Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

Solitary wave solutions to higher-order traffic flow model with large diffusion

This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.     

MESHLESS METHOD FOR NUMERICAL SIMULATION OF SHOCK-INDUCED COMBUSTION

发展了基于无网格方法的激波诱导燃烧流场数值模拟算法. 该算法采用二维多组分Euler方程,在点云离散的基础上采用曲面逼近计算空间导数,引入多组分HLLC （Harten-Lax-van Leer-contact） 格式计算无黏通量,运用四阶Runge-Kutta 法进行时间显式推进,化学动力学采用有限速率反应模型. 对不同预混气体中的激波诱导燃烧流场进行了数值模拟,结果同相关文献吻合较好,验证了算法的正确性.     

Numerical simulation of the vertical structure of discontinuous flows

A numerical method to solve the Reynolds‐averaged Navier–Stokes equations with the presence of discontinuities is outlined and discussed. The pressure is decomposed into the sum of a hydrostatic component and a hydrodynamic component. The numerical technique is based upon the classical staggered grids and semi‐implicit finite difference methods applied for quasi‐ and non‐hydrostatic flows. The advection terms in the momentum equations are approximated in order to conserve mass and momentum following the principles recently developed for the numerical simulation of shallow water flows with large gradients. Conservation of these properties is the most important aspect to represent near local discontinuities in the solution, following from sharp bottom gradients or hydraulic jumps. The model is applied to reproduce the flow over a step where a hydraulic jump forms downstream. The hydrostatic pressure assumption fails to represent this type of flow mainly because of the pressure deviation from the hydrostatic values downstream the step. Fairly accurate results are obtained from the numerical model compared with experimental data. Deviation from the data is found to be inherent to the standard k–ε model implemented. Copyright © 2001 John Wiley & Sons, Ltd.     

Negative-order integrable modified KdV equations of higher orders

Nonlinear Dynamics - A variety of negative-order integrable modified KdV (mKdV) equations of higher orders is constructed. The inverse profile of the recursion operator of the modified KdV equation...     

Nonlinear surface waves on a ferromagnetic fluid of variable depth

A nonlinear ray method is used to study surface waves on a ferromagnetic fluid of variable depth subject to a horizontal magnetic field, and an equation of the KdV type with variable coefficients is derived. An approximate solution of the equation representing a three-dimensional soliton with varying amplitude and phase is constructed and numerical results are presented.     

3-D numerical simulation of contact angle hysteresis for microscale two phase flow

Understanding the physics of microscale two-phase flow is important for a broad variety of engineering applications including compact PEM fuel cells and heat exchangers. The low Bond number and confined geometry make it critical to consider both the surface tension at the liquid–gas interfaces and the surface forces acting at the channel boundaries. Within the framework of a numerical volume of fluid (VOF) approach, the present work proposes a model to account for surface adhesion forces by considering the effects of contact angle hysteresis. A transient model is developed by correcting boundary force balances through specification of the local contact angle and instantaneously updating the local angle values based on the variation of the volume fraction from previous time steps. The model compares very well with new data provided here for droplets on a rotating disk and liquid slug flow in microchannel. The simulation reveals that the contact angle distribution along the slug profile in the microchannel flow can be approximated using a piecewise linear function. This study indicates that the asymmetric distribution of the contact angle might be responsible for several phenomena observed in the microchannel experiments, including slug instability.     

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.     

A procedure for calculation of the Wagner model velocity profile in the Poiseuille flow

The presented procedure enables calculation of a velocity profile for the Wagner fluid in the Poiseuille flow. The velocity profile can be approximated with a prescribed accuracy, thus enabling boundary conditions for the Wagner model, that are required for numerical simulations to be defined. Convergence analysis for the procedure indicates the existence of a critical Deborah number, which limits the validity of the approximation.     

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.     

OPTICAL DIAGNOSTIC AND MODELING SOLUTION GROWTH PROCESS OF SODIUM CHLORATE CRYSTALS

Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.     

A plastic indentation model for sandwich beams with metallic foam cores

Light weight high performance sandwich composite structures have been used extensively in various load bearing applications.Experiments have shown that the indentation significantly reduces the load bearing capacity of sandwiched beams.In this paper,the indentation behavior of foam core sandwich beams without considering the globally axial and flexural deformation was analyzed using the principle of virtual velocities.A concisely theoretical solution of loading capacity and denting profile was presented.The denting load was found to be proportional to the square root of the denting depth.A finite element model was established to verify the prediction of the model.The load-indentation curves and the profiles of the dented zone predicted by theoretical model and numerical simulation are in good agreement.     

Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation

A group of asymmetric difference schemes to approach the Korteweg-de Vries(KdV)equation is given here.According to such schemes,the full explicit difference scheme and the fun implicit one,an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed.The scheme is linear unconditionally stable by the analysis of linearization procedure,and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.     

Simulation of the Action of a Permeable Barrier on an Ideal Incompressible Channel Flow

Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers.     

An improved three-dimensional coupled fluid–structure model for Coriolis flowmeters

The paper presents a coupled numerical model built to simulate the operation of Coriolis flowmeters, which exploit the alteration of the vibration mode shape of the measuring tube for the mass flow rate measurement. The explained measuring effect is a consequence of the interaction between the motion of the tube, vibrating at its natural frequency, and the fluid flow in it. The numerical model is realized by coupling of a finite volume (FV) code for fluid flow analysis with a finite element (FE) code for structural analysis using the conventional staggered solution procedure, with added inner iterations to achieve strong coupling. The simulation algorithm is divided into two steps. A free vibration of the measuring tube considered in the first step is complemented in the second step, after the numerical free vibration response is properly stabilized, with the harmonic excitation force actuating the measuring tube at its resonant frequency of several hundreds of Hertz to resemble the operation of actual Coriolis flowmeters. Different scenarios using zero-order or three-point fluid load predictor and soft application of the fluid load in the initial stages of the simulation are compared to yield a simulation strategy, which will minimize the time needed to obtain the stabilized steady-state response of the vibrating measuring tube. The proposed simulation procedure was applied on a straight-tube Coriolis flowmeter and used for the estimation of the velocity profile effect. The results exhibit sufficient stability (low scatter) to be used for the estimation of sensitivity variations of order of magnitude around tenths of a percent.     

A numerical method for KdV equation using collocation and radial basis functions

Recently, there has been an increasing interest in the study of initial boundary value problems for Korteweg–de Vries (KdV) equations. In this paper, we propose a numerical scheme to solve the third-order nonlinear KdV equation using collocation points and approximating the solution using multiquadric (MQ) radial basis function (RBF). The scheme works in a similar fashion as finite-difference methods. Numerical examples are given to confirm the good accuracy of the presented scheme.     

Control of the aerodynamic characteristics of a profile oscillating with respect to the incidence angle in subsonic viscous flow

The results of a numerical simulation of the unsteady subsonic viscous gas flow around a two-dimensional profile oscillating with respect to the incidence angle are presented and the possibility of controlling the nonstationary aerodynamic characteristics is considered. The hysteresis phenomena typical of oscillatory profile motions are investigated, the dependence of the lift force and drag is found for various laws of periodic variation of the incidence angle with time, and the effect of the frequency and amplitude of the angular profile oscillations on the shape of the hysteresis curves is studied. The calculations were based on the numerical solution of the nonstationary Navier-Stokes equations averaged in the Reynolds sense (Reynolds equations) which were closed using the k-ω turbulence model with modeling of the laminar/turbulent transition.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

A generalized Rusanov method for the Baer‐Nunziato equations with application to DDT processes in condensed porous explosives

The paper addresses a numerical approach for solving the Baer‐Nunziato equations describing compressible 2‐phase flows. We are developing a finite‐volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer‐Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration‐to‐detonation transition (DDT) in porous reactive materials.     

Tailing wavetrain generation in precursor soliton generation in two-layer flow

A theory of tailing wavetrain generation for the precursor soliton generation in two-layer flow is presented by using averaged KdV equations (AKdV), which are derived by the authors in terms of Whitham's method of averaging^[1,2]. From the AKdV equations, group velocities of the tailing wavetrain generation are obtained by means of generating conditions of the tailing wavetrains, furthermore an analytical solution of the tailing wavetrain generation is found theoretically. A comparison between the theoretical and numerical results is carried out in the present paper, which shows that the theoretical results are in good agreement with the numerical ones, obtained from the fKdV equation in two-layer flow with the depth of unity in the rest. The project is supported by the National Natural Science Foundation of China (No. 49776284)