The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

The implementation of an adaptive mesh‐embedding (h‐refinement) scheme using unstructured grid in two‐dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an‐isotropic refinement in the interfacial cells between refined and non‐refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high‐speed driven cavity flow. The results show an improved flow resolution as compared with that of un‐adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near‐continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non‐uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd.     

悬浮颗粒运动的格子Boltzmann数值模拟

将固体颗粒的牛顿力学和格子Boltzmann方法相结合,研究不规则形状悬浮颗粒在流场中的运动。通过受力分析,精确求得其所受合力、合力矩、合力作用中心等。提出了跟随颗粒运动的动网格计算域技术和模拟悬浮颗粒转动运动的局部数组方法及Euler-Lagrange两套坐标技术。通过对椭圆颗粒运动的数值模拟和对照他人对矩形颗粒的研究,分析了其复杂运动规律,并提供了合理的物理解释。结果表明:运用格子Boltzmann方法和上述特殊技术可以得到与有限元方法相同的模拟精度,且具有计算速度快、对复杂形状边界处理方便灵活、程序简单及特别适合大规模并行计算等优点。     

任意平面区域的高质量有限元网格自动剖分

实现了任意平面区域的高质量三角形有限元网格自动剖分。初始化时利用广度优先搜索查找孔及凹槽中需删除的三角形 ,不需定义有向边界 ,可十分方便地定出实际剖分区域 ;给出了一种方便、快捷的点定位法 ,可大大提高程序运行速度 ;利用Delaunay网格优化算法实现了对三角形形状的控制 ,可使三角形最小角达到 35° ;分割坏三角形时 ,按最小角由小到大的顺序处理 ,使三角形网格在满足质量要求的同时网格数量较少     

A VIRTUAL MESH METHOD FOR THE OPTIMIZED DESIGN OF COMPLEX STRUCTURES

Concepts for a virtual 3D space and a hyper-sphere are proposed and the formulae for determining the computable nodes of the mesh are derived. Then a new optimization design method (‘Virtual Mesh Method‘ or V.M.M) is developed. Three examples are given, showing that the method proposed is especially suitable for the optimized design of complex structures, and that the global approximate optimal solution can be searched with remarkably reduced computational work.     

复杂三维组合曲面的有限元网格生成方法

提出一种基于映射法的复杂三维组合曲面的有限元网格全自动生成方法。通过引入虚边界解决了闭合曲面在参数域中边界不完整的问题；通过调节虚边界提高了复杂组合曲面网格生成的质量。改进二维多边形区域的裁减算法，解决了闭合曲面在参数空间中的边界环形成问题。对曲面片公共边界进行统一离散化处理，以满足有限元网格的相容性要求。以边界表示(B—Rep)数据结构为基础，实现了组合曲面全自动网格剖分的总成算法．改进了曲面网格剖分布点算法，并结合局部连接、诊断交换等技术，优化了网格的整体质量。     

牛顿流体挤出胀大模拟的网格依赖性

应用有限元法模拟了牛顿流体的挤出胀大，通过方差分析得到胀大结果具有网格依赖性．基于四边形等参单元，得到出口后首排单元沿轴向的长度和近壁处首行单元沿径向的高度显著影响牛顿流体的挤出胀大．     

IrO_2改性钛网对固体聚合物电解质电解器集电极层电化学性能的影响

采用亚当斯熔融法(Adams fusion method)在钛网上包覆Ir O2催化剂,并将其用作固体聚合物电解质(SPE)电解器的阳极集电极,发现其可以显著降低电解过电位.通过X射线多晶衍射(XRD)和透射电子显微镜(TEM)分析发现,包裹在钛网上的Ir O2催化剂晶粒为2.0~3.0 nm,结晶度良好;交流阻抗谱(EIS)和循环伏安(CV)分析结果表明,改性的钛网集电极层可增加三相反应活性点,使三相反应通道由催化层延伸到集电极层,活性催化剂表面积增大,从而大幅度降低了活化阻抗,电解性能获得提升.通过对不同Ir O2催化剂负载量改性的钛网进行研究发现,随着钛网负载Ir O2量的增加,在相同电流密度下,极化曲线的过电位先减小后增加,当Ir O2负载量为1.38%(质量分数)时,电解池的过电位最低,在1 A/cm2电流密度下,过电位为2.028 V.     

The H,H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

The one electron systems H, H , and HeH confined by an impenetrable spheroidal cavity are revisited in the frame of the Lagrange‐mesh method. The Born–Oppenheimer approximation where the nuclei are clamped at the foci is considered. Benchmark results of the total energy are obtained as a function of the interfocal distance R and the eccentricity of the cavity . Dipole oscillator strengths are calculated for the molecular ions H and HeH .     

Nonstable <Emphasis Type="Italic">K</Emphasis>-theory for Graph Algebras

We compute the monoid V(L _K (E)) of isomorphism classes of finitely generated projective modules over certain graph algebras L _K (E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of L _K (E) and the lattice of order-ideals of V(L _K (E)). When K is the field of complex numbers, the algebra is a dense subalgebra of the graph C ^*-algebra C ^*(E), and we show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra of any row-finite graph turns out to satisfy the stable weak cancellation property. The first author was partially supported by the DGI and European Regional Development Fund, jointly, through Project BFM2002-01390, the second and the third by the DGI and European Regional Development Fund, jointly, through Project MTM2004-00149 and by PAI III grant FQM-298 of the Junta de Andalucía. Also, the first and third authors are partially supported by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.     

Biorthogonal multiple wavelets generated by vector refinement equation

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form (?)(x)=(?)a(α)(?)(Mx-α),x∈R~s, where the vector of functions(?)=((?)_1,...,(?)_r)~T is in(L_2(R~s))~r,a=:(a(α))_(α∈Z~s)is a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim_(n→∞)M~(-n)=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.