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121.
Extending fixed‐grid time integration schemes for unsteady CFD applications to moving grids, while formally preserving their numerical stability and time accuracy properties, is a nontrivial task. A general computational framework for constructing stability‐preserving ALE extensions of Eulerian multistep time integration schemes can be found in the literature. A complementary framework for designing accuracy‐preserving ALE extensions of such schemes is also available. However, the application of neither of these two computational frameworks to a multistage method such as a Runge–Kutta (RK) scheme is straightforward. Yet, the RK methods are an important family of explicit and implicit schemes for the approximation of solutions of ordinary differential equations in general and a popular one in CFD applications. This paper presents a methodology for filling this gap. It also applies it to the design of ALE extensions of fixed‐grid explicit and implicit second‐order time‐accurate RK (RK2) methods. To this end, it presents the discrete geometric conservation law associated with ALE RK2 schemes and a method for enforcing it. It also proves, in the context of the nonlinear scalar conservation law, that satisfying this discrete geometric conservation law is a necessary and sufficient condition for a proposed ALE extension of an RK2 scheme to preserve on moving grids the nonlinear stability properties of its fixed‐grid counterpart. All theoretical findings reported in this paper are illustrated with the ALE solution of inviscid and viscous unsteady, nonlinear flow problems associated with vibrations of the AGARD Wing 445.6. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history. 相似文献
124.
Pavel M. Polestshuk 《Journal of computational chemistry》2013,34(3):206-219
The approach for the integration over a region covered by zero‐flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE . The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well‐known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10?6 to 10?5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc. 相似文献
125.
《Analytical letters》2012,45(10):1274-1285
Prints are one of the most popular artistic forms. They consist of an original matrix that is printed on a paper support. The stamps are part of a series, and each series is composed of a particular number of prints. Many contemporary prints are made using oil inks and synthetic pigments (reds and yellows). Inks are mainly composed of pigments (organic or inorganic) and a binding medium. The analysis of inks has the potential to facilitate and complement the identification of stamps of different origins. Fourier transform infrared spectroscopy (FTIR) and Scanning Electron Microscopy-Energy Dispersive X-ray (SEM-EDX) are techniques that are typically available in museums and centers related to the study of works of art. Both can be classified as micro-destructive and provide complementary information about the organic and some inorganic compounds (FTIR), and the elemental composition (SEM-EDX). In this article, the two techniques were used to analyze the composition of red ink in prints. As a result of these analyses, it was possible to distinguish among nearly all of the pigments and inks, indicating that the composition of the red ink can be reliably used to differentiate between stamps of different origins in a series of prints. 相似文献
126.
This paper puts forward a new method to solve the electromagnetic parabolic equation (EMPE) by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo- lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana- lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm. 相似文献
127.
Hong Sun Frederick Roussel Wing Shun Cheung B. M. Fung Sandy S. Keast Mark Lohman 《Liquid crystals》2013,40(10):1483-1486
Liquid crystals (LCs) with diazo linkages have high dielectric and optical anisotropy. Two newly synthesized liquid crystalline compounds were dissolved in room temperature LC hosts, E7 and PTTP-24/36, to assess their properties. It was found that these mixtures have higher birefringence, larger dielectric anisotropy, and better elastic properties than the hosts. Satisfactory viscoelastic coefficients were also obtained for these mixtures, showing that they are promising LC materials for applications in the near IR region. 相似文献
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Xuan Thinh Duong Irina Holmes Ji Li Brett D. Wick Dongyong Yang 《Journal of Functional Analysis》2019,276(4):1007-1060
In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian on the upper half space and the reflection Neumann Laplacian on with respect to the weights associated to and respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt weights with while the previously known related results cover only . We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian on . 相似文献