一维多介质可压缩Euler方程的高精度RKDG有限元方法

采用RKDG有限元目的、Level Set目的和改进的带"Isentropic"修正的Ghost Fluid目的模拟了一维多介质可压缩Euler方程,其中Euler方程、Level Set方程和重新初始化方程都采用了三阶精度的RKDG有限元目的进行离散,并对一维两种介质可压缩流体进行了数值实验,得到了较高分辨率的计算结果.     

非定常Navier-Stokes方程基于两重网格离散的有限元并行算法

基于两重网格离散和区域分解技巧,提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步,在粗网格上采用Oseen迭代法求解非线性问题,在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散,时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.     

基于对偶混合变分原理的Signorini问题的数值模拟

基于Signorini问题的对偶混合变分形式,提出了一种非协调有限元逼近格式,证明了离散的B-B条件,获得了Raviart-Thomas(k=0)有限元逼近的误差界O(h^3/4),并且Uzawa型算法对协调与非协调有限元逼近格式进行了数值求解.根据数值结果的分析和比较,表明应用非协调有限元逼近格式求解更有效.     

Design sensitivity analysis for sequential structural-acoustic problems

A design sensitivity analysis of a sequential structural-acoustic problem is presented in which structural and acoustic behaviors are de-coupled. A frequency-response analysis is used to obtain the dynamic behavior of an automotive structure, while the boundary element method is used to solve the pressure response of an interior, acoustic domain. For the purposes of design sensitivity analysis, a direct differentiation method and an adjoint variable method are presented. In the adjoint variable method, an adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process for the structural part. The proposed sensitivity results are compared to finite difference sensitivity results with excellent agreement.     

An improved method to calculate the radio interference of a transmission line based on the flux-corrected transport and upstream finite element method

The radio interference (RI) from HVDC transmission lines can block communication systems. In this paper the RI of a HVDC transmission line has been analyzed by the superposition of the electromagnetic field generated by the corona current based on phase-model transformation, where the corona current can be solved by the flux-corrected transport and finite difference method combining the upstream finite element method for bipolar conductor model instead of corona cage or excitation function. Our calculated values for 0.5 MHz RI from the proposed method compare well with measured values from a 800 kV HVDC test line established in China. With this validation, we find that RI should increase with temperature, increase with altitude, and vary in a complex way with relative humidity. Therefore, the proposed method can be adopted in transmission lines design and electromagnetic environment evaluation.     

Hybrid uncertainty propagation of coupled structural–acoustic system with large fuzzy and interval parameters

Based on the finite element framework and uncertainty analysis theory, this paper proposes a first-order subinterval perturbation finite element method (FSPFEM) and a modified subinterval perturbation finite element method (MSPFEM) to solve the uncertain structural–acoustic problem with large fuzzy and interval parameters. Fuzzy variables are used to represent the subjective uncertainties associated with the expert opinions; whereas, interval variables are adopted to quantify the objective uncertainties with limited information. By using the level-cut strategy and subinterval methodology, the original large fuzzy and interval parameters are decomposed into several subintervals with small uncertainty level. In both FSPFEM and MSPFEM, the subinterval matrix and vector are expanded by the Taylor series. The inversion of subinterval matrix in FSPFEM is approximated by the first-order Neumann series, while the modified Neumann series with higher order terms is adopted in MSPFEM. The eventual fuzzy interval frequency responses are reconstructed by the interval union operation and fuzzy decomposition theorem. A numerical example evidences the remarkable accuracy and effectiveness of the proposed methods to solve engineering structural–acoustic problems with hybrid uncertain parameters.     

Numerical simulation of corona discharge in N2

A numerical study of a negative corona discharge in nitrogen in a point-plane gap using a Monte Carlo method is presented. The simulation provides a detailed structure of avalanches, propagation of successive avalanches and ion distribution can be discerned. The development of electron avalanches is due to ionization and photoionization in the high-field region, while the quenching of the avalanches is due to the low electric field near the plane electrode. Also the accumulation of electrons and positive ions are displayed in detail. The space charge field distortion is studied.     

Finite element method for radiation heat transfer in multi-dimensional graded index medium

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium.     

间断有限元方法求解一维非平衡辐射扩散方程

研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.     

A finite volume method for electrostatic three species negative corona discharge simulations with application to externally charged powder bells

A three species model for steady-state negative corona discharge is studied. Ionization, attachment, and recombination reactions are modeled. A novel unstructured finite volume algorithm to solve the equations is presented, using the secondary emission of electrons from the cathode to set boundary values for the electrons.To show the usefulness of the method for industrial applications it is used to characterize the electrostatic properties of an externally charged rotary powder bell used in the automotive industry. Experimental current density profiles are reconstructed with good accuracy, which validates the model and the method with real experimental data.     

水位骤变时的饱和-不饱和渗流数值计算

本文应用全隐式交替方向迭代法对水位骤变时的饱和-不饱和渗流问题求出了数值解。对于赤井模型,计算结果与实验结果十分接近,比有限元法的计算结果好。对于大尺度的驹田蓄水池模型,计算结果与有限元法的结果基本一致。     

考虑渗透率张量的非均质油藏有限元数值模拟方法

针对具有混合边界的非均质油藏,考虑全张量形式的渗透率,建立弹性微可压缩单相流体不稳定渗流问题的数学模型.根据变分原理,将压力微分方程的边值问题转化为泛函的极值问题,建立渗流模型的有限元方程.针对典型的均质和非均质渗流问题进行模拟计算,得到油藏内压力动态分布曲线,并分析曲线特征.研究表明,有限元法计算精度很高,适用于求解利用渗透率张量表征的非均质油藏渗流问题.为非均质油藏的开发和精细油藏数值模拟提供了理论依据.     

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss–Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.     

一维双曲守恒律的龙格-库塔控制体积间断有限元方法

给出数值求解一维双曲守恒律方程的新方法——龙格-库塔控制体积间断有限元方法(RKCVDFEM),其中空间离散基于控制体积有限元方法,时间离散基于二阶TVB Runge-Kutta技术,有限元空间选取为分段线性函数空间.理论分析表明,格式具有总变差有界(TVB)的性质,而且空间和时间离散形式上具有二阶精度.数值算例表明,数值解收敛到熵解并且对光滑解的收敛阶是最优的,优于龙格-库塔间断Galerkin方法(RKDGM)的计算结果.     

Impact on short length bars

A finite element method for the solution of an axisymmetric wave propagation problem of a bar of finite length is proposed. The results are obtained for a uniform bar with (i) a displacement input and (ii) a stress input. Also results are obtained for a discontinuous bar with stress input. They are compared with the existing finite difference solutions and experimental results. It is observed that the results are in close agreement. The study is then extended to the case of bars with an hemispherical end. The advantage of using the finite element method for such problems is indicated. Finally the results for a composite bar comprising a hallow cylinder and hemisphere are obtained by using the finite element method. Experiments are conducted to verify these results.     

应用离散偶应力单元分析弹性Cosserat介质

讨论了平面弹性偶应力问题的有限元方法,提出了离散偶应力单元的理论和构造方法,其特点是独立假设单元的位移和微观转角,偶应力理论中微观转角和宏观转角相等的假设在单元中以离散形式强加.该类单元列式简单,易于编程,且有满意的精度.并构造了一个三角形九自由度离散偶应力单元DCT9(discrete Coss-erat triangular).数值结果表明该单元能够较好地描述Cosserat介质的力学性质.     

基于交互模式的柔性体接触碰撞动力学建模方法

目前对于任意形状的柔性体接触碰撞问题,一般采用有限元离散,通用的建模方法有两类:罚函数法和附加约束法.罚函数法将接触作用视为弹簧阻尼力元,无需求解约束方程,但依赖于碰撞力参数的选取;附加约束法可严格满足接触约束条件,但数值求解更为复杂.针对两类接触模型各自的优缺点,提出基于交互模式的建模方法.该方法将整个模型分为局部静力学模块和主体动力学模块,在每个积分步内,局部静力学模块求解接触力,主体动力学模块求解运动学变量,两个模型之间进行位移和力的交互.该方法综合了附加约束法和罚函数法各自的优点,既无需人为选取碰撞参数,又满足局部区域互不嵌入的约束条件,同时数值求解方便.通过杆-板碰撞的实验算例及滑块-滑槽多点碰撞的数值算例,验证了该方法的有效性.     

Reducing the calculation workload of the Green function for electromagnetic scattering in a Schwarzschild gravitational field

When the finite difference time domain(FDTD) method is used to solve electromagnetic scattering problems in Schwarzschild space-time, the Green functions linking source/observer to every surface element on connection/output boundary must be calculated.When the scatterer is electrically extended, a huge amount of calculation is required due to a large number of surface elements on the connection/output boundary.In this paper, a method for reducing the calculation workload of Green function is proposed.The Taylor approximation is applied for the calculation of Green function.New transport equations are deduced.The numerical results verify the effectiveness of this method.     

辛体系下利用棱单元的电磁波导的计算

为了解决复杂形状横截面的电磁波导问题,根据电磁波导的Hamilton体系,在辛几何形式下采用有限元半解析横向离散的方法对电磁波导进行求解.该方法可应用于任意各向异性材料,且便于处理不同介质的界面条件,求解用解析方法难以求解的复杂问题.利用棱单元进行有限元离散,给出矩形波导、T隔膜矩形波导、分层波导等多种波导的具体算例,其数值结果逼近于真实解,且伪解消除,表明该方法有效.     

Efficient Analysis of Millimeter Wave Ferrite Circulators by the GMRES Iterative Algorithm

The finite element method (FEM) combined with the perfectly matched layers (PML) is given for simulation of waveguide ferrite circulators. The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. The formulation of FEM and the algorithm of GMRES method are described in detail. The reflection and insertion losses of millimeter wave waveguide circulator are analyzed and the results are compared with those obtained from literature.