二维波动方程的高精度隐格式及其多重网格算法

提出了数值求解二维波动方程的两种高精度三层紧致隐格式．利用Fourier分析方法证明了格式均是无条件稳定的．并在此基础上提出了求解该问题的多重网格算法．从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷，大大加快了迭代收敛速度．提高了求解效率．数值实验结果验证了方法的精确性和可靠性．     

A local adaptive grid procedure for incompressible flows with multigridding and equidistribution concepts

An adaptive grid solution procedure is developed for incompressible flow problems in which grid refinement based on an equidistribution law is performed in high-error-estimate regions that are flagged from a preliminary coarse grid solution. Solutions on the locally refined and equidistributed meshes are obtained using boundary conditions interpolated from the preliminary coarse grid solution, and solutions on both the refined and coarse grid regions are successively improved using a multigrid approach. For this purpose, suitable correction terms for the coarse grid equations are derived for all variables in the flagged regions. This procedure with Local Adaptation, Multigridding and Equidistribution (LAME) concepts is applied to various flow problems to demonstrate the accuracy improvements obtained using this method.     

地层倾角井下仪精度分析

本文详尽地研究了目前油田正使用的一种地层倾角测井仪的误差范围及各传感器误差对仪器总体误差的贡献,为设计和研制更高精度的仪器提出了改进意见。     

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit time-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.The work reported was performed in the framework of the BRITE-EURAM Aeronautics R&D Programme of the European Communities (Contract No. AER2-CT92-0040). The work was started during the second author's visit to CWI in 1993.     

Breakdown and near-breakdown control in the CGS algorithm using stochastic arithmetic

In the Conjugate-Gradient-Squared method, a sequence of residualsr _k defined byr _k=P _k ² (A)r₀ is computed. Coefficients of the polynomialsP _k may be computed as a ratio of scalar products from the theory of formal orthogonal polynomials. When a scalar product in a denominator is zero or very affected by round-off errors, situations of breakdown or near-breakdown appear. Using floating point arithmetic on computers, such situations are detected with the use of _i in some ordering relations like |x _i . The user has to choose the _i himself and these choices condition entirely the efficient detection of breakdown or near-breakdown. The subject of this paper is to show how stochastic arithmetic eliminates the problem of the _i with the estimation of the accuracy of some intermediate results.     

Identification of micro-scale calorimetric devicesIV. Descriptive models in 3-D

The experimental analysis of conventional conduction calorimeters shows excellent reproducibility and relevant systematic errors in comparison with thermodynamic values established via adiabatic calorimeters. Two examples: a DSC and a liquid flow device are schematically analyzed. When an increased accuracy will be obtained the positional effects on the experimental set-up and on the measurement process need to be modelled. From experimental measurements realized on the Xensor liquid nano-calorimeter representative models can be built. To evaluate the reliability of measurement routines, established from experimental basis, several different dissipation structures inside the working space can be simulated. Two experimental configurations related to drop to drop reaction and to continuous mixing are modelled via RC approach. The RC formalism is extended to evaluate the carried energy effect produced by the continuous inflow/outflow of reactants in the mixing enthalpy chamber. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monitoring accuracy and precision — Improvements by introducing robust and resistant statistics

A method is presented to monitor for accuracy and precision of chemical analyses based on the use of a control reference sample (CRS) and blind duplicates of project samples. The major advantage of the method is that it works with real samples instead of international (or laboratory) reference standards. Thus, it will take into account changes in absolute or relative errors over the whole observed concentration range. For each project and each sample type, respectively, and for all elements analysed, it provides realistic estimates of precision and — if there are any determinations at low concentrations — of the practical instead of the rather meaningless theoretical detection limit. By introducing robust and resistant statistics it is possible to drastically reduce the number of samples necessary for the monitoring procedure. As an additional advantage, these statistics are independent of any distribution model and solely reflect the data structure. A program for the whole monitoring procedure, the Laboratory Control Package (LCP), has been written in FORTRAN. It can be implemented on any personal computer with graphic capabilities.     

Examination of numerical accuracy on fragment-DFT calculations with integral values of total electron density functions

Fragment molecular orbital (FMO) method gives a powerful tool to investigate electronic structures for biological substances, and ABINIT-MP program has been developed to implement ab initio FMO calculations effectively. We introduced DFT code into ABINIT-MP and applied fragment-DFT (F-DFT) calculations to model polypeptides. The total accuracy of numerical integrations employed in those calculations was examined by the total numbers of electrons in the molecules. It is shown that the numerical integral of the total density function under the fragment approximation works as an indicator for the numerically total accuracy on the F-DFT implementation.     

Kernel energy method illustrated with peptides

We describe a kernel energy method (KEM) for applying quantum crystallography to large molecules, with an emphasis on the calculation of the molecular energy of peptides. The computational difficulty of representing the system increases only modestly with the number of atoms. The calculations are carried out on modern parallel supercomputers. By adopting the approximation that a full biological molecule can be represented by smaller “kernels” of atoms, the calculations are greatly simplified. Moreover, collections of kernels are, from a computational point of view, well suited for parallel computation. The result is a modest increase in computational time as the number of atoms increases, while retaining the ab initio character of the calculations. We describe a test of our method, and establish its accuracy using 15 different peptides of biological interest. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Studies of the wetting kinetics of liquid drops on solid surfaces

The viscosity _L and the surface tension _L of the liquid as well as the equilibrium contact angle _e are essential parameters governing the wetting kinetics of liquids on solids. By means of a contact angle apparatus with video image digitization, the dynamic contact angle and the radiusr of the contact area of sessile drops on solid surfaces have simultaneously been determined in dependence on time after drop application between about 3·10^–2 s and long times.The measurements were performed with series of liquids: polydimethylsiloxanes with different molecular masses and solutions of polyisobutylene in decalin and polyacrylic acid in water, covering a wide range of concentrations. The liquids in each series have a constant surface tension, but viscosities ranging over about four orders of magnitude, allowing the influence of _L and _L to be studied independently. Solids such as glass, polyethylene and polytetrafluoroethylene were chosen so that the cases of complete wetting (spreading) and partial wetting ( _e) could be studied.The curves of cos andr/R ₀ vs. time for the different liquids of a series can be superimposed to a master curve by plotting them against _L·t _L·R ₀, whereR ₀ is the radius of the original drop. All these master curves coincide at small wetting times, with exception of the data for the polysiloxanes. That means that the early stage of the wetting process is determined only by the properties of the wetting liquid. The influence of the solid surface, characterized by the equilibrium contact angle _e becomes significant only at the end of the wetting process.Dedicated to Professor Dr. H. Willersinn on the occasion of his 65^th birthday