对流扩散方程的无网格解法

边界节点法是一种将边界积分方程和移动最小二乘近似方案相结合的无网格法,它同时具有边界元法降维和无网格法不需要划分网格的优势．本文提出了一种用边界节点法和径向基函数求解定常对流扩散问题的无网格法．     

周期性水波与淹没障碍物相互作用的数值研究

The interaction between regular water waves and a submerged obstacle in a channel is studied numerically. The fluid viscosity is taken into account and the volume of fluid method is used to deal with the free surface. The incident regular waves are generated by use of numerical absorbing wave maker paddle. The present method can be used to predict the nonlinear deformations of the transmitted regular waves, and to simulate the vortex flow near the obstacle and the shear flows beneath the free surface.     

Numerical Study of Interactions between Regular Water Waves and a Submerged Obstacle

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Finite particle method for kinematically indeterminate bar assemblies

This study presents a structural analysis algorithm called the finite particle method （FPM） for kinematically indeterminate bar assemblies. Different from the traditional analysis method, FPM is based on the combination of the vector mechanics and numerical calculations. It models the analyzed domain composed of finite particles. Newton＇s second law is adopted to describe the motions of all particles. A convected material flame and explicit time integration for the solution procedure is also adopted in this method. By using the FPM, there is no need to solve any nonlinear equations, to calculate the stiffness matrix or equilibrium matrix, which is very helpful in the analysis of kinematically indeterminate structures. The basic formulations for the space bar are derived, following its solution procedures for bar assemblies. Three numerical examples are analyzed using the FPM. Results obtained from both the straight pretension cable and the suspension cable assembly show that the FPM can produce a more accurate analysis result. The motion simulation of the four-bar space assembly demonstrates the capability of this method in the analysis ofkinematically indeterminate structures.     

Adaptive finite element-element-free Galerkin coupling method for bulk metal forming processes

An adaptive finite element-element-free Galerkin （FE-EFG） coupling method is proposed and developed for the numerical simulation of bulk metal forming processes. This approach is able to adaptively convert distorted FE elements to EFG domain in analysis. A new scheme to implement adaptive conversion and coupling is presented. The coupling method takes both advantages of finite element method （FEM） and meshless methods. It is capable of handling large deformations with no need of remeshing procedures, while it is computationally more efficient than those full meshless methods. The effectiveness of the proposed method is demonstrated with the numerical simulations of the bulk metal forming processes including forging and extrusion.     

A semi-implicit three-step method based on SUPG finite element formulation for flow in lid driven cavities with different geometries

A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.     

薄壁铸件反重力充填的守恒标量法研究

1　Introduction　SofarthemainalgorithmsadaptedtothenumericalsimulationformouldfillingareMAC ,SMAC[1] ,SOLA VOF[2 ] ,SIMPLEconservativescalarmethod[3] ,etc .Tosimulatemoldfilling ,MACandSMACmethodswilloccupylargequantityofcomputermemory ,andcostmuchcomputationtime .Atpresent ,thealgorithmsusedtosimulatemouldfillingofcastingsmainlyfocusonSOLA VOFandSIMPLEconservativescalar .Com paringwithSOLA VOF ,SIMPLEconservativescalaralgorithmismuchmoresuperior .Inaspectofmomen tumequat…     

一种求解与时间有关的二维薛定谔方程的数值算法

在有限差分和径向基函数的基础上,利用无网格法中的特解方法来给出与时间有关的二维薛定谔方程的一种数值算法,同时给出了两个例子来说明这种方法良好的准确性,并取得了比较好的数值结果.     

High velocity flow simulation using lattice Boltzmann method with no-free-parameter dissipation scheme

A finite difference lattice Boltzmann method of second-order accuracy in time is developed based on non-oscillatory scheme with no-free-parameter dissipation (NND) difference scheme in this paper. The NND lattice Boltzmann method is used to simulate high-speed flows by constructing a new equilibrium distribution function of the lattice Boltzmann method.Compared with a variation of lattice Boltzmann method developed by Qu, et al., the present method can capture shock waves and handle oscillations of high velocity flows accurately in larger time steps and in shorter computing time. Numerical results indicate the correctness and capability of simulating shock wave interactions of the NND lattice Boltzmann method.     

An efficient numerical shape analysis for light weight membrane structures

The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method （FPM）, this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight mem- branes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of parti- cles linked by elements, and the motion of the free particles is directly described by Newton＇s second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes pro- duced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.     

Wiped-Film Molecular Distillation Process

Based on the Bhatnagar-Gross-Krook distillation for two components in the presence equation, a new scheme of wiped-film molecular of inert gas is developed. The equations in the scheme are solved numerically by the method of finite difference and iteration. The new scheme is used to simulate the molecular distillation of dibutyl phthalate and dibutyl sebacate （ DBP-DBS ） mixture. The effects of the inert gas pressure, the distance between the evaporation surface and condensation surface, the rotation rate of blade, and the number of blades on the distillation rate and separation factor are discussed.     

基于多孔介质湿热迁移的混凝土收缩数值模拟

为了对处于环境温、湿度中的混凝土的收缩变形进行有效数值模拟分析,提出了一种数值解析与有限元分析相结合的方法.根据多孔介质热质传输原理描述混凝土中湿热迁移过程的耦合偏微分方程组,借助Laplace变换及传递函数将其简化为拉氏域内的简单微分方程并求解,然后通过Laplace逆变换得到物理空间内的温度和含湿量.在此基础上利用有限元分析方法得到混凝土湿热耦合收缩变形.该方法克服了其他求解过程中特征值复杂、耦合困难及准确性差的问题,并有效解决了现有有限元软件难以处理湿度应力及变形的难题.以Hundt试验为算例的数值计算表明,模拟结果与试验数据具有良好的相关性.     

Radial point collocation method （RPCM） for solving convection-diffusion problems

INTRODUCTION Meshfree methods are increasingly becoming popular as they are effective for dealing with com-putational mechanics problems including both solid and fluid problems. Most of various approaches proposed in (Liu, 2002) are based on Galerkin form (weak form) which need background meshes for numerical integrations, and are actually not truly meshfree methods. Other approaches are based on collocation form (strong form), such as finite point method (FPM) (Onate et al., 1996), ra…     

Numerical investigation of flow characteristics around two side-by-side cylinders by immersed boundary-lattice Boltzmann flux solver

In this paper, to study the characteristics of the flow in a laminar regime, an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) is applied to numerically simulate the unsteady viscous flows around two fixed and rotating circular cylinders in side-by-side arrangement. This method applies finite volume discretization to solve the macroscopic governing equations with the flow variables defined at cell centers. At the cell interface, numerical fluxes are physically evaluated by a local lattice Boltzmann solution. In addition, the no-slip boundary condition is accurately imposed by using the implicit boundary condition-enforced immersed boundary method. Due to the simplicity and high efficiency of IB-LBFS on non-uniform grids, it is suitable for simulating fluid flows with complex geometries and moving boundaries. Firstly, numerical simulations of laminar flow past two side-by-side cylinder are performed with different gap spacings at Reynolds numbers of 100 and 200. The simulation results show that a small gap spacing induces a biased flow and forms an irregular big wake behind two cylinders at a low Reynolds number. As the gap spacing increases, an in-phase or anti-phase flow is observed. Then, the effects of the main important parameters on flow characteristics are analyzed for flow past two side-by-side rotating cylinders, including the rotational speed, Reynolds number, and gap spacing. As the rotational speed is increased, the numerical results illustrate that unsteady wakes are suppressed and the flow becomes steady. As the gap spacing is increased, two separate vortex streets behind each cylinder are formed with a definite phase relationship and single shedding frequency.     

台阶地形上波浪的传播与破碎(英文)

通过对开边界、入射边界、自由表面边界以及底边界的合理处理,用有限元法建立了基于Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的二维数值波浪水槽．利用这一数值模型,计算了波浪在台阶地形上的传播变形．基于运动学指标判断了波浪破碎的发生,并给出了临界破碎波高．实验结果证实了本文模型的可靠性,并给出了破碎后波高的衰减规律．     

Korteweg-de-Vries方程有限谱数值格式

以kdV方程为模型,利用有限谱方法构造数值计算格式,检验有限谱法计算含有色散项的非线性方程的精度,并对孤立波的演化及孤立波的碰撞进行了数值模拟,结果说明有限谱数值格式能较准确地模拟孤立波的行为.同时,把有限谱数值格式的计算结果同解析解进行对比,结果表明有限谱法具有较高的精度.     

Numerical method for solving relativistic hydrodynamic equation including quark-fragment effect

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｈｅｎｏｍｅｎａｏｃｃｕｒｉｎｇｉｎｕｌｔｒａｒｅｌａｔｉｖｉｓｔｉｃｃｅｎｔｒａｌｃｏｌｉｓｉｏｎｏｆｔｗｏｈｅａｖｙｉｏｎｓｍａｋｅｉｔｐｏｓｓｉｂｌｅｔｏｓｅｔｔｌｅｔｈｅｑｕｅｓｔｉｏｎｗｈｅｔｈｅｒｔｈｅＱ...     

双液滴垂直冲击薄液膜的数值模

The normal impingement process of two water droplets upon a thin film on the solid surface was numerically investigated. The numerical treatment was based on the finite volume solution of the Navier-Stokes （N-S） equations combined with the volume of fluid method （VOF）. Physically reasonable results for the process of two droplets impacting on the thin film were obtained. The effects of the droplet velocity, the fihn thickness and the spacing between the two droplets on the splash and spread process of the impact were examined.     

分数阶Cable方程的半离散问题的稳定性与误差分析

Cable方程是模拟神经元动力学最重要的方程之一,有关该方程的研究得到了越来越多的关注.最近的研究发现,用带有分数阶导数的Cable方程来模拟神经元的动力学行为效果更好.本文旨在考察时间分数阶Cable方程的初边值问题,构造了时间分数阶Cable方程的有限差分格式.对于时间半离散格式,我们证明了格式的稳定性,并给出了误差估计式.     

Meshless local discontinuous Petrov-Galerkin method with application to blasting problems

A meshless local discontinuous Petrov-Galerkin (MLDPG) method based on the local symmetric weak form (LSWF) is presented with the application to blasting problems. The derivation is similar to that of mesh-based Runge-Kutta Discontinuous Galerkin (RKDG) method. The solutions are reproduced in a set of overlapped spherical sub-domains, and the test functions are employed from a partition of unity of the local basis functions. There is no need of any traditional non-overlapping mesh either for local approximation purpose or for Galerkin integration purpose in the presented method. The resulting MLDPG method is a meshless, stable, high-order accurate and highly parallelizable scheme which inherits both the advantages of RKDG and meshless method (MM), and it can handle the problems with extremely complicated physics and geometries easily. Three numerical examples of the one-dimensional Sod shock-tube problem, the blast-wave problem and the Woodward-Colella interacting shock wave problem are given. All the numerical results are in good agreement with the closed solutions. The higher-order MLDPG schemes can reproduce more accurate solution than the lower-order schemes.