2011 Vol. 32, No. 10

Display Method:
Exact Analytical Solution of the Magnetohydrodynamic Sink Flow
ZHANG Ji, FANG Tie-gang, ZHONG Yong-fang
2011, 32(10): 1139-1147. doi: 10.3879/j.issn.1000-0887.2011.10.001
Abstract(1138) PDF(706)
An exact analytical solution of the famous Falkner-Skan equation for magneto-hydro-dynamic (MHD) flow was obtained for a special case,namely the sink flow with a velocity power index of -1.The solution was given in a closed form.Multiple solution branches were observed.The effects of the magnetic parameter and the wall stretching parameter were analyzed.Interesting velocity profiles were observed with reversal flow regions even for a stationary wall.These solutions provide a rare case of the Falkner-Skan MHD flow with exact analytical closed form formula and greatly enrich the analytical solution to the celebrated Falkner-Skan equation and the understanding of this important and interesting equation.
Peristaltic Flow of MHD Jeffrey Fluid Through a Finite Length Cylindrical Tube
D. Tripathi, N. Ali, T. Hayat, M. K. Chaube, Awatif A. Hendi
2011, 32(10): 1148-1160. doi: 10.3879/j.issn.1000-0887.2011.10.002
Abstract(1236) PDF(771)
The peristaltic flow of Jeffrey fluid through a tube of finite length was studied.The fluid was electrically conducting in the presence of an applied magnetic field.Analysis was carried out under the assumption of long wavelength and low Reynolds number approximations.Expressions of pressure gradient,volume flow rate,average volume flow rate and local wall shear stress were obtained.The effects of relaxation time,retardation time and Hartman number on pressure,local wall shear stress and mechanical efficiency of peristaltic pump were studied.Reflux phenomenon was also investigated.Here the case of propagation of a non-integral number of waves along the tube walls was also examined,which were inherent characteristics of finite length vessels.
Robust Airfoil Optimization Based on Improved Particle Swarm Optimization Method
WANG Yuan-yuan, ZHANG Bin-qian, CHEN Ying-chun
2011, 32(10): 1161-1168. doi: 10.3879/j.issn.1000-0887.2011.10.003
Abstract(1293) PDF(1211)
A robust airfoil optimization platform was constructed based on modified particle swarm optimization method(i.e.second-order oscillating particle swarm method),which consists of an efficient optimization algorithm,a precise aero dynamic analysis program,a highac-curacy surrogate model and a classical airfoil parametric method.There are two improvements for the modified particle swarm method compared to standard particle swarm method.Firstly,particle velocity was represented by the combination of particle position and variation of position,which makes the particle swarm algorithm become a second-order precision method with respect to particle position.Secondly,for the sake of adding diversity to the swarm and enlarging parameter searching domain to improve the global convergence performance of the algorithm,an oscillating term was introduced to the update formula of particle velocity.At last,taking two airfoils as examples,the aerodynamic shapes were optimized on this optimization platform.It is shown from the optimization results that the aerodynamic characteristic of the airfoils was greatly improved at a broad design range.
Multidomain Pseudospectral Methods for Nonlinear Convection-Diffusion Equations
JI Yuan-yuan, WU Hua, MA He-ping, GUO Ben-yu
2011, 32(10): 1169-1181. doi: 10.3879/j.issn.1000-0887.2011.10.004
Abstract(1315) PDF(862)
Multidomain pseudospectral approximations to nonlinear convection-diffusion equations were considered.The schemes were formulated in the Legendre-Galerkin method but the nonlinear term was collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval.Appropriate base functions were introduced so that the matrix of system was sparse and the method can be implemented efficiently and in parallel.The stability and the optimal rate of convergence of the methods were proved.Numerical results were given for both the single domain and the multidomain methods to make a comparison.
Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems
ZHANG Yun-zhang, HOU Yan-ren, WEI Hong-bo
2011, 32(10): 1182-1198. doi: 10.3879/j.issn.1000-0887.2011.10.005
Abstract(885) PDF(762)
An adaptive mixed least squares Galerkin/Petrov finite element method was developed for the stationary conduction convection problems.The mixed least squares Galerkin/Petrov finite element method was consistent and stable for any combination of discrete velocity and pressure spaces (without requiring a Babuška-Brezzi stability condition).Using the general theory of Verfürth,the a posteriori error estimates of residual type are derived for the problems.Finally,some numerical tests are presented to illustrate the method's efficiency.
Numerical Simulation of the Inhibiting Effects on Solid Tumour Cells in Anti-Angiogenic Therapy: an Application of Coupled Mathematical Model of Angiogenesis With Tumour Growth
CAI Yan, WU Jie, XU Shi-xiong, LONG Quan, YAO Wei
2011, 32(10): 1199-1207. doi: 10.3879/j.issn.1000-0887.2011.10.006
Abstract(1359) PDF(858)
To investigate the inhibiting effects of anti-angiogenic factor angiostatin and anti-angiogenic drug endostatin on tumour angio genesis and tumour cells,a coupled mathematical model of tumor angiogenesis with tumour growth and blood perfusion was developed.The simulation results showed that angiostatin and endostatin could improve the abnormal microenvironment inside the tumour tissue,by effectively inhibiting the process of tumor angiogenesis and decreasing the number of tumour cells.The present model can be used as a valid theoretical method in the investigation of tumour anti-angiogenic therapy.
Simplified Method for the Simulation of Ergodic Spatially Correlated Seismic Ground Motions
GAO Yu-feng, WU Yong-xin, LI Bing
2011, 32(10): 1208-1225. doi: 10.3879/j.issn.1000-0887.2011.10.007
Abstract(1337) PDF(732)
A simplified method for the simulation of ergodic spatially correlated seismic ground motions was proposed,based on the commonly used original spectral representation method.Firstly,the phase angles,to represent the correlation among ground motions,were given by explicit items with a clear physical.By using these explicit items,computational efficiency can be increased by changing the decomposition of complex cross-spectral matrix into the decom-position of real incoherence coefficient matrix.Double-indexing frequencies were introduced to simulate ergodic seismic ground motions,and the ergodic feature of the improved method was demonstrated theoretically.Subsequently,an explicit solution of the elements of the lower triangular matrix under Cholesky decomposition was given.By using this explicit solution,the improved method had been simplified,and the computational efficiency can be increased greatly,by avoiding repetitive Cholesky decomposition of cross-spectral matrix in every frequency step.At last,a numerical example was employed to illustrate the good character of the improved method.
Study of Dynamic Response in a Two Dimensional Transversely Isotropic Thick Plate With Spatially Varying Heat Sources and Body Forces
Mohsin Islam, Sadek Hossain Mallik, Mridula Kanoria
2011, 32(10): 1226-1240. doi: 10.3879/j.issn.1000-0887.2011.10.008
Abstract(1260) PDF(726)
A two dimensional problem for a transversely isotropic thick plate having heat source and body force was studied.The upper surface of the plate was stress free with prescribed surface temperature while the lower surface of the plate rest on a rigid foundation and was thermally insulated.The study was carried out in the context of generalized thermoelasticity proposed by Green and Naghdi.The governing equations for displacement and temperature fields were obtained in Laplace-Fourier transform domain by applying Laplace and Fourier transform techniques.The inversion of double transform had been done numerically.The numerical inversion of Laplace transform was done by using a method based on Fourier series expansion technique.Numerical computations had been done for magnesium (Mg) and the results were presented graphically.The results for an isotropic material (Cu) had been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).The effect of body force was also studied.
Asymptotic and Other Estimates for a Semilinear Parabolic Problem in a Semi-Infinite Cylinder
J. C. Song
2011, 32(10): 1241-1246. doi: 10.3879/j.issn.1000-0887.2011.10.009
Abstract(1066) PDF(745)
The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries was investigated.A second-order differential inequality that was to show the spatial decay O(exp{-z2/[4(t+t0)]}) for an L2p cross-sectional measure of the solution was obtained.A first-order differential inequality leading to growth or decay was derived.In the case of growth an upper bound for blow-up in space was obtained while in the case of decay an upper bound for the total energy in terms of data was obtained.
Existence of the Weak Solution for Quantum Zakharov Equations for Plasmas Model
FANG Shao-mei, JIN Ling-yu, GUO Bo-ling
2011, 32(10): 1247-1253. doi: 10.3879/j.issn.1000-0887.2011.10.010
Abstract(1143) PDF(799)
Zakharov equations have a fairly abundant physical background.The existence of weak global solution for quantum Zakharov equations for plasmas model,by means of Arzela-Ascoli theorem,Faedo-Galerkin methods and compactness property was obtained.
A Projected Subgradient Method for Non-Lipschitz Set-Valued Mixed Variational Inequalities
TANG Guo-ji, HUANG Nan-jing
2011, 32(10): 1254-1264. doi: 10.3879/j.issn.1000-0887.2011.10.011
Abstract(1531) PDF(793)
A projected subgradient method for solving a class of set-valued mixed variational inequalities when the mapping was not necessarily Lipschitz was proposed.Under some suitable conditions,it is proved that the sequence generated by the method was strongly convergent to the unique solution of the problem in Hilbert spaces.