Simplified Navier-Stokes equations (SNSE)

Ten kinds of the simplified Navier-Stokes equations (SNSE) are reviewed and also used to calculate the Jeffery-Hamel flow as well as to analyze briefly the seven kinds of flows to which the exact solutions of the complete Navier-Stokes equations (CNSE) have been found. Analysis shows that the actual differences among the solutions of the different SNSE can go beyond the range of the order of magnitude of Re-1/2 and result even in different flow patterns, therefore, how to choose the viscous terms included in the SNSE is worthy of notice where Re=S∞u∞ L/μ∞ is the Reynolds numbers. For the aforesaid eight kinds of flows, the solutions to the inner-outer-layer-matched SNSE and to the thin-layer-2-order SNSE agree completely with the exact solutions to CNSE. But the solutions to all the other SNSE are not completely consistent with the exact solutions to CNSE and not a few of them are actually the solutions of the classical boundary layer theory. The innerouter-layer-matched SNSE contains the shear stress causing angular displacement of the inormal axis with respect to the streamwise axis and the normal stress causing expansion-contraction in the direction of the normal axis and the viscous terms being of the order of magnitude of the normal stress; and it can also reasonably treat the inertial terms as well as the relation between the viscous and inertial terms. Therefore, it seems promising in respects of both mechanics and mathematics.

同位非结构和结构网格摄动有限体积法(PFV)求解二维Navier-Stokes方程组

根据NS方程组的一阶迎风和二阶中心有限体积(UFV和CFV)格式,导出NS方程组迎风和中心摄动有限体积(UPFV和CPFV)格式.该格式通过把控制体界面质量通量摄动展开成网格间距的幂级数,并由守恒方程本身求得幂级数系数而获得.迎风和中心摄动有限体积格式使用了与一阶迎风和二阶中心格式相同的基点数和相同的表达形式,宜于计算机编程.顶盖驱动方腔流和驻点流标量输运的数值实验证明,迎风PFV格式比一阶UFV、二阶CFV格式有更高的精度,更高的分辨率.尤其是良好的鲁棒特性.对顶盖驱动方腔流,在Re数从102到104范围内,亚松弛系数可在0.3～0.8任取,收敛性能良好.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Salieri Speaks: Peter Shaffer's two version of Amadeus

Eguíluz, Federico; Merino, Raquel; Olsen, Vickie; Pajares, Eterio; Santamaría, José Miguel (eds.)

Navier-Stokes(NS)方程组差分计算中的物理和网格尺度效应及NS方程组的简化

对于高Re数流动计算,在通常二阶精度NS差分格式和网格数条件下,存在某些粘性项落入修正微分方程截断误差项的问题。这类NS方程组计算实际是计算某种简化NS方程组,而且重复计算误差物理粘性项既浪费机时和内存,误差积累又会对数值解产生不可预测的影响。避免上述缺陷的办法一个是提高NS差分格式的精度,另一个是丢掉可能落入截断误差项的物理粘性项,把NS方程组简化为广义NS方程组。广义NS计算避免了误差物理粘性项误差积累对数值解的不可知影响,又可节省内存和机时,对高Re数流体工程计算很有好处。利用广义NS方程组计算超声速绕前向和后向台阶流动的结果表明:广义NS方程组与NS方程组的数值结果很好相符。

Imaging properties of coherent anti-Stokes Raman scattering microscope

The coherent anti-Stokes Raman scattering (CARS) microscope with the combination of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labelling. CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscope. In this paper, the intensity distribution and the polarization property of the optical field near the focus was calculated. By using the Green function, the precise analytic solution to the wave equation of a Hertzian dipole source was obtained. We found that the intensity distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscope (e.g. the point spread function) will fail to describe the imaging properties of the CARS microscope.

The intensity distributions of collected signals in coherent anti-Stokes Raman scattering microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy with the combining of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labeling. The CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscopy. In this paper, we calculated the propagation of CARS signals by using the wave equation in medium and the slowly varying envelope approximation (SVEA), and find that the intensity angular distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscopy (e.g.. the point spread function) will fail to descript the imaging properties of CARS microscopy. (c) 2004 Elsevier B.V. All rights reserved.

Augmented Peter Pan: un cuento multilingüe con Realidad Aumentada

[SPA] El objetivo de este Trabajo de Fin de Grado ha sido diseñar un cuento multilingüe que incorpora una innovación tecnológica, la Realidad Aumentada, para favorecer el proceso de enseñanza-aprendizaje lingüístico en la escuela. Para ello, hemos analizado algunos cuentos con Realidad Aumentada que se pueden encontrar en el mercado. Al no encontrar ningún cuento que cumpliese nuestras expectativas, hemos creado un cuento multilingüe con Realidad Aumentada adaptando el cuento clásico “Peter Pan”, que cumple los objetivos de fomentar el aprendizaje de diferentes idiomas y el gusto por la lectura, valorar las lenguas inmigrantes en las aulas y promover el uso de las TIC.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.