Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance the pressure difference between the inside and outside of FCI,are considered with a slot in Hartmann wall or a slot in side wall,respectively.The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects,which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket.The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.

A unified gas-kinetic scheme for multiscale and multicomponent flow transport

Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.

Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using OpenFOAM

Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme （UDS） is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes （HRS） were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all I-IRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E ~ 5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.

Flow Dynamics in Restricted Geometries: A Mathematical Concept Based on Bloch NMR Flow Equation and Boubaker Polynomial Expansion Scheme

Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.

EULER SCHEME AND MEASURABLE FLOWS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

For a stochastic differential equation with non-Lipschitz coefficients, we construct, by Euler scheme, a measurable flow of the solution, and we prove the solution is a Markov process.

TRANSONIC FLOW CALCULATION OF EULER EQUATIONS BY IMPLICIT ITERATING SCHEME WITH FLUX SPLITTING

Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity and linear velocity-density relationship. Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density. The LWR model is treated as an initial value problem and its numerical simulations are presented using numerical schemes. A variety of numerical schemes are available in literature to solve first order hyperbolic equations. Of these the well-known ones include one-dimensional explicit: Upwind, Downwind, FTCS, and Lax-Friedrichs schemes. Having been studied carefully the space and time mesh sizes, and the patterns of all these schemes, a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme. Tolesa numerical scheme is one of the conditionally stable and highest rates of convergence schemes. All the said numerical schemes are applied to solve advection equation pertaining traffic flows. Also the one-dimensional explicit Tolesa numerical scheme is another alternative numerical scheme to solve advection equation and apply to traffic flows model like other well-known one-dimensional explicit schemes. The effect of density of cars on the overall interactions of the vehicles along a given length of the highway and time are investigated. Graphical representations of density profile, velocity profile, flux profile, and in general the fundamental diagrams of vehicles on the highway with different time levels are illustrated. These concepts and results have been arranged systematically in this paper.

High Order Central Schemes Applied to Relativistic Multi-Component Flow Models

The dynamics of inviscid multi-component relativistic fluids may be modeled by the relativistic Euler equations, augmented by one (or more) additional species equation(s). We use the high-resolution staggered central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. The current schemes can handle strong shocks and the oscillations near the interfaces are negligible, which usually happens in the multi-component flows. The schemes also guarantee the exact mass conservation for each component, the exact conservation of total momentum, and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validate the application of these schemes to relativistic multi-component flows.

High velocity flow simulation using lattice Boltzmann method with no-free-parameter dissipation scheme

A finite difference lattice Boltzmann method of second-order accuracy in time is developed based on non-oscillatory scheme with no-free-parameter dissipation （NND） difference scheme in this paper. The NND lattice Boltzmann method is used to simulate high-speed flows by constructing a new equilibrium distribution function of the lattice Boltzmann method. Compared with a variation of lattice Boltzmann method developed by Qu, et al., the present method can capture shock waves and handle oscillations of high velocity flows accurately in larger time steps and in shorter computing time. Numerical results indicate the correctness and capability of simulating shock wave interactions of the NND lattice Boltzmann method.

Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.

Lax-Friedrich Scheme for the Numerical Simulation of a Traffic Flow Model Based on a Nonlinear Velocity Density Relation

A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich’s scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.

白河包营枢纽船闸下游口门区优化方案研究

包营枢纽下游引航道口门区流场复杂、混乱。为保障内河船舶通航安全,对枢纽下游河道整体水域进行数值模拟研究,分别对比分析扩宽河道、扩宽河道+口门区设置导流墩、扩宽河道+布置隔流堤3种优化方案前后的枢纽通航条件。结果表明,原始方案中,当流量最大时横流、纵流最大流速分别为0.95、3.60 m∕s,超出0.65、1.60 m∕s的安全限值,且延长隔流堤导致末尾处下泄主流出现较大回流、横流的不良流态。最终选定在扩宽河道的基础上设置导流墩为最佳优化方案,与其他方案相比,此方案可加强主流与口门区局部流场的动量交换,减小速度梯度以及主流与口门区夹角,显著改善口门区水流条件,保障船舶通航安全。

Water Flow and Sediment Flux Forecast in the ChókwèIrrigation Scheme, Mozambique

This study sought to forecast water flow and sediment flux in the scheme as potential contributions for improved management in the Chókwè Irrigation Scheme (CIS). Fieldwork data was collected during dry (DS) and wet (WS) seasons. Flow measurement was performed at 9 stations using a calibrated flow meter OTT C31. Water flow and sediment flux from 2004 to 2019 were used. Hydrodynamic forecast simulations were performed using Mann-Kendall test and ARIMA model for determination of temporal trends. Findings suggest higher values during DS for water discharge and sediment flux. Mann-Kendall test for sediment discharge trends was not significant at 95% significance level, except for the Offtake in WS. ARIMA test for the sediment discharges, at the Intake, for DS and WS, sediments were well described by the ARIMA model and gave a good result for the sediments. Good fit between the observed and the predicted ARIMA model was found. ARIMA model for sediment discharge at CIS based on AIC has a good fit for AR (p = 1), whereby, at the Intake the ARIMA p-value was 0.822 and 0.932, for WS and DS, respectively. Whilst in the Offtake, the ARIMA p-value was 0.877 and 0.893, respectively. These results can be used to improve the CIS management, both for water flow and sediment flux.

Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.

Gas-kinetic numerical schemes for one- and two-dimensional inner flows

Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.

平行式快速路出口交通组织方法研究

针对平行式快速路出口排队溢出的交通问题,本文提出平行式快速路出口在无信号控制和信号控制情况下的5种交通组织方法,根据主辅车流的车头时距分布,建立主辅车流产生延误的计算模型。从方案选择的角度,以车均延误为评价指标,研究平行式快速路不同交通流量状态下出口最适合采用的交通组织方法。结果表明:当平行式快速路主路驶出车流和辅路车流的总流量低于1500 pcu·h^(-1)时,采取无信号让行的控制方法。主路驶出交通量较高时,采用主路驶出优先控制;辅路交通量较高时,采用辅路优先控制。当总流量在[1500,2300]pcu·h^(-1)时,采用辅路信号与让行相结合的控制方法。当主路驶出交通量较大时,采用辅路信号主路优先控制;当辅路交通量较大时,采用辅路信号辅路优先控制。当总流量高于2300 pcu·h^(-1)时,采用主辅全信号的控制方法。

非对称运行西河泵站前池试验分析

为明确西河泵站非对称机组运行时前池的流态特征,基于物理模型试验的方法对西河泵站的前池及进水流道进行整体物理模型试验,共获取4种不同开机方案时西河泵站前池的流场和速度分布规律,并采用计算流体动力学技术对最低水位时8台机组全开的方案进行数值分析。结果表明:在0.75负荷排涝时,非对称机组运行方案2的前池两侧有微弱旋流,开机方案3和开机方案4前池流态均平稳,开机方案3泵站进口断面的底流速分布均匀度为78.2%;推荐两侧边机组和中间机组各2台开机运行;在全负荷排涝流量且最低水位时,机组全开时两边机组流道进口的水力性能指标最低,在实际运行时应注意两侧边机组运行的安全稳定性。研究成果可为西河泵站的实际运行管理提供一定的参考。

基于改进的多元宇宙算法的晶圆生产调度算法

针对以最小化最大完工时间为目标的晶圆生产制造系统的调度问题,提出了改进的多元宇宙算法。根据晶圆生产制造系统的特征,构建了一个整数规划模型。针对原始多元宇宙算法的局限性,分别从使用启发式规则生成初始种群、重新定义向最优宇宙移动策略和宇宙更新策略三个方面对算法进行改进。将原始多元宇宙算法、遗传算法、NEH启发式算法、迭代贪婪算法以及通过不同策略改进的多元宇宙算法进行对比实验,结果表明,所提方法可以高效地解决晶圆制造过程中的复杂现象。

低流速、低对比剂注射方案在老年患者肺动脉CTA检查中的应用价值

目的:探讨低流速、低对比剂注射方案在老年患者肺动脉CT血管造影(computedtomographyangiography,CTA)检查中的应用价值。方法:选取2020年4月至2023年1月于某院接受肺动脉CTA检查的60例老年患者,根据对比剂注射方案的不同,将患者分为对照组(30例)和实验组(30例)。对照组采用常规对比剂注射方案,实验组采用低流速、低对比剂的优化对比剂注射方案。观察2组患者的肺动脉强化程度、肺动脉主干和分支的显示情况以及图像血管边缘的锐利程度、上腔静脉对比剂硬化伪影程度并进行主观评分,对2组患者的肺动脉干、左肺静脉及右肺静脉的强化CT值进行客观评价,记录2组患者对比剂外渗情况。采用SPSS25.0软件进行统计学分析。结果:2组肺动脉CTA图像质量评分比较差异无统计学意义(P>0.05);实验组上腔静脉对比剂硬化伪影评分低于对照组,差异有统计学意义(P<0.05)。2组图像的肺动脉干、左肺静脉及右肺静脉CT值比较差异无统计学意义(P>0.05)。实验组未出现对比剂外渗患者;对照组出现1例严重外渗患者,4例轻、中度外渗患者。结论:在老年患者行肺动脉CTA检查时采用低流速、低对比剂注射方案能够在保证图像质量的前提下避免对比剂外渗,提升了患者的就医体验和安全性。