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25 September 2009, Volume 26 Issue 5 Previous Issue    Next Issue

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High Order Schemes for CFD: A Review CHENG Juan, SHU Chi-Wang 2009, 26(5): 633-655.  Abstract ( )   PDF (1273KB) ( )   Over the past two decades there have been many research activities in the design and application of high order accurate numerical methods in computational fluid dynamics (CFD). High order methods are especially desirable for simulating flows with complicated solution structures. We give a review on the development and application of several classes of high order schemes in CFD, mainly concentrating on the simulation of compressible flows. An important feature of the compressible flow is the existence of shocks, interfaces and other discontinuities and often also complicated structure in the smooth part of the solution. This gives a unique challenge to the design of high order schemes to be non-oscillatory and yet still maintaining their high order accuracy. We concentrate our discussion on the essentially non-oscillatory (ENO), weighted ENO (WENO) finite difference,finite volume schemes and discontinuous Galerkin (DG) finite element methods. We attempt to describe their main properties and their relative strength and weakness. We also briefly review their developments and applications, concentrating mainly on the results over the past five years.

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Finite Volume Element Method in Air Pollution Model WANG Ping, ZHANG Zhiyue 2009, 26(5): 656-664.  Abstract ( )   PDF (388KB) ( )   A finite volume element method is used in an air pollution model.Trial function space and test function space are chosen linear element function space and piecewise constant function space,respectively.Error estimates of L2 and H1 are given.Numerical results of the finite volume element method and the finite difference method are analyzed and compared.It shows that the finite volume element method is much better and effective.

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Scaled Boundary Finite-element Method for Seepage Free Surfaces Analysis LI Fengzhi 2009, 26(5): 665-670.  Abstract ( )   PDF (299KB) ( )   A scaled boundary finite-element method(SBFEM) is used for determining free surfaces in two-dimensional steady-state seepage problems.Equations of SBFEM for a seepage problem are derived with a transformation from Cartesian coordinates to scaled coordinates.Governing equations are discretized on boundary of computational domain by SBFEM,which reduces spatial dimension by one,and analytical procedure is applied in the reduced direction.As scaled centre is at intersection point of upstream and impermeable straight boundary of the dam bottom,only free surface and its downstream boundaries are discretized.A governing point method is used to control overflow point in the free surface.A 2-D steady seepage with a free surface in a homogeneous dam is analyzed and compared with experimental result.It shows that the method has satisfactory convergence,accuracy and less amount of data preparation.

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Explicit Compatible Finite Element Method for Lagrangian Hydrodynamics in Three-dimensional Cartesian Geometry JIA Zupeng, YU Xijun, ZHAO Guiping 2009, 26(5): 671-678.  Abstract ( )   PDF (379KB) ( )   We present an explicit compatible finite element method for fluid dynamics problems in three-dimensional Cartesian geometry.Trilinear brick elements with a staggered-grid placement of the spatial variables are used to discretize fluid equations.An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks.Subzonal perturbed pressure is adopted to resist spurious grid motions.Artificial viscosity forces and subzonal pressure forces agree well with general compatibility.Numerical examples show accuracy and robustness of the method.

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An Implicit Preconditioning Method for Steady and Unsteady Flows HAN Zhonghua, SONG Wenping, QIAO Zhide 2009, 26(5): 679-684.  Abstract ( )   PDF (430KB) ( )   An LU-SGS based Choi-Merkle matrix preconditioning method is implemented within the framework of dual-time stepping and geometric multigrid method.An efficient method for steady and unsteady flows past aircraft configurations with Mach numbers from incompressible to transonic regime is developed.LU-SGS time stepping method is modified according to the preconditioned system.An efficient and robust splitting method for Jacobian matrix is presented.In simulation of viscous flows past NACA0012 airfoil ONERA M6 wing and DLR F4 wing/body configuration,the method obtains nearly Mach number-independent convergence at low-Mach numbers and improves efficiency slightly for transonic flows.Compared with Runge-Kutta based preconditioning method,LU-SGS based preconditioning method is more efficient.In simulation of unsteady viscous flow past an oscillating NACA 0012 airfoil convergence of sub iteration of dual time stepping is improved slightly.

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Flow Heat Transfer Integrated Method Overcoming Stiffness in Two-equation Turbulence Models HU Haiyang, WANG Qiang 2009, 26(5): 685-692.  Abstract ( )   PDF (532KB) ( )   A integrated method solving fluid and solid simultaneously is used to deal with complicated flow and solid temperature field coupling problems.A simple but effective approach is proposed to overcome stiffness in two-equation turbulence models.Related theory is provided.With this method,efficiency in multigrids and LUSGS implicit temporal stepping method is increased remarkably.

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Multi-symplectic Scheme and Norm Conserving Law of Generalized Nonlinear Schrödinger Equation HUANG Langyang 2009, 26(5): 693-698.  Abstract ( )   PDF (243KB) ( )   Multi-symplectic system for generalized nonlinear Schrödinger equation is constructed by canonical transformation.A new norm conserving multi-symplectic scheme is derived.Numerical experiments show that the multi-symplectic scheme shows excellent long-time numerical behavior and preserves norm conserving law better than both leap-frog scheme and symplectic Euler middle scheme.

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Parallel Computing of Clamp Structure in Tahoe Frame FAN Xuanhua, WU Ruian, HAO Zhiming, HE Yingbo 2009, 26(5): 699-702.  Abstract ( )   PDF (300KB) ( )   In Tahoe frame (an open source software) and finite element (FE) pre-processing/post-processing soft wares (MSC.Patran and Tecplote),an FE model of clamp structure was created.Serial and parallel computations of a model with 2.62 million-freedom degree are achieved successfully with domain decomposition,compiling of interfaces and iterative algorithm solvers provided in PHG solvers(preconditioned conjugate gradient methods).It indicates that convergence of parallel computation is faster than serial one's,and computation time of a four-procedure parallel is less than one forth of that of serial one.Accuracy of computing is validated by comparing with result of MSC.Nastran.Parallel computing performance of the frame is tested with a large parallel computer.The maximum testing number is 32 nodes.It shows that an updated Tahoe frame is feasible in parallel computing of large-scale freedom degree models.Parallel computing time is nearly linearly reduced with increasing of computing nodes.

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High-order Accurate Alternating Group 8-point Scheme for Convection Diffusion Problems ZHANG Shouhui, WANG Wenqia 2009, 26(5): 703-711.  Abstract ( )   PDF (302KB) ( )   A high accurate alternating group 8-point scheme for convection diffusion problems is given. It can be used for parallel computing and is proved unconditionally stable. Numerical experiments show that the scheme has high accuracy.

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Quadrature Sets in Synthetic Kernel Method for Radiation Transport GAO Chan, LI Maosheng 2009, 26(5): 712-718.  Abstract ( )   PDF (340KB) ( )   We introduce briefly a synthetic kernel method for radiation transport equation and analyse computational error and convergence.Quadrature sets and error amendment technique are proposed to improve computational accuracy of synthetic kernel method.By using quadrature sets and error amendment technique synthetic kernel method yields accurate results even with low orders.

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Comparative Study of Numerical Algorithms for "Anomalous" Diffusion Equation with Spatial Fractional Derivatives SUN Hongguang, CHEN Wen, CAI Xing 2009, 26(5): 719-724.  Abstract ( )   PDF (304KB) ( )   We use explicit difference scheme,implicit difference scheme,and Crank-Nicholson difference scheme to discretize an anomalous diffusion equation with spatial fractional derivatives,and analyze their performances in terms of truncation error,stability and computing expense.A numerical example is examined to validate the results.

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Improvement on Three-dimensional Gaussian and Savitzky-Golay Filters in Denoising of Monte Carlo Dose Distributions YANG Zhu, LI Guoli, LIN Hui, TAO Lei, ZHOU Jinbin, CAO Ruifen, JING Jia, WU Aidong, WU Yican, HUANG Jiabing 2009, 26(5): 725-730.  Abstract ( )   PDF (434KB) ( )   With three-dimensional(3D) filtering in Monte Carlo rough dose distributions with less particle history and short simulation time convergence is accelerated.We improve 3D Gaussian and Savitzky-Golay filters considering features of Monte Carlo dose distribution. Parallel and cascade mixture methods with 3D Gaussian and Savitzky-Golay filters are compared.A method simplifying mixture filter structure using equivalent convolution kernel is put forward.It shows that the improved Gaussian and Savitzky-Golay filters enhance denoising.The mixture filter reduces local errors of filtering results.Two types of mixture filters reduce noise in Monte Carlo dose distributions.Filtering of cascade mixture filter is slightly better than that of parallel mixture filter.

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Interpolation Iterative Arithmetic in Design of Diffractive Optical Elements LIU Qiang, LI Ke, YANG Jia, LI Yongping 2009, 26(5): 731-736.  Abstract ( )   PDF (398KB) ( )   Based on an Input-Output algorithm,a precise design method of DOE is proposed adapting fast Fourier transform algorithm.Numerical simulation indicates that this method improves beam shaping effectively.With same diffractive efficiency,interpolation iterative arithmetic reduces PV by 14% and RMS by 4%.The algorithm provides better initial phases of DOE for simulating annealing optimization than primitive Input-Output algorithm.

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Wavelet Theory for Inverse Blackbody Radiation MIN Tao, ZHANG Haiyan, WANG Guoting 2009, 26(5): 737-742.  Abstract ( )   PDF (244KB) ( )   An inverse blackbody radiation problem is discreted to a linear ill-posed system.A wavelet transform method is proposed for solution of the problem.With a combination of wavelet transformation and regularization method we convert the ill-posed problem into a posed problem in coarse space,which takes full advantage of compact support of wavelet.Numerical results show feasibility and robust reconstruction of the method.

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Multiscale Simulation of Time and Space in Damage of a Pre-tensioned Aluminum Plate Under Laser Irradiation ZHANG Rui, TANG Zhiping 2009, 26(5): 743-750.  Abstract ( )   PDF (713KB) ( )   A multiscale algorithm with element/mesh momentum transfer of parameters and variable information exchange in coupling transition zone between discrete element method (DEM) and finite element method (FEM) is deduced.Multiscale computation of time and space with coupling of DEM and FEM is established.The algorithm and the model are applied to damage of a pre-tensioned aluminum plate under laser irradiation.Compared with results in FEM model,multiscale model of space and multiscale model of time and space,the multiscale model of time and space by coupling DEM and FEM is shown accurate and highly efficient.Damage of a pre-tensioned aluminum plate under laser irradiation is simulated in multiscale model of time and space from macro-and meso-scale.Simulated results are coincident with experimental resuts.

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Simulation on Ar Ion Assisted Deposition of Hydrogen Diamond-like Carbon Films LI Yunchao, KAI Hua, LI Shuang, GUO Decheng, LI Zhijie 2009, 26(5): 751-757.  Abstract ( )   PDF (474KB) ( )   Molecular dynamics (MD) simulation is made to study growth of diamond-like carbon (DLC) films via ion-beam-assisted deposition (IBAD).C2 molecules and H ions are selected as deposition projectiles and Ar ions are selected as assistance projectiles.At fixed incident energy and varied ration (Ar/C),assisted deposition of film is investigated.Transient mobility and migration of C atoms due to Ar impact is investigated.It shows that the impact-induced high recoil energy and displacement of deposited C atoms play a key role in growth of DLC films.It is attributed to incident energy and momentum of assistance Ar.The results agree well with experimental observation.It helps understanding of the growth mechanism.

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Monte Carlo Simulation of Cluster Growth at Different Temperatures XU Xiaojun, WANG Fengfei 2009, 26(5): 758-762.  Abstract ( )   PDF (300KB) ( )   Binding energy of substrate,coupling energy of nearest neighbor particles and strain field are introduced to diffusion barrier.Cluster growth process at different temperatures is investigated with Monte Carlo simulation.It shows that as 400 K≤T ≤ 480 K the average width of ramified clusters is independent on temperature T and is almost equal to the diameter of single particle.As 500 K≤T ≤ 680 K,however,width of the ramified cluster increases gradually to that of 4 particles with increasing temperature.As T increases further,clusters with large number of particles disappear,due to strong activity of particles.Average number of particles in each cluster is smaller than 2.Evolution of cluster morphology during growth process and number of cluster at temperatures are studied as well.

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Numerical Calculation of Vesicle Shapes with High Topological Genus XIE Liqiang 2009, 26(5): 763-766.  Abstract ( )   PDF (344KB) ( )   With numerical calculation on shapes of genus 2 vesicle with small reduced volume,interesting shapes and new phase transition branches are found.More supports for the curvature model are expected with experimental observations.

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Transversal Electronic Transport of Base Pairs with a Silver Ion ZHANG Xia, DONG Ruixin, CUI Shouxin, BAN Ge, LI Ke, HAN Hongwen 2009, 26(5): 767-772.  Abstract ( )   PDF (399KB) ( )   Electronic transport of a two-probe system consisting of Au (111) electrodes and two base pairs sandwiched between Au (111) contacts is investigated with density functional theory combined with non-equilibrium Green's function method.It shows that conductance of base pairs is sensitive to distance between electrodes and oscillates.At a fixed gap between electrodes,transverse transport of base pairs under low bias is calculated and is compared with base pairs with a silver ion.It shows that conductive capability of G-C decreases and that of A-T increases as silver ions are combined with base pairs.

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Population of Dense V-type Three-level Medium in Few-cycle Laser Pulses TAN Xia, WANG Lei, WANG Zhendong, FAN Xijun 2009, 26(5): 773-780.  Abstract ( )   PDF (424KB) ( )   Full Maxwell-Bloch equations are solved with PC-FDTD method to investigate population evolution of dense V-type three-level medium in few-cycle laser pulses.It is shown that the ratio of transition dipole moments(γ) has strong influence on appearing time and oscillation frequency of population inversion.As γ=1 population inversion with LFC appears later than that without LFC and near dipole-dipole(NDD) interaction delays population inversion.As γ>1,appearing with LFC is earlier than that without LFC and NDD interaction accelerates the population inversion.The number of population inversion with unequal transition dipole moments is more than that with equal transition dipole moments.Moreover,evolution of populations in a dense medium is quite different from that in a dilute medium.At input surface,in a dilute medium,population inversion appears with time evolution.With increasing of medium density,populations show quasi-periodicity oscillation and oscillation frequencies of populations with LFC are less than that without LFC.

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Structure and Potential Energy Functions of CuTe, Cu2 and Cu2Te Molecules HUANG Duohui, WANG Fanhou, ZHU Zhenghe 2009, 26(5): 781-785.  Abstract ( )   PDF (264KB) ( )   With relativistic effective cores potential(RECP) for Cu and Te atom,B3LYP method with LANL2DZ basis set is used to optimize structure of CuTe,Cu2 and Cu2Te molecules.It shows that the ground state of CuTe and Cu2 molecules is 2Π and 1∑g+ respectively and the ground state of Cu2Te molecule is C2V symmetry 1A1 state.Dissociation energy,harmonic frequency and force constant are calculated.Murrell-Sorbie potential energy functions of CuTe and Cu2 molecules are fitted by least square fitting.Potential energy function of Cu2Te ground state is given by many-body expansion theory.Potential surface shows clearly structure of Cu2Te molecule at ground state.

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Simulation of Water Adsorption on PuO2 Surface CHEN Piheng, DONG Ping, BAI Bin, LI Ju 2009, 26(5): 786-790.  Abstract ( )   PDF (272KB) ( )   We simulate water adsorption on PuO2 surfaces with kinetic Monte Carlo.Desorption activity energies of layers are obtained by fitting experimental data of Statebake and Haschke et al.We predict TDMS of water at different temperature increasing rates,adsorption isothermal and adsorption isotonic curves at different temperatures and water partial pressures.