A finite volume method for viscous incompressible flows using a consistent flux reconstruction scheme

An incompressible Navier–Stokes solver using curvilinear body‐fitted collocated grid has been developed to solve unconfined flow past arbitrary two‐dimensional body geometries. In this solver, the full Navier–Stokes equations have been solved numerically in the physical plane itself without using any transformation to the computational plane. For the proper coupling of pressure and velocity field on collocated grid, a new scheme, designated ‘consistent flux reconstruction’ (CFR) scheme, has been developed. In this scheme, the cell face centre velocities are obtained explicitly by solving the momentum equations at the centre of the cell faces. The velocities at the cell centres are also updated explicitly by solving the momentum equations at the cell centres. By resorting to such a fully explicit treatment considerable simplification has been achieved compared to earlier approaches. In the present investigation the solver has been applied to unconfined flow past a square cylinder at zero and non‐zero incidence at low and moderate Reynolds numbers and reasonably good agreement has been obtained with results available from literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Challenges in predicting ΔrxnG in solution: Hydronium,hydroxide, and water autoionization

Standard non‐semiempirical continuum‐dielectric orbital‐based methods horribly overpredict, by 26‐50 kcal mol⁻¹, the Gibbs energy for the water autoionization reaction 2 H₂O_(l) → H₃O⁺_(aq) + OH^–_(aq). Here, we demonstrate these errors, fully investigate the reasons for these errors, and show that the use of 4 explicit solvent within the continuum (the “semicontinuum,” “cluster‐continuum,” or “hybrid” technique) can reduce the error of a standard continuum model from 50 to 2 kcal mol⁻¹. Results from pure cluster, pure continuum (several versions including semiempirical ones), and semicontinuum modeling are each presented and discussed. We recommend use of 3 waters around hydronium and 4 waters around hydroxide with standard continua whenever these ions are involved in reaction. To the possible surprise of some, time‐consuming molecular‐dynamics simulations are not needed to reproduce this problematic energy.     

Rang moyen de familles de courbes elliptiques et lois de Sato-Tate

The goal of this note is to give some complements to an article of Fouvery and Pomykala: by anad-hoc method, they bound on average the rank of elliptic curves over in polynomial families:y ²=x ³=a(t)x+b(t) whent varies in under some generic conditions on the polynomials (over a(t),b(t). Here, by a more systematic treatment, we are able to relax most of these conditions, keeping only the natural one (the family is not geometricaly trivial). However, this result, specialized to the case treated by Fouvry and Pomykala, yields a better bound; our method depends on the distribution of the number of points in families of elliptic curves over finite fields (known as the vertical Sato-Tate law), which itself depends on the work of Deligne on the Weil conjectures.

     

A Family of Trigonometrically-Fitted Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related Problems

In this paper a family of trigonometrically-fitted symmetric ten-step methods for the efficient solution of the Schrödinger equation and related problems is presented. Construction and stability analysis of the new methods is described. Numerical results obtained for the resonance problem of the one-dimensional Schrödinger equation show the efficiency of the new methods when they are compared with known methods in the literature.     

Trigonometrically fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation

In this paper we construct two trigonometrically fitted methods based on a classical Runge–Kutta method of England with fifth algebraic order. The methods will be used for the integration of the radial Schrödinger equation and have high efficiency as the results show. The efficiency is higher when using higher energy and this can be explained by the error analysis of the methods. More specifically the new methods have lower powers of the energy in the local truncation error and that keeps the error at lower values.PACS: 0.260, 95.10.EActive Member of the European Academy of Sciences and Arts     

基于神经网络的隐式显化方法在结构可靠度分析中的应用

针对结构可靠度分析中极限状态方程不能明确表达的情况,结合神经网络技术,提出了隐式极限状态方程转换为显式表达式的方法.该方法利用神经网络的非线性映射能力,构造出显式表达的极限状态方程,从而可以很方便的引入一次二阶矩等其他基本求解方法进行结构可靠度分析.实例数值结果表明,基于神经网络将隐式函数转化为明确表达的极限状态方程是可行的,同时该方法具有较高的精度,为结构可靠度计算提供了新的有效思路和手段.     

CEV模型下美式期权的差分算法

假设标的股价服从不变方差弹性(CEV)模型下,推导出美式看跌期权所遵循的变分不等方程.利用显式有限差分格式,给出具体的数值算法,并对格式的适定性进行分析,最后将其应用于实例,验证了算法的有效性.     

热方程的非古典势对称群与不变解

主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解．研究表明对于守恒形式的偏微分方程,可通过其伴随系统求得的非古典势对称群生成元来构造其显式解．这些显式解不能由方程本身的Lie对称群生成元或Lie-B?cklund对称群生成元构造得到．     

High‐order accurate p‐multigrid discontinuous Galerkin solution of the Euler equations

Discontinuous Galerkin (DG) methods have proven to be perfectly suited for the construction of very high‐order accurate numerical schemes on arbitrary unstructured and possibly nonconforming grids for a wide variety of applications, but are rather demanding in terms of computational resources. In order to improve the computational efficiency of this class of methods a p‐multigrid solution strategy has been developed, which is based on a semi‐implicit Runge–Kutta smoother for high‐order polynomial approximations and the implicit Backward Euler smoother for piecewise constant approximations. The effectiveness of the proposed approach is demonstrated by comparison with p‐multigrid schemes employing purely explicit smoothing operators for several 2D inviscid test cases. Copyright © 2008 John Wiley & Sons, Ltd.     

ON RITZ METHOD OF ANINTEGRO-DIFFERENTIAL EQUAITON

This paper deals with the Ritz method of an integro-differential equation related with Riemann zeta-function.