Valence Tautomerism in Octahedral and Square‐Planar Phenoxyl–Nickel(II) Complexes: Are Imino Nitrogen Atoms Good Friends?

The two tetradentate ligands H(2)L and H(2)L(Me) afford the slightly distorted square-planar low-spin Ni(II) complexes 1 and 2, which comprise two coordinated phenolate groups. Complex 1 has been electrochemically oxidized into 1(+), which contains a coordinated phenoxyl radical, with a contribution from the nickel orbital. In the presence of pyridine, 1(+) is converted into 1(Py) (+), an octahedral phenolate nickel(III) complex with two pyridines axially coordinated: An intramolecular electron transfer (valence tautomerism) is promoted by the geometrical changes, from square planar to octahedral, around the metal center. The tetradentate ligand H(2)L(Me), in the presence of pyridine, and the hexadentate ligand H(2)L(Py) in CH(2)Cl(2) afford, respectively, the octahedral high-spin Ni(II) complexes 2(Py) and 3, which involve two equatorial phenolates and two axially coordinated pyridines. At 100 K, the one-electron-oxidized product 2(Py) (+) comprises a phenoxyl radical ferromagnetically coupled to the high-spin Ni(II) ion, with large zero-field splitting parameters, while 3(+) involves a phenoxyl radical antiferromagnetically coupled to the high-spin Ni(II) ion.     

Ethylene oligomerisation and polymerisation with nickel phosphanylenolates bearing electron-withdrawing substituents: Structure-reactivity relationships

Three SHOP-type catalysts, in which the C=C(O) double bond was substituted by electron-withdrawing substituents, [Ni{Ph2PC(R1)=C(R2)O}Ph(PPh3)] (2: R1,R2 = -C(Me)=NN(Ph)-; 3: R1 = CO2Et, R2 = Ph; 4: R1 = CO2Et, R2 = CF3), were assessed as ethylene-oligomerisation and -polymerisation catalysts and compared to Keim's complex, [Ni{Ph2PCH=C(Ph)O}Ph(PPh3)] (1). A rationale for the influence of the double-bond substituents of the P,O-chelate unit on the catalytic properties is proposed, on the basis of X-ray diffraction studies, spectroscopic data and DFT-B3 LYP calculations. Whatever their relative electron-withdrawing strength, the R1 and R2 substituents induce an increase in activity with respect to catalyst 1. For those systems in which the basicity of the oxygen atom is decreased relative to that of the phosphorus atom, the chain-propagation rate increases with respect to that for catalyst 1. Reduction of the basicity of the P relative to that of the O, however, induces higher chain-termination rates.     

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.     

网格模型PDE曲面重建中的边界曲线构造

利用偏微分方程(PDE)进行曲面拟合是计算机图形学研究领域中的常用方法,该类方法通过选取适当的边界条件来构造PDE,用PDE的解来表示几何曲面.基于网格简化方法和离散曲面测地线计算等技术,提出一种从网格模型提取PDE曲面片边界条件曲线的方法.首先,对复杂模型进行简化并分片处理;通过计算离散曲面的测地线为每个分片定义相应的PDE边界条件曲线,进而构造复杂模型的PDE拟合表面.最后,通过细分方法建立原模型的多分辨率表示.实验表明,该方法可以对具有不同几何复杂度的网格模型进行处理,产生具有细分连通性的多分辨网格模型.     

A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowup when the underlying continuous problem does. In situations where the continuous problem has infinite time blowup, the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases. The inadequacy of a uniform mesh solution is clearly demonstrated.     

A Pseudo-Stokes Mesh Motion Algorithm

This work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criterion is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.     

Transient flow around an impulsively started cylinder using a dynamic mesh method

The finite volume method (FVM) with a dynamic mesh method (DMM) to deal with the moving boundary was applied to the simulation of two-dimensional incompressible viscous flow past a circular cylinder that is impulsively started into rotation and translation. The non-dimensional rotating to translating speed ratio α is varied from 0.28 to 2.07, with the Reynolds number being 200 for the range of α. The computation covers a period, during which the cylinder translates seven times its diameter. The current scheme handles the impulsively moving boundary directly by DMM, which is implemented using both mesh deforming and local remeshing. The instantaneous asymmetrical flow configurations for various α are presented and compared with the experimental visualizations. Quantitatively, the velocity distributions with drag and lift coefficients are also compared with the experimental and numerical results. Results show that the flow is strongly influenced by the rotation. Comparisons are found to be satisfactory.     

High-order ALE method for the Navier–Stokes equations on a moving hybrid unstructured mesh using flux reconstruction method

The flux reconstruction (FR) formulation can unify several popular discontinuous basis high-order methods for fluid dynamics, including the discontinuous Galerkin method, in a simple, efficient form. An arbitrary Lagrangian–Eulerian (ALE) extension to the high-order FR scheme is developed here for moving mesh fluid flow problems. The ALE Navier–Stokes equations are derived by introducing a grid velocity. The conservation law are spatially discretised on hybrid unstructured meshes using Huynh’s scheme (Huynh 2007) on anisotropic elements (quadrilaterals) and using Correction Procedure via Reconstruction scheme on isotropic elements (triangles). The temporal discretisation uses both explicit and implicit treatments. The mesh movement is described by node positions given as a time series, instead of an analytical formula. The geometric conservation law is tested using free stream preservation problem. An isentropic vortex propagation test case is performed to show the high-order accuracy of the developed method on both moving and fixed hybrid meshes. Flow around an oscillating cylinder shows the capability of the method to solve moving boundary viscous flow problems, with the numeric method further verified by comparison of the result on a smoothly deforming mesh and a rigid moving mesh.     

三维空间二阶精度流体体积界面重构方法

给出三维空间网格模板含81个单元的最小二乘流体体积界面重构方法,并和Youngs方法及网格模板含125个单元的最小二乘流体体积界面重构方法进行比较.静态和动态的测试例子均表明:该方法能精确重构任意方向的平面界面,对C²光滑曲面它能达到二阶收敛精度.和网格模板含125个单元的最小二乘流体体积界面重构方法相比,在达到同样网格精度的条件下,减少了计算量,节省了计算时间,提高了计算效率.     

两种湍流模型时域颤振计算方法研究

采用时域计算分析方法进行了机翼跨音速颤振特性研究。在结构运动网格的基础上,采用格点格式有限体积方法进行空间离散和双时间全隐式方法进行时间推进求解雷诺平均N-S方程。针对流动粘性分别应用了SST湍流模型和SSG雷诺应力模型,通过对跨音速标模算例AGARD445.6机翼的计算结果与实验值的对比分析,其中应用SST湍流模型得到的颤振速度与实验值最为接近,特别是在跨音速段平均相对误差在3%以内;并且计算结果整体上反映了跨音速颤振"凹坑"物理特性,验证了方法的有效性。