Local refinement techniques for elliptic problems on cell-centered grids; II. Optimal order two-grid iterative methods

Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

二维圆柱坐标系中五角形共形网格算法

 时域有限差分（FDTD）算法求解电磁问题时，如果目标结构不能和传统网格体系共形，往往采用局部共形网格或非正交网格算法。详细讨论了二维圆柱坐标系中五角形共形网格算法，该算法能方便地对倾斜薄层媒质或电导率不均匀的倾斜媒质等复杂结构建模,并以锥形电磁脉冲天线为例，验证了该算法的有效性。     

Validity and Accuracy of Equivalent Circuit Models of Passive Inductive Meshes. Definition of a Novel Model for 2D Grids

Accuracy of equivalent circuit models of periodic grids is investigated in amplitude and phase in the visible region. The grids studied here are one-dimensional (1D) and two-dimensional (2D) inductive thin metal meshes. They are located in free space and are illuminated by a plane wave under normal incidence. The range of validity and the accuracy of conventional circuit models are defined by comparison with rigorous results obtained with the Finite-Difference Time-Domain (FDTD) method. In particular, it is shown that electrical models of 1D grids are accurate, whereas equivalent circuits of 2D grids should be used very cautiously. Then, a new formulation is proposed to overcome this major drawback. In the non-diffraction region, the agreement between our model and the FDTD results is within 2% for the power reflectivity and 1° for the phase over a very wide range of strip widths.     

A parallel adaptive mesh approach for flowfields with shock waves

A simple and efficient implementation of Adaptive Mesh Refinement (AMR) with distributed-memory approach is presented. Introducing a lookup table including grid connectivity information and simplified algorithms for AMR, the procedures for reconstructing adaptive grids are carried out in parallel, with local data to a large extent. A simple static load-balancing scheme is adopted, and the grids are not repartitioned and no data redistribution is performed. A numerical example on two different parallel computers shows that the proposed implementation of AMR is effective to reduce the computational time for unsteady flows with shock waves. Received 23 October 2000 / Accepted 30 March 2001 Published online 11 June 2002     

Viscous waves and wave-structure interaction in a tank using adapting quadtree grids

Viscous waves and waves over a submerged cylinder in a stationary tank are simulated using a volume-of-fluid numerical scheme on adaptive hierarchical grids. A high resolution interface-capturing method is used to advect the free surface interface and the Navier–Stokes equations are discretised using finite volumes with collocated primitive variables and solved using a Pressure Implicit with Splitting of Operators (PISO) algorithm. The cylinder is modelled by using the technique of Cartesian cut cells. Results of flow of a single fluid past a cylinder at Reynolds number Re=100 are presented and found to agree well with experimental and other numerical data. Viscous free surface waves in a tank are simulated using uniform and quadtree grids for Reynolds numbers in the range from 2 to 2000, and the results compared against analytical solutions where available. The quadtree-based results are of the same accuracy as those on the equivalent uniform grids, and retain a sharp interface at the free surface while leading to considerable savings in both storage and CPU requirements. The nonlinearity in the wave is investigated for a selection of initial wave amplitudes. A submerged cylinder is positioned in the tank and its influence on the waves as well as the hydrodynamic loading on the cylinder is investigated.     

Adaptive unstructured finite element method for two-dimensional detonation simulations

A non-equilibrium reacting flow methodology has been added to a conservative, monotonic, compressible flow solver to allow numerical simulations of gas detonations. This flow solver incorporates unstructured dynamically adaptive meshes with the Finite Element Method – Flux Corrected Transport (FEM-FCT) scheme, which has shown excellent predictive capability of various non-reacting compressible flows. A two-step induction parameter model was used to model the combustion of the gas phase coupled with an energy release equation which was simulated with a point implicit finite element scheme. This combustion model was then applied to a two-dimensional detonation test case of a hypothetical fuel:oxygen mixture. The detonation simulation yielded two transverse waves which continued to propagate. This feature and the detonation shock speed mean and fluctuations were found to be grid-independent based on a resolution of about twenty elements within the average induction length. The resolution was efficiently achieved with the unstructured dynamically adaptive finite elements, which were three orders of magnitude less in number then required for uniform discretization. Received 26 August 1996 / Accepted 31 March 1997     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

基于SIMPLER算法的多重网格方法研究

以二维方腔顶盖驱动流为模型,将多重网格方法和SIMPLER算法进行耦合,对不同雷诺数下多重网格加速SIMPLER算法和SIMPLER算法的计算效率进行了对比,数值计算表明:多重网格加速SIMPLER算法不仅能够解决SIMPLER算法不能准确模拟较高雷诺数流场的问题,而且其计算效率远远高于SIMPLER算法.本文也对松弛因子的选取、多重网格实现形式以及网格层数对多重网格加速SIMPLER算法的影响进行了研究,从而为多重网格加速SIMPLER算法的实施提供了计算技术.     

局部荷载作用下网架结构的拟夹层板分析法

把正交正放类网架结构简化为构造上正交异性的夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论来分析，给出了网架结构在局部荷载作用下的内力、位移解析计算公式，并用有限元方法进行了验证．