.  doi:10.1007/s10483-013-1716-8

Abstract ( 723 )   PDF (341KB) ( 695 )  

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The mixed covolume method for the regularized long wave equation is developed and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.