2-D/3-D finite-element solution of the steady Euler equations for transonic lifting flow by stream vector correction

In this paper we study the validation of the new formulation (potential-stream vector) of the steady Euler equations in 2-D/3-D transonic lifting regime flow. This approach, which is based on the Helmholtz decomposition of a velocity vector field, is designed to extend the potential approximation of Euler equations for severe situations such as high transonic or rotational subsonic flows. Different results computed by a fixed point algorithm on the stream vector correction are shown and discussed by comparing them with those obtained by the full potential approach.     

关于Euler数一个猜想的证明

研究Euler数的猜想:对于任何素数p≡1 mod4,E(p-1)／20 mod p．根据Euler数本身的性质和Fourier级数对于Gauss和的应用,证明了这个猜想是成立的．     

Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.     

Difference Independence of the Euler Gamma Function*

In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma function Г. More precisely,if P is a polynomial of n+1 variables in C[X,Y₀,…,Y_n-1] such that P(s,Г(s+a₀),…,Г(s+a_n-1))≡0 for some(a₀,…,a_n-1) ∈ Cⁿ and a_i-a_j ■ Z for any 0≤i相似文献   

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

DISCUSSION ON TWO PROBLEMS OF THEORETICAL MECHANICS IN COLLEGE MECHANICS COMPETITION1)

针对两道力学竞赛试题,从欧拉动力学方程出发分别给出了更加简化的固连系选取方法,分别命名为"Serret-Andoyer近似固连系"和"虚固连系",在此基础上对第1届全国青年力学竞赛理论力学试题第9题,拓展讨论了大球同步旋转时,小球的稳 定性条件,结果表明后者的稳定临界转速要求更低,这将更有利于提高旋转结构的稳定性;对第12届全国周培源大学生力学 竞赛第3题,剖析了任一纬度的运动规律,发现当体系初始角动量为零时会出现一种简洁又优美的运动模式。     

Transient gas flow simulation using an Adaptive Method of LinesSimulation d'écoulements dans un gazoduc par la méthode adaptative de lignes

Designing natural gas pipelines to safely and efficiently handle unsteady flows, requires knowledge of pressure drop, flowrate and temperature distribution throughout the system. The accurate prediction of these parameters is essential in order to achieve optimum cumulative deliverability, and safe and reliable operation. An Adaptive Method of Lines algorithm is formulated for the solution of Euler system of equations, which fully simulates slow and fast transients. Two test cases present the improvement of the numerical solution from grid adaptation. Good results are obtained both for slow and fast transients simulations proving that the suggested numerical procedure is appropriate for such predictions. To cite this article: E. Tentis et al., C. R. Mecanique 331 (2003).     

Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.     

Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions

Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the independent variable u is the argument of Jacobian elliptic function theory. This allows a limitless number of indefinite integrals with respect to the amplitude to be derived for these three elliptic integrals. Sample results are given, including the integrals derived from powers of the 12 Glaisher elliptic functions. New recurrence relations and integrals are also given for the 12 Glaisher elliptic functions.