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2014年 第35卷 第7期    刊出日期：2014-07-01

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论文

High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations

姜振华;阎超;于剑

2014, 35(7):  799-812.  doi:10.1007/s10483-014-1834-9

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Efficient and robust solution strategies are developed for discontinuous Galerkin (DG) discretization of the Navier-Stokes (NS) and Reynolds-averaged NS (RANS) equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational efficiency for highly anisotropic meshes. A simple and effective technique to use the mod- ified Baldwin-Lomax (BL) model on the unstructured meshes for the DG methods is proposed. The compact Hermite weighted essentially non-oscillatory (HWENO) limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high- order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing com- plex flow structures and giving reliable predictions of benchmark turbulent problems.

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

N. S. AKBAR;Z. H. KHAN;R. U. HAQ;S. NADEEM

2014, 35(7):  813-820.  doi:10.1007/s10483-014-1836-9

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The present article investigates the dual nature of the solution of the magnetohydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting method. It is found that the dual solutions of the flow exist for certain values of the velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.

Exact solutions for unsteady flow of second grade fluid generated by oscillating wall with transpiration

M. ABDULHAMEED;I. KHAN;D. VIERU;S. SHAFIE

2014, 35(7):  821-830.  doi:10.1007/s10483-014-1837-9

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A problem of unsteady flow of a second grade fluid over flat plates with the impulsive and oscillating motion, starting from rest, and with the wall transpiration is considered. The exact solutions are derived by the Laplace transform, the perturbation techniques, and an extension of the variable separation technique together with similarity arguments. These solutions are written as the sum between the permanent solutions and the transient solutions. The variations of fluid behaviors with various physical parameters are shown graphically and analyzed. The results are validated by comparing the limiting cases of the present paper with the results of the related published articles.

Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

M. M. RASHIDI;A. HOSSEINI;I. POP;S. KUMAR;N. FREIDOONIMEHR

2014, 35(7):  831-848.  doi:10.1007/s10483-014-1839-9

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The main purpose of this study is to survey numerically comparison of twophase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics (CFD) prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models (mixture, volume of fluid (VOF), and Eulerian). The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature field in the single phase and two-phase models are greater than those in the hydrodynamic field. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.

Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

A. NAYAK;S. PANDA;D. K. PHUKAN

2014, 35(7):  849-862.  doi:10.1007/s10483-014-1830-9

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This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of the stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

陈宜舟

2014, 35(7):  863-874.  doi:10.1007/s10483-014-1831-9

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This paper presents a closed form solution and numerical analysis for Eshelby's elliptic inclusion in an infinite plate. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

B. AMIRIAN;R. HOSSEINI-ARA;H. MOOSAVI

2014, 35(7):  875-886.  doi:10.1007/s10483-014-1835-9

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This paper deals with the free vibration analysis of circular alumina (Al₂O₃) nanobeams in the presence of surface and thermal effects resting on a Pasternak foundation. The system of motion equations is derived using Hamilton's principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

梁文彦;王振清;刘方;刘晓铎

2014, 35(7):  887-896.  doi:10.1007/s10483-014-1838-9

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For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface cracktip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

Highly efficient H¹-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

石东洋;廖歆;唐启立

2014, 35(7):  897-912.  doi:10.1007/s10483-014-1833-9

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A highly efficient H¹-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h²) for both the original variable u in H¹(Ω) norm and the flux p = u in H(div,Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h³) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

Existence results for generalized vector equilibrium problems with applications

杨明歌;黄南京

2014, 35(7):  913-924.  doi:10.1007/s10483-014-1867-9

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By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

丁协平

2014, 35(7):  925-934.  doi:10.1007/s10483-014-1832-9

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A new bilevel generalized mixed equilibrium problem (BGMEP) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.