由扩散张量导出的各向异性扩散模型的隐式数值模拟

研究了由扩散张量导出的各向异性扩散的图像处理模型,并构造了隐式差分格式,形成了有13条对角线的大型稀疏矩阵.利用代数多重网格法求解了这个线性代数方程组.并进行了数值试验.     

Two-sided approximations for unilateral variational inequalities by multi-grid methods

For the numerical solution of unilateral variational inequalities two iterative schemes are developed which provide approximations from below resp. from above. Both schemes are based on some kind of active set strategy and require the solution of an algebraic system of equations at each iteration step which is done by means of multigrid techniques. Convergence results are established and illustrated by some numerical results for the elastic-plastic torsion problem     

用粘性体力方法计算轴流叶轮机械内部流场

阐述了一种用于叶轮机械内部三维粘性流场计算程序。该程序以有限体积显式时间推进方法为基础,用Baldwin-Lomax模型模拟湍流流动,用局部时间步长和多重网格方法提高计算效率。使用上述方法计算了NASA 37^#跨音速压气机转子流场,并与实验结果进行了比较,从而证明文中提出的方法能够快速、准确地模拟轴流叶轮机械内部复杂三维流场,该方法具有较强的工程实用意义。     

Multi-grid simulation of pedestrian counter flow with topological interaction

We investigate the dynamics of pedestrian counter flow by using a multi-grid topological pedestrian counter flow model.In the model,each pedestrian occupies multi-rather than only one grid,and interacts with others in the form of topological interaction,which means that a moving pedestrian interacts with a fixed number of those nearest neighbours coming from the opposite direction to determine his/her own moving direction.Thus the discretization of space and time are much finer,the decision making process of the pedestrian is more reliable,which all together makes the moving behaviour and boundary conditions much more realistic.When compared with field observations,it can be found that the modified model is able to reproduce well fitted pedestrian collective behaviour such as dynamical variation of lane formation,clustering of pedestrians in the same direction,etc.The fundamental diagram produced by the model fits also well with field data in the free flow region.Further analyses indicate that with the increase of the size of pedestrian counter flow system,it becomes harder for the system to transit into a jamming state,while the increase of interaction range does not change the transition point from free flow to jamming flow in the multi-grid topological counter flow model.It is also found that the asymmetry of the injection rate of pedestrians on the boundaries has direct influence on the process of transition from free flow to jamming flow,i.e.,a symmetric injection makes it easier for the system to transit into jamming flow.     

基于贝叶斯理论的恢复力模型参数识别方法

提出了基于贝叶斯理论的恢复力模型参数识别方法,该方法考虑了模型误差的影响,结合实测滞回曲线数据,不仅可以得到模型参数的最有可能值,而且可以得到模型参数的定量的不确定性。以密肋复合墙体在低周反复荷载作用下所得滞回曲线为例,提出了可考虑刚度降低、捏拢滑移及极限荷载后强度降低现象的恢复力模型,建立了基于贝叶斯理论的恢复力模型参数识别计算框架,推导得到了模型参数的负对数似然函数,据此可得到模型参数的最有可能值及协方差矩阵。对标准密肋复合墙体预制试件和现浇试件的恢复力模型参数进行了识别,将根据模型参数最有可能值得到的滞回曲线及根据模型参数最有可能值及协方差矩阵得到的骨架曲线,与相应的实测值进行了对比,验证了所提方法的可行性及识别结果的合理性,更新的模型参数概率分布可用于后续的抗震风险评估。     

An adaptive multi-grid chemistry (AMC) model for efficient simulation of HCCI and DI engine combustion

There is a need to reduce the computational expense of practical multidimensional combustion simulations. Simulation of Homogeneous Charge Compression Ignition (HCCI) engine processes requires consideration of detailed chemistry in order to capture the ignition and combustion characteristics. Even with relatively coarse numerical meshes and reduced chemistry mechanisms, calculation times are still unacceptably long. For the simulation of Direct Injection (DI) engines, fine meshes are needed to achieve the resolution required by the spray and mixing models, and they are computationally expensive even with reduced chemistry. In addition, the increasing application of CFD for engine design optimization is pushing the demand to reduce computational time. In current design optimizations, depending on the size of the parametric space, hundreds of individual simulations are needed.

This work presents an efficient Adaptive Multi-grid Chemistry (AMC) model that can be used in engine CFD codes for simulations of HCCI and DI engines with detailed chemistry. It was found that the number of cells computed with the chemistry solver can be reduced by two orders of magnitude for HCCI engines. The results predicted by the present KIVA AMC code are also consistent with those calculated by the original code using every cell.

In the method, progressively coarser grids are used for cells with similar gas properties in the chemistry calculation (up to four neighbour levels) or in the global method, cells are grouped without regard for their locations in the cylinder. Averaged and gradient-preserving remapping techniques used in multi-zone engine simulations were also explored. A parametric study was conducted for determining the model variables, such as the degree of local homogeneity for the multi-grid solvers.

The simulation results were compared with experimental data obtained from a Honda engine operated with n-heptane under HCCI conditions for which directly measured in-cylinder temperature and H₂O mole fraction data are available. In addition, simulation results were found to agree well with experimental data from a DI diesel engine operated under PCCI conditions with ultra-high EGR rates. It was found that computer time was reduced by a factor of ten for HCCI cases and two to three for DI cases without losing prediction accuracy.     

A new algorithm for total variation based image denoising

We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.     

一种有效的广义特征值分析方法

提出了一种适合于自适应有限元分析中求解广义特征值问题的多重网格方法．这种方法充分利用了初始网格下的结果，通过插值或最小二乘拟合技术来得到网格变化后的新的近似特征向量，然后由多重网格迭代过程实现对结构广义特征值问题的求解．在多重网格迭代的光滑步中，选择了收敛梯度法以提高其收敛率；在粗网格校正步中，则导出了一种近似求解特征向量误差的方程．这种方法将网格离散过程和数值求解过程很好地相结合，建立了一个网格细分后广义特征值问题的快速重分析方法，与传统有限元方法相比较，具有计算简便、计算量少等特点，可以作为结构动力问题自适应有限元分析的一种十分有效的工具．     

二次发射微波电子枪的数值计算方法

阐述了在rfz轴对称坐标系下,计算二次发射微波电子枪中电子束运动的一种数值方法.通过在束流运动区域建立网格,把空间中的电荷密度分布转化为网格上各顶点的电荷密度分布.在束团运动坐标系中,用多重网格法求解Poisson方程,得到束团的空间电荷场.用5阶Runge?Kutta法直接求解相对论下的电子运动方程.通过实例计算,并和MAFIA的计算结果对比,证明其是一种可靠的方法.     

外框密肋复合墙抗剪机理及承载力计算

在外框密肋复合墙低周反复荷载试验的基础上,对墙体的抗剪机理进行了分析;依据极限平衡理论引入砌体抗剪承载力影响系数和框格承载力影响系数,同时考虑RC框格与填充砌块之间的相互作用;提出了外框密肋复合墙抗剪承载力计算公式;本文公式计算结果与试验结果、有限元数值模拟结果进行了比较。研究表明:本文基于水平薄弱层破坏建立的外框密肋复合墙抗剪公式较传统基于斜截面破坏建立的抗剪公式具有更明确的物理意义;本文公式计算精度较高,与试验结果、有限元数值模拟结果相差不到10%。