Development of superconducting power devices in Europe

Europe celebrated last year (2008) the 100-year anniversary of the first liquefaction of helium by H. Kammerling Onnes in Leiden. It led to the discovery of superconductivity in 1911. Europe is still active in the development of superconducting (SC) devices. The discovery of high critical temperature materials in 1986, again in Europe, has opened a lot of opportunities for SC devices by broking the 4 K cryogenic bottleneck.     

Hybrid mesh generation with embedded surfaces using a multiple marching direction approach

This paper proposes a method for the creation of hybrid meshes with embedded surfaces for viscous flow simulations as an extension of the multiple marching direction approach (AIAA J. 2007; 45 (1):162–167). The multiple marching direction approach enables to place semi‐structured elements around singular points, where valid semi‐structured elements cannot be placed using conventional hybrid mesh generation methods. This feature is discussed first with a couple of examples. Elements sometimes need to be clustered inside a computational domain to obtain more accurate results. For example, solution features, such as shocks, vortex cores and wake regions, can be extracted during the process of adaptive mesh generation. These features can be represented as surface meshes embedded in a computational domain. Semi‐structured elements can be placed around the embedded surface meshes using the multiple marching direction approach with a pretreatment method. Tetrahedral elements can be placed easily instead. A couple of results are presented to demonstrate the capability of the mesh generation method. Copyright © 2008 John Wiley & Sons, Ltd.     

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

Attack structural vulnerability of power grids: A hybrid approach based on complex networks

Power grids have been studied as a typical example of real-world complex networks. Different from previous methods, this paper proposes a hybrid approach for structural vulnerability analysis of power transmission networks, in which a DC power flow model with hidden failures is embedded into the traditional error and attack tolerance methodology to form a new scheme for power grids vulnerability assessment and modeling. The new approach embodies some important characteristics of power transmission networks. Furthermore, the simulation on the standard IEEE 118 bus system demonstrates that a critical region might exist and when the power grid operates in the region, it is vulnerable to both random and intentional attacks. Finally, a brief theoretical analysis is presented to explain the new phenomena.     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

A multigrid method with unstructured adaptive grids for steady Euler equations

The multigrid method based on multi-stage Jacobi relaxation, earlier developed by the authors for structured grid calculations with Euler equations, is extended to unstructured grid applications. The meshes are generated with Delaunay triangulation algorithms and are adapted to the flow solution.     

Fast topological analysis of 2D and 3D grids of data: application to the atoms in molecule (AIM) and the electron localization function (ELF)

The topological analysis of grids of data is used for determination of surfaces or volumes around maxima. The volumes are then related to chemical information such as atoms or bonds, and can be used for integration of local properties such as electronic population. The problem of global connectivity is reversed into the question of local connectivity yielding a linear scaling partition algorithm. Two packages are developed for a very fast analysis and partition of 2D or 3D grids of data, applications being made to C2H2, C2H4, C6H6, H2CO, and H2CS molecules using the Atoms in Molecule (AIM) or Electron Localization Function (ELF).     

钝体后湍流预混燃烧的PDF模拟

本文采用PDF方法对矩形燃烧室内钝体后的湍流预混火焰进行了数值模拟。脉动速度-频率-标量联合的PDF输运方程用Monte Carlo方法求解,质量、动量和能量的平均值由基于无结构网格的有限体积法求解,压力通过状态方程获得。PDF方程中所需的平均密度、平均速度和压力由有限体积法提供,并将用Monte Carlo方法求出的雷诺应力、化学反应源项和比热比传递给有限体积法。本文对丙烷和空气燃烧的不同简化化学反应机理进行了研究,并与实验结果进行比较,获得满意的结果。     

Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.

Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.