Adaptive collision meshing and satellite droplet formation in spray simulations

Improved numerical methods and physical models have been applied to droplet collision modeling. Numerically, an adaptive collision mesh method is developed to calculate collision rate. This method produces a collision mesh that is independent of the gas phase mesh and adaptively refined according to local parcel number density. An existing model describing the satellite droplet formation during the collision process is improved to reflect the experimental findings that the satellite droplets are much smaller than the parent droplets. The adaptive collision mesh and the improved satellite model have been used to simulate three impinging spray experiments. The model was able to qualitatively predict the occurrence of small satellite drops and bi-modal post-collision drop size distributions. The effect of the collision mesh and the satellite droplet model on a high-speed non-evaporating diesel spray is also assessed.     

A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L₂ norm error estimator is proposed for thePoisson equation. The error estimator can be applied to anisotropictetrahedral or triangular finite element meshes. The estimatoris rigorously analysed for Dirichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropicbubble functions and the corresponding inverse inequalities.The upper error bound utilizes non-standard anisotropic interpolationestimates. Its proof requires H² regularity of the Poisson problem,and its quality depends on how good the anisotropic mesh resolvesthe anisotropy of the problem. This is measured by a so-called‘matching function’. A numerical example supports the anisotropic error analysis.     

黏性边界层网格自动生成

高雷诺数黏性流动在壁面附近存在边界层,在计算模拟中自动生成可靠且有效的计算网格仍然是计算流体力学存在的瓶颈.三棱柱/四面体混合网格技术在一定程度上缓解了这个困难.然而,对于复杂外形的情况,在边界层内自动高效生成高质量的三棱柱单元仍然十分困难.常用的层推进法在凹凸区域及角点处生成的边界层网格单元质量较差,边界层网格最外层尺寸不均匀.针对这些问题,发展了一种黏性边界层网格自动生成方法,通过顶点周围边的二面角识别物面网格特征确定多生长方向,预估并调整生长高度处理相交情况.同时提出一种三维前沿尺寸调节方式,提高了边界层网格单元的正交性,保证了边界层网格与远场网格尺寸的光滑过渡.通过ONERA M6翼型以及带发动机短舱的DLR-F6翼身组合体等外形的网格生成实例及绕流数值模拟,将计算值与标准实验值进行对比,结果表明:该方法能够自动高效地生成满足数值计算需求的混合网格.     

High order generalized upwind schemes and numerical solution of singular perturbation problems

High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation problems are taken into account to emphasize the main features of the proposed methods. AMS subject classification (2000)  65L10, 65L12, 65L50     

有限元网格自动生成及自动调整技术

本文给出了一种任意平面域内三角形网格自动生成及自动调整算法，并编制了相应的程序。通过对带Ｕ形槽的三点变曲试件的分析，证明本文算法是可行的，并且具有稳定性能好、收敛速度快的优点。     

计算钝感炸药爆轰过程的一种新反应率模型

根据钝感炸药爆轰过程中含有激化过程和慢反应,建立了一种新的反应率模型。与其他反应率模型相比,这种反应率模型可以应用于较粗的网格。在每厘米50个网格条件下,炸药驱动铝飞片和钽飞片的自由面计算结果与实验结果很接近。同时,应用此反应率模型计算了钝感炸药驱动LiF过程,在每厘米50个网格的条件下,炸药与LiF间速度的计算值同实验值接近,且误差随网格尺寸变小而变小。这些表明,此反应率模型能够在较粗的网格条件下,比较准确地描述钝感炸药驱动飞片过程,有利于在工程实际中应用。     

一类雨量预报准确性评价方法

给出了一种利用网格点的预报雨量来模拟区域内任一点预报雨量的方法,建立了预报雨量函数,进而得出预报雨量与实测雨量的整体偏方差的数学模型;利用QPF方法建立出准确率、预报效率、空报率、漏报率等评价预报方法优劣指标的数学模型,并对两种预报方法得出的数据进行了计算,得出上述模型中的数值如下:方案方法总体偏方差预报准确率漏报率空报率预报效率方法1 0.99987×10679.431%11.463%25.621%62.256%方法2 1.00518×10657.509%26.976%31.705%58.936%比较这些指标,可得第一种预报结果较好.     

An ?-uniform hybrid scheme for singularly perturbed delay differential equations

In this paper, a singularly perturbed delay differential equation of first order has been considered. The problem is solved by using a hybrid scheme on a Shishkin mesh. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Truncation errors are obtained. Finally, numerical experiments are carried out on a test problem, confirming the effectiveness of the proposed technique.     

基于工业CT图像重构的网格模型的保特征简化方法

对基于工业CT图像重构的网格模型进行网格简化时,大多数现有网格模型简化算法会丢失特征,出现网格质量不好的问题。因此提出一种网格模型保特征简化方法,该方法用三角形折叠法对原始模型进行简化,当简化后模型的平均二面角角度误差达到允许误差后,再使用边折叠法对模型进行简化。在三角形折叠法中提出了利用被折叠三角形的法向量、各个顶点的高斯曲率及其在周边三角形上的投影确定该三角形的折叠点,利用局部体积误差与二面角角度误差的无因次化和确定折叠代价的方法;在边折叠法中提出了将二面角角度误差引入到二次误差测度（QEM）法的折叠代价中的改进QEM法。实验结果表明：与其他算法相比,该方法能够生成保特征、高质量、低几何误差的网格模型。