Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.     

Immersed boundary method for the simulation of 2D viscous flow based on vorticity–velocity formulations

A new immersed boundary method based on vorticity–velocity formulations for the simulation of 2D incompressible viscous flow is proposed in present paper. The velocity and vorticity are respectively divided into two parts: one is the velocity and vorticity without the influence of the immersed boundary, and the other is the corrected velocity and the corrected vorticity derived from the influence of the immersed boundary. The corrected velocity is obtained from the multi-direct forcing to ensure the well satisfaction of the no-slip boundary condition at the immersed boundary. The corrected vorticity is derived from the vorticity transport equation. The third-order Runge–Kutta for time stepping, the fourth-order finite difference scheme for spatial derivatives and the fourth-order discretized Poisson for solving velocity are applied in present flow solver. Three cases including decaying vortices, flow past a stationary circular cylinder and an in-line oscillating cylinder in a fluid at rest are conducted to validate the method proposed in this paper. And the results of the simulations show good agreements with previous numerical and experimental results. This indicates the validity and the accuracy of present immersed boundary method based on vorticity–velocity formulations.     

Analysis of the interface configuration and flow characteristics in tanks in a multiphase liquid–gas system using numerical simulation

A multiphase study was conducted using a turbulence model of large eddy simulation to investigate the interaction between the gaseous phase and the interface and its respective behaviour until the liquid phase movement was established, first in the near interface, as well as the presence of turbulent structures in the study of transport between phases. The results are shown for three surface configurations: a surface with waves in which the Reynolds number and friction velocity of the gaseous phase are, respectively, 210 and 0.25 m/s; a surface with small undulations, 86 and 0.10 m/s; and a flat surface, 43 and 0.05 m/s. Coherent structures are detected on both sides of the interface; these are intensified and less elongated for larger Reynolds numbers. Additionally, the interface exhibits distinct behaviour with regard to the examined phases. For the gaseous phase, it behaves like a no-slip surface.     

Nonlinear Rayleigh–Taylor instability of the cylindrical fluid flow with mass and heat transfer

The nonlinear Rayleigh–Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg–Landau equation. The F-expansion method is used to get exact solutions for a nonlinear Ginzburg–Landau equation. The region of solutions is displayed graphically.     

Approximate solutions of the Wei Hua oscillator using the Pekeris approximation and Nikiforov–Uvarov method

The approximate analytical bound-state solutions of the Schrödinger equation for the Wei Hua oscillator are carried out in N-dimensional space by taking Pekeris approximation scheme to the orbital centrifugal term. Solutions of the corresponding hyper-radial equation are obtained using the conventional Nikiforov–Uvarov (NU) method.     

Three-body interactions and the Landau levels using Nikiforov–Uvarov method

In this article, the eigenvalues for the three-body interactions on the line and the Landau levels in the presence of topological defects have been regenerated by the Nikiforov–Uvarov (NU) method. Two exhaustive lists of such exactly solvable potentials are given.     

Hydrodynamics and mass-transfer characteristics analysis of vapor–liquid flow of dual-flow tray

In the present study, the behavior and details of vapor–liquid contact on the dual-flow trays (DFTs) were investigated using a 3D CFD model within the two-phase Eulerian framework. The simulation provided good agreement with experimental results, which verified the reliability of the model. Firstly, the operation range was divided into four regimes having different characteristics of flow phenomena, and most attention was paid to the hydrodynamic behavior of froth regime and fluctuating regime due to its importance in operation and structure improvement. Then, the liquid flow characteristics of these two regimes were revealedwith the analysis of velocity profiles and liquid phase distribution contour. Meanwhile, some in-depth picturing of local events of hydrodynamics and mass-transfer performance was also presented through the discussion of cyclohexane liquid volume fraction distribution and vapor-phase mole fraction distribution. The froth regime was proved to have higher and homogeneous point efficiency at bulk zone around the plate center area than the fluctuating regime. Thus, the improvement of DFT should be focused on the restriction of “free-flow” to prolong the froth regime and delay the formation of vortex flow with circulation cells. Finally, an orthogonal wave tray (OWT) was designed and compared with DFT for evaluation of the effect of proposed modifications on the enhancement of tray hydraulics, mass-transfer efficiency and stability.     

Studies on the analytical potential energy function of diatomic molecular ion XY~+ using variational method

It is well-known that the accurate behavior of potential energy function of molecular ion plays an important role in the studies such as solution chemistry, atmosphere chemistry, nebular medium, plasma physics, and gun powder, etc.[1, 2]. The values of potential energy function of diatomic molecular ion could significantly influence the optical efficiency of laser pump using ion vapors as working substrate[3]. The ionic potential is very important for the studies on low-energy ion-atom collisi…     

Analytical solution of the Korteweg–de Vries equation and microtubule equation using the first integral method

In this paper, the first integral method is applied to solve the Korteweg–de Vries equation with dual power law nonlinearity and equation of microtubule as nonlinear RLC transmission line. This method is manageable, straightforward and a powerful tool to find the exact solutions of nonlinear partial differential equations.     

Characterization of chaotic dynamic behavior in the gas–liquid slug flow using directed weighted complex network analysis

Understanding the nonlinear and complex dynamics underlying the gas–liquid slug flow is a significant but challenging problem. We systematically carried out gas–liquid two-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. In particular, we construct directed weighted complex networks (DWCN) from time series and then associate different aspects of chaotic dynamics with the topological indices of the DWCN and further demonstrate that the DWCN can be exploited to detect unstable periodic orbits of low periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach. We construct and analyze numbers of DWCNs for different gas–liquid flow patterns and find that our approach can quantitatively distinguish different experimental gas–liquid flow patterns. Furthermore, the DWCN analysis indicates that slug flow shows obvious chaotic behavior and its unstable periodic orbits reflect the intermittent quasi-periodic oscillation behavior between liquid slug and large gas slug. These interesting and significant findings suggest that the directed weighted complex network can potentially be a powerful tool for uncovering the underlying dynamics leading to the formation of the gas–liquid slug flow.     

Influence of flow shear on localized Rayleigh–Taylor and resistive drift wave instabilities

The impact of velocity shear on the localized solutions of Rayleigh–Taylor (RT) and resistive drift wave (DW) instabilities has been investigated. Slab geometry is used, and the plasma density gradient is assumed to have a finite spatial structure. It demonstrates that the velocity shear has quite different effects on these instabilities: while it stabilizes RT instability and causes tilting of the eddies of equipotential contour, it has a very mild impact on the resistive DW instability and simply shifts the eddies with no tilting.     

Letter to the Editor: On the evolution of dissipation rate and resolved kinetic energy in ALDM simulations of the Taylor–Green flow

We correct a data processing error in the article “Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex” by Dieter Fauconnier, Chris De Langhe and Erik Dick published in the Journal of Computational Physics 228 (2009), pp. 8053–8084.     

Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.     

Controlling the size of ZnO quantum dots using the dressed photon–phonon-assisted sol–gel method

We developed a sol–gel method using the dressed photon–phonon (DPP) process. DPPs are selectively exited in nanoscale structures at photon energies that are lower than the bandgap energy, which allows one to increase the growth rate of smaller ZnO quantum dots (QDs). Thus, we obtained a smaller size variance of ZnO QDs. The growth rate was proportional to the power of the light used for DPP excitation. The results were confirmed using a rate equation that accounted for the concentration of the sol–gel solution.     

An accurate and efficient method for the incompressible Navier–Stokes equations using the projection method as a preconditioner

The projection method is a widely used fractional-step algorithm for solving the incompressible Navier–Stokes equations. Despite numerous improvements to the methodology, however, imposing physical boundary conditions with projection-based fluid solvers remains difficult, and obtaining high-order accuracy may not be possible for some choices of boundary conditions. In this work, we present an unsplit, linearly-implicit discretization of the incompressible Navier–Stokes equations on a staggered grid along with an efficient solution method for the resulting system of linear equations. Since our scheme is not a fractional-step algorithm, it is straightforward to specify general physical boundary conditions accurately; however, this capability comes at the price of having to solve the time-dependent incompressible Stokes equations at each timestep. To solve this linear system efficiently, we employ a Krylov subspace method preconditioned by the projection method. In our implementation, the subdomain solvers required by the projection preconditioner employ the conjugate gradient method with geometric multigrid preconditioning. The accuracy of the scheme is demonstrated for several problems, including forced and unforced analytic test cases and lid-driven cavity flows. These tests consider a variety of physical boundary conditions with Reynolds numbers ranging from 1 to 30000. The effectiveness of the projection preconditioner is compared to an alternative preconditioning strategy based on an approximation to the Schur complement for the time-dependent incompressible Stokes operator. The projection method is found to be a more efficient preconditioner in most cases considered in the present work.