Application of pressure‐ and density‐based methods for different flow speeds

In this paper, pressure‐based and density‐based methods are studied at different flow speeds. The methods are intended for steady flows, and the goal is to find as general an approach as possible to cover different Mach number regimes. The solution methods are based on a finite‐volume approach. Various forms of inviscid fluxes are applied and connected with either a pressure‐based or density‐based implicit solution. For this purpose, a new pressure‐correction method is developed that can be applied for incompressible and for compressible flows. Another option is a standard density‐based approximate factorization method. In both cases, a convergence is accelerated with a Full Approximation Scheme (FAS) multigrid approach. Sample problems in the range of Ma = 0…6 are simulated using different approaches, and their efficiency and accuracy are compared. On the basis of the quality of the solutions, recommendations are made. © 2015 The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd.     

Diffraction of a solitary wave by a thin wedge part 2. Effects of viscous boundary layers

Based on the study on the Mach reflection of a solitary wave in [3], we continue to investigate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it represents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.     

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 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.     

Low‐cost implicit schemes for all‐speed flows on unstructured meshes

Matrix‐free implicit treatments are now commonly used for computing compressible flow problems: a reduced cost per iteration and low‐memory requirements are their most attractive features. This paper explains how it is possible to preserve these features for all‐speed flows, in spite of the use of a low‐Mach preconditioning matrix. The proposed approach exploits a particular property of a widely used low‐Mach preconditioner proposed by Turkel. Its efficiency is demonstrated on some steady and unsteady applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Improvements to compressible Euler methods for low‐Mach number flows

In the present study improvements to numerical algorithms for the solution of the compressible Euler equations at low Mach numbers are investigated. To solve flow problems for a wide range of Mach numbers, from the incompressible limit to supersonic speeds, preconditioning techniques are frequently employed. On the other hand, one can achieve the same aim by using a suitably modified acoustic damping method. The solution algorithm presently under consideration is based on Roe's approximate Riemann solver [Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43 : 357–372] for non‐structured meshes. The numerical flux functions are modified by using Turkel's preconditioning technique proposed by Viozat [Implicit upwind schemes for low Mach number compressible flows. INRIA, Rapport de Recherche No. 3084, January 1997] for compressible Euler equations and by using a modified acoustic damping of the stabilization term proposed in the present study. These methods allow the compressible Euler equations at low‐Mach number flows to be solved, and they are consistent in time. The efficiency and accuracy of the proposed modifications have been assessed by comparison with experimental data and other numerical results in the literature. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

An integrated Mach–Zehnder interferometric biosensor with a silicon oxynitride waveguide by plasma-enhanced chemical vapor deposition

We report the design and fabrication of an integrated Mach–Zehnder interferometric (MZI) biochip based on silicon oxynitride layers deposited with a plasma-enhanced chemical vapor deposition (PECVD) process. A rib waveguide for an integrated MZI sensor has been designed to have a high surface sensitivity and a single-mode behavior by using an effective index method. The integrated MZI chip operating at 637 nm is fabricated via conventional photolithography and reactive ion etching. As a biosensor application, the real-time and label-free detection of the covalent immobilization and hybridization of DNA strands is performed and verified with this device.     

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.