An L2‐stable approximation of the Navier–Stokes convection operator for low‐order non‐conforming finite elements

We develop in this paper a discretization for the convection term in variable density unstationary Navier–Stokes equations, which applies to low‐order non‐conforming finite element approximations (the so‐called Crouzeix–Raviart or Rannacher–Turek elements). This discretization is built by a finite volume technique based on a dual mesh. It is shown to enjoy an L² stability property, which may be seen as a discrete counterpart of the kinetic energy conservation identity. In addition, numerical experiments confirm the robustness and the accuracy of this approximation; in particular, in L² norm, second‐order space convergence for the velocity and first‐order space convergence for the pressure are observed. Copyright © 2010 John Wiley & Sons, Ltd.     

Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps

Shock reflection phenomena over nonstraight surfaces have been investigated. The models used in this experiment are ordinary circular cylindrical concave and convex wedges and step-like wedges which simulate the former. The step-like wedges were used to investigate the process of reflected-wave formation over circular cylindrical wedges (method of multiple steps). The reflected-wave structure has been photographed with a schlieren apparatus. The formation of the reflected wave over circular cylindrical wedges is physically well understood by comparing it with shock reflection over step-like wedges. In particular, the reason why the reflected wave over a concave circular cylindrical wedge is very weak away from the reflection point is elucidated. Moreover, the structure and the formation mechanism of the so-called transitioned regular reflection (TRR) are illustrated in detail. As a by-product, based on acoustic theory, analytical formulae for the transition wedge angle are found. They are in good agreement with experiments. Received Received 28 February 1996 / Accepted 7 August 1996     

SOLUTION ALGORITHM FOR LOW-PECLET-NUMBER REACTING FLOW

An enhanced solution strategy based on the SIMPLER algorithm is presented for low-Peclet-number mass transport calculations with applications in low-pressure material processing. The accurate solution of highly diffusive flows requires boundary conditions that preserve specified chemical species mass fluxes. The implementation of such boundary conditions in the standard SIMPLER solution procedure leads to degraded convergence that scales with the Peclet number. Modifications to both the non-linear and linear parts of the solution algorithm remove the slow convergence problem. In particular, the linearized species transport equations must be implicitly coupled to the boundary condition equations and the combined system must be solved exactly at each non-linear iteration. The pressure correction boundary conditions are reformulated to ensure that continuity is preserved in each finite volume at each iteration. The boundary condition scaling problem is demonstrated with a simple linear model problem. The enhanced solution strategy is implemented in a baseline computer code that is used to solve the multicomponent Navier–Stokes equations on a generalized, multiple-block grid system. Accelerated convergence rates are demonstrated for several material-processing example problems. © 1997 John Wiley & Sons, Ltd.     

The phenomena of shock wave reflection — a review of unsolved problems and future research needs

Although the phenomenon of shock wave reflection was discovered more than a hundred years ago, active research related to this phenomenon still goes on in many countries in the world (e.g., Australia, Canada, China, Germany, Israel, Japan, Poland, Russia and United States of America). As a matter of fact the research activity increased so drastically in the past decade and a half that a special scientific meeting dedicated to better understanding the reflection phenomena of shock waves, namely The International Mach Reflection Symposium was initiated in 1981 and was held since then in the major research centers actively involved in the research of shock wave reflections. In the present paper the status of the research of the phenomenon of shock wave reflection will be discussed in general, and unresolved problems and future research needs will be pointed out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The Mach reflection triple-point locus for internal and external conical diffraction of a moving shock wave

This paper examines the different behavior that occurs for the Mach reflection triple-point loci between the two fundamental axisymmetric cases, these being the external diffraction by a cone and the internal diffraction within a conically contracting channel. From equations derived in this paper using a shock dynamics approach, it has been shown that, for external diffraction over a cone, a possible solution is that the triple-point locus is a straight line which corresponds to the experimental results available, while for internal diffraction along a conically converging channel, it cannot be straight and is, in fact, a convex curve. In the latter case, a transition point is noted on the triple-point locus before which the locus is nearly straight but after which the curvature becomes marked. The second region diminishes as a proportion of the total locus with decreasing half cone angle.For the external case, a set of simple, axisymmetric equations are derived which allow a rapid estimation of the triple point locus angle and the Mach stem strength for any incident shock Mach number and cone angle combination. The equations for internal diffraction are similar and allow a quick computation of both the curved triple-point locus and the strength of the diffracting front of the shock wave. A comparison with experiment has been carried out and agreement is good.     

A Photonic mm-Wave Frequency Sextupler Using an Integrated Mach–Zehnder Modulator with Three Arms

Abstract

A novel photonic mm-wave frequency sextupling scheme based on an integrated Mach–Zehnder modulator with three arms is proposed in this article. Without any optical filter, a high-quality frequency sextupling mm-wave signal can be generated. Compared with mm-wave generation schemes based on traditional two-arm Mach–Zehnder modulators, the proposed scheme does not need DC bias and a complex electrical bias control circuit. Some non-ideal factors are taken into consideration to verify its performance, which proves that a slight deviation of the ideal values does not cause great degradation of the performance of the mm-wave generation scheme.     

克服光纤Mach-Zehnder干涉仪信号衰落的新方法及分析

为了克服光纤Mach-Zehnder干涉仪易受环境因素影响而引起偏置相位漂移从而导致输出信号衰落(波动)的问题,提出一种新的简单方法,即:将干涉仪输出信号分为直流和交流两个分量,通过直流分量的大小来计算交流信号的补偿因子,以达到克服交流信号衰落、稳定检测传感信号的目的在小信号测量情况下,该方法在很大范围内能有效抑制随机温度涨落等因素引起的信号衰落的问题文中对补偿方法的误差和局限性也做了分析和讨论.     

马赫-曾德尔干涉仪消光比和单通道光开关

对马赫-曾德尔(M—Z)干涉仪的滤光消光比特性进行了研究，提出了一种在其一端加上光纤全反镜的方法，大大改善了马赫一曾德尔干涉仪的输出谱特性，由此提出并设计了一种单通道光开关，实验得到了约37．4dB的开关动态范围。     

A deferred correction coupling strategy for low Mach number flow with complex chemistry

We present a new thermodynamic coupling strategy for complex reacting flow in a low Mach number framework. In such flows, the advection, diffusion and reaction processes span a broad range of time scales. In order to reduce splitting errors inherent in Strang splitting approaches, we couple the processes with a multi-implicit spectral deferred correction strategy. Our iterative scheme uses a series of relatively simple correction equations to reduce the error in the solution. The new method retains the efficiencies of Strang splitting compared to a traditional method-of-lines approach in that each process is discretised sequentially using a numerical method well suited for its particular time scale. We demonstrate that the overall scheme is second-order accurate and provides increased accuracy with less computational work compared to Strang splitting for terrestrial and astrophysical flames. The overall framework also sets the stage for higher-order coupling strategies.     

Simulation of Third-Order Intermodulation Distortion Suppression Incorporating Dual-Parallel Mach–Zehnder Modulator in a CR-SSB Modulation

A novel scheme is proposed to enlarge the spurious free dynamic range (SFDR) of microwave photonic (MWP) link by using dual-parallel Mach–Zehnder modulator, which modifies the single sideband signal and replaces the optical carrier with an unmodulated one to remove the optical main sources of third-order intermodulation distortion (IMD3). Simulation results show that the IMD3 and fifth-order intermodulation distortion can be suppressed greatly even when the modulation depth increases to a high value, and the link is limited by seventh-order intermodulation distortion and the SFDR is improved by 34.2 dB Hz in a 1-Hz bandwidth. The error vector magnitude of the MWP link with the proposed scheme is improved significantly for the transmitted 1-Gbit/s 16- quadrature amplitude modulation (QAM) signal.