A discontinuous Galerkin method/HLLC solver for the Euler equations

This paper proposes a fully three‐dimensional non‐linear Euler methodology for solving aerodynamic and acoustic problems in the presence of strong shocks and rarefactions. It uses a discontinuous Galerkin method (DGM) within the element, and a Riemann solver (HLLC) at the boundaries to propagate rarefactions while preserving the entropy condition and capturing shocks with no spurious oscillations. This approach is thought to marry the best aspects of finite element and finite volume methods, achieving conservation while not requiring the solution of a large matrix. Examples in which shock and rarefaction waves are well captured are presented and the propagation of acoustic pulses is well demonstrated. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

有限元节点编号优化

从分析最简单最优的矩形单元节点编号着手，分析其特点，得出各个节点的相邻单元节点编号总和除以该节点相邻单元数所得的节点商以及相邻单元最小最大节点编号和都为升序排列。总结出一种新型的有限元节点重编号方法，并举例说明该算法能减少有限元的带宽。     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

合成丙交酯中微量水分分析

合成丙交酯中微量水分分析徐溢，柳胜春（重庆大学化工学院分析教研室６３００４４）关键词丙交酯，微量水，定量分析丙交酯是人工合成骨材料聚乳酸的合成中间体，其性能决定着合成产品的品质，要获得高质量的合成材料，对中间体的分析和监测十分重要。一般要求丙交酯中间...     

四磺酸基酞菁锌在水和非水溶剂中的电化学性质研究

在非水溶剂（二甲基亚砜（ＤＭＳＯ）及Ｎ,Ｎ＿二甲基甲酰胺（ＤＭＦ））中的伏安曲线．呈现三对电流峰,表明存在三个可逆或准可逆酞菁配体的单电子转移过程,而在水溶液中则不呈现准可逆行为,且波形改变很大．此外,还比较了四磺酸基酞菁锌的水溶液在自然光和红光（６００～７００ｎｍ）照射下的循环伏安曲线,其氧化还原峰的数目和峰电位基本不变,但在红光照射下比自然光照射下的峰电流明显增大．     

Zn(II)-selective membrane electrode based on tetra(2-aminophenyl) porphyrin

A new PVC membrane electrode for Zn²⁺ ions based on tetra(2-aminophenyl) porphyrin (TAPP) as membrane carrier is prepared. The sensor exhibits a linear stable response over a wide concentration range (5.0×10⁻⁵ to 1.0×10⁻¹ M) with a slope of 26.5 mV/decade and a limit of detection 3.0×10⁻⁵ M (1.96 ppm). It has a response time of about l0 s and can be used for at least 8 months without any divergence in potential. The propose membrane sensor revealed good selectivities for Zn²⁺ over a wide variety of other metal ions and can be used in pH range of 3.0–6.0. It was successfully applied to the direct determination of zinc in a pharmaceutical sample and also as an indicator electrode in potentiometric titration of Zn²⁺ ions.