Development and Comparison of Numerical Fluxes for LWDG Methods

The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing （TVD） Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure （LWDG） based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.     

A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE SHALLOW WATER EQUATIONS

In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory     

Phainanoids的4,5-螺环骨架的合成探索

本工作报道了用铑(I)催化芳基化环化反应和芳香亲核取代反应为关键步骤,合成天然产物Phainanoids的4,5-螺环骨架的探索.从已知化合物1出发,经过结构修饰得到炔酮5,在铑(I)催化条件下,与苯硼酸发生芳基化环化反应,构建了多取代环丁烯6.随后经过羟基保护和臭氧解反应得到α-烷氧基环丁酮8,其与格氏试剂9发生加成反应得到环丁醇10.最后在碱性条件下发生芳香亲核取代反应,在酸性条件下脱除乙氧基甲基(ethoxymethyl, EOM)和缩酮保护基,得到了4,5-螺环骨架结构18.格氏试剂9与邻烷氧基环丁酮8未能按照Cram’schelation模型进行与天然产物Phainanoids中螺环手性中心一致的立体选择性加成.综合文献报道和相关实验,可能的原因是:邻烷氧基环丁酮8的相对刚性结构,增加了镁离子与羰基氧原子和邻位烷氧基螯合过渡态的能垒;以及格氏试剂9中的氟原子与镁离子发生分子内螯合,抑制了镁离子与羰基邻位的烷氧基的螯合作用.     

Cortistatin类型天然产物的不对称形式全合成:金催化串联Semi-Pinacol重排反应策略

本工作详细报道了Cortistatin类型天然产物不对称形式全合成的研究路线.以近期作者发展的金催化串联semi-pinacol重排反应构建[3,2,1]七元氧桥环结构的方法学为基础,进一步将其应用于复杂体系,高效构建了Cortistatin类型天然产物独特的七元氧桥环核心骨架,从而完成了该类型天然产物的不对称形式全合成.     

A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes

The selection of time step plays a crucial role in improving stability and efficiency in the Discontinuous Galerkin (DG) solution of hyperbolic conservation laws on adaptive moving meshes that typically employs explicit stepping. A commonly used selection of time step is a direct extension based on Courant-Friedrichs-Levy (CFL) conditions established for fixed and uniform meshes. In this work, we provide a mathematical justification for those time step selection strategies used in practical adaptive DG computations. A stability analysis is presented for a moving mesh DG method for linear scalar conservation laws. Based on the analysis, a new selection strategy of the time step is proposed, which takes into consideration the coupling of the $α$-function (that is related to the eigenvalues of the Jacobian matrix of the flux and the mesh movement velocity) and the heights of the mesh elements. The analysis also suggests several stable combinations of the choices of the $α$-function in the numerical scheme and in the time step selection. Numerical results obtained with a moving mesh DG method for Burgers' and Euler equations are presented. For comparison purpose, numerical results obtained with an error-based time step-size selection strategy are also given.     

Efficient synthesis of maleimides and carbazoles via Zn(OTf)(2)-catalyzed tandem annulations of isonitriles and allenic esters

Lewis acid Zn(OTf)(2)-catalyzed tandem annulations of isonitriles and allenic esters which lead to efficient and flexible syntheses of a range of biologically significant maleimides and carbazoles and related compounds are reported. A mechanistic rationale is proposed to account for the observed reactivity.     

含芘环的缩氨基硫脲类化合物的合成及其对汞离子的识别

合成了芘甲醛-4-甲基缩氨基硫脲(1)、芘甲醛-4-(4-乙苯基)缩氨基硫脲(2)、芘甲醛-4,4-二甲基缩氨基硫脲(3)三个化合物,并通过质谱、元素分析、傅立叶红外光谱和核磁共振氢谱进行了结构表征.利用荧光激发和发射光谱,对其荧光活性进行研究,并考察了对溶液中汞离子的识别作用.在分别向三种化合物的溶液中逐步滴加汞离子时,其特征的荧光发射波长处对应的强度值都呈现规律性变化.因此可利用比率荧光法实现对汞离子配合过程的观测.结果表明,三种化合物都能与汞离子形成1:1的配合物,配合常数分别为4.57×104,5.54×104和2.12×104L/mol,其检测下限分别为4.56×10-6,2.61×10-6和5.49×10-6mol/L.     

Isolation and Asymmetric Total Synthesis of Perforanoid A

A novel limonoid, perforanoid A, was isolated, and an asymmetric total synthesis was achieved in 10 steps. The key steps are chiral tertiary aminonaphthol mediated enantioselective alkenylation of an aldehyde to an allylic alcohol, Pd‐catalyzed coupling of the allylic alcohol with vinyl ether to form the γ‐lactone ring, and cyclopentenone ring formation through a Rh‐catalyzed Pauson–Khand reaction. Preliminary studies show that perforanoid A is cytotoxic towards HEL, K562, and CB3 tumor cell lines.     

Weighted essential non‐oscillatory schemes for tidal bore on unstructured meshes

In this paper, the third‐order weighted essential non‐oscillatory (WENO) schemes are used to simulate the two‐dimensional shallow water equations with the source terms on unstructured meshes. The balance of the flux and the source terms makes the shallow water equations fit to non‐flat bottom questions. The simulation of a tidal bore on an estuary with trumpet shape and Qiantang river is performed; the results show that the schemes can be used to simulate the current flow accurately and catch the stronger discontinuous in water wave, such as dam break and tidal bore effectively. Copyright © 2008 John Wiley & Sons, Ltd.