Anisotropic mesh adaptation: towards user‐independent,mesh‐independent and solver‐independent CFD. Part I: general principles

The present paper is the lead article in a three‐part series on anisotropic mesh adaptation and its applications to structured and unstructured meshes. A flexible approach is proposed and tested on two‐dimensional, inviscid and viscous, finite volume and finite element flow solvers, over a wide range of speeds. The directional properties of an interpolation‐based error estimate, extracted from the Hessian of the solution, are used to control the size and orientation of mesh edges. The approach is encapsulated into an edge‐based anisotropic mesh optimization methodology (MOM), which uses a judicious sequence of four local operations: refinement, coarsening, edge swapping and point movement, to equi‐distribute the error estimate along all edges, without any recourse to remeshing. The mesh adaptation convergence of the MOM loop is carefully studied for a wide variety of test cases. The mesh optimization generic coupling of MOM with finite volume and finite element flow solvers is shown to yield the same final mesh no matter what the starting point is. It is also shown that on such optimized meshes, the need for computational fluid dynamics (CFD) stabilization artifices, such as upwinding or artificial viscosity, are drastically reduced, if not altogether eliminated, in most well‐posed formulations. These two conclusions can be considered significant steps towards mesh‐independent and solver‐independent CFD. The structure of the three‐part series is thus, 1, general principles; 2, methodology and applications to structured and unstructured grids; 3, applications to three‐dimensional flows. Copyright © 2000 John Wiley & Sons, Ltd.     

物理实验的拓展

实验教学是物理教学中的一个重要环节,也是一个突出的薄弱环节.实验教学是帮助学生建立正确的概念、掌握科学规律、获得系统知识、形成技能技巧和具备各种能力的重要手段.但长期以来,由于应试教育的影响,以及对实验教学理解的偏差与局限,普遍存在着教师为"应试"而教,学生为"应试"而学,使实验在教学中的应有作用难以充分体现.如何搞好实验教学,提高实验教学水平,是广大物理教师都在探索的问题.现就实验教学过程中如何通过实验拓展方式,培养学生的创新能力,谈谈做法.     

On Schwarz Alternating Methods for the Subsonic Full Potential Equation

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. The full potential equation is derived from the Navier–Stokes equations assuming the fluid is compressible, inviscid, irrotational and isentropic. It is being used by the aircraft industry to model flow over an airfoil or even an entire aircraft. This paper shows that the additive and multiplicative versions of the Schwarz alternating method, when applied to the full potential equation in three dimensions, converge to the true solution geometrically. The assumptions are that the initial guess and the true solution are everywhere subsonic. We use the convergence proof by Tai and Xu and modify it for certain closed convex subsets.     

Prediction of wall thickness distribution in thermoformed mouldings

Polystyrene, polyethylene, polyvinyl butyral and PVC sheets have been vacuum formed into conical and truncated cone shaped moulds in an attempt to predict the variation in wall thickness in the mouldings. It has been found that, for conical moulds, the thickness distribution can be predicted accurately using previously published analysis; for the more practical truncated cone shapes, it was necessary to develop a special equation. This equation predicted wall thicknesses in good agreement with the measured results in four different moulds and could also be used to predict the results reported by other workers.     

Oxygen isotope effects on electron transfer to O2 probed using chemically modified flavins bound to glucose oxidase

Apo-glucose oxidase has been reconstituted with flavins modified in the 7 and 8 positions and characterized with regard to the catalytic rate of O(2) reduction and oxygen-18 isotope effects on this process. Kinetic studies as a function of driving force indicate a reorganization energy for electron transfer to O(2) of lambda = 28 kcal mol(-)(1) at optimal pH, which is similar to the value obtained earlier from temperature dependencies of rates (Roth, J. P.; Klinman, J. P. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 62-67). For the various enzyme-bound flavins, competitive oxygen-18 kinetic isotope effects fall within the narrow range of 1.0266(5) to 1.0279(6), apparently because of the dominant contribution of outer-sphere reorganization to the activation barrier; within the context of semiclassical and quantum mechanical electron transfer theories, the magnitude of the isotope effects reveals the importance of nuclear tunneling.     

The aerobic methylation of arsenic by microorganisms in the presence of l-methionine-methyl-d3

The microorganisms Scopulariopsis brevicaulis, Candida humicola, and Gliocladium roseum growing aerobically, methylate a range of arsenic compounds to produce R′R″As(CH₃) (R′  R″  CH₃; R′  n-C₄H₉, R″  CH₃). When l-methionine-methyl-d₃ is added to the cultures the CD₃ label is incorporated, intact, in the evolved arsine to a considerable extent, indicating that S-adenosylmethionine or some related sulphonium compound is involved in the biological process.     

尿素刀豆生物传感器的研制

本文报告了尿素刀豆生物传感器的制备和性能。斜率46.0—49.7mv.dec~(-1)、线性范围2×10~(-4)—5×10~(-3)mol.L~(-1),检测下限2.5×10~(-5)mol.L~(-1)。该传感器用于血液中尿氮含量的测定,此测定结果与分光光度法测定结果无明显差异。     

Beyond structural motifs: the frontier of actinide-containing metal–organic frameworks

In this perspective, we feature recent advances in the field of actinide-containing metal–organic frameworks (An-MOFs) with a main focus on their electronic, catalytic, photophysical, and sorption properties. This discussion deviates from a strictly crystallographic analysis of An-MOFs, reported in several reviews, or synthesis of novel structural motifs, and instead delves into the remarkable potential of An-MOFs for evolving the nuclear waste administration sector. Currently, the An-MOF field is dominated by thorium- and uranium-containing structures, with only a few reports on transuranic frameworks. However, some of the reported properties in the field of An-MOFs foreshadow potential implementation of these materials and are the main focus of this report. Thus, this perspective intends to provide a glimpse into the challenges, triumphs, and future directions of An-MOFs in sectors ranging from the traditional realm of gas sorption and separation to recently emerging areas such as electronics and photophysics.

This perspective deviates from exclusively focusing on structural features of actinide-containing metal-organic frameworks and pivots towards their prospect as avant-garde materials with an emphasis on their physicochemical properties.     

对甲苯磺酸催化合成乳酸异戊酯

报道了对甲苯磺酸在异戊醇和乳酸酯化反应中的应用 ,讨论了合成条件。实验表明其催化活性良好。