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.

Experimental study on the type change of liquid flow in broken coal samples

A test system of the permeability of broken coal samples mainly consists of a CMT5305 electronic universal test machine, crushed rock compaction containing cylinder and a self-designed seepage circuit, which is composed of a gear pump, a reversing valve, a relief valve and other components. By using the steady penetration method, the permeability and non-Darcy flow β factor of broken coal samples under five different porosity levels were measured, the grain diameters of the coal samples were selected as 2.5-5 mm, 5-10 mm, 10-15 mm, 15-20 mm, 20-25 mm and 2.5-25 ram, respectively. After measuring the permeability under each porosity, the overfall pressure of the relief valve continuously increased until the coal sample was broken down. In this way, the flow type of liquid inside the broken coal samples changed from seepage to pipe flow. The correlation between breakdown pressure gradient （BPG） and porosity was analyzed, and the BPG was compared with the pressure gradient when seepage instability occurred. The results show that, ①the non-Darcy flow β factor was negative before broken coal samples with six kinds of diameters were broken down; ②the BPG of coal samples with a grain size of 2.5-25 mm was lower than that of the others; ③ the BPG of coal samples with a single diameter under the same porosity increased as the grain size increased; ④ the BPG could be fitted by an exponential function with porosity, and the exponent decreased as the grain size increased for coal samples with a single diameter; ⑤ the BPG was slightly less than the seepage instability pressure gradient. The change in liquid flow type from seepage to pipe flow could be regarded as the performance of the seepage instability.

Effect of Gardenia extract ZG on the adsorption quantity of herpes simplex virus type 1 (HSV-1)

To observe the effect of Gardenia extract ZG on the adsorption quantity of herpes simplex virus type 1 （HSV-1） so as to explore the mechanism of its antiviral activity, fluorescein isothiocyanate （FITC） was used as the fluorescent probe to label viruses and heparin sodium was used as control. Meanwhile, the effect of Gardenia extract ZG on the adsorption quantity on the surface of Hep-2 cells was determined by flow cytometry. It was demonstrated that adsorption of HSV-1 on the surface of Hep-2 cells exhibited the character of saturation and specificity and heparin sodium could prevent attachment of viruses on these ceils. These results are in accord with those reported previously. It was also proved that the manner of drug-use prior to adsorption or simultaneous use of drug and adsorption was better than adsorption prior to drug-use, and the inhibition rates of the former and latter manner were 84.76% and 82.92% respectively. Three manners of drug-use with Gardenia extract ZG were all effective to reduce the adsorption quantity of viruses, especially the manner of simultaneous use of drug and adsorption with an adsorption inhibition rate of 68.46%. From the above observation, it is apparent that the mechanism of anti-viral activity of Gardenia extract ZG may be via several steps involved in the HSV-1 adsorption.

Influence of an inserted bar on the flow regimes in the hopper

We investigated the influence of an inserted bar on the hopper flow experimentally.Three geometrical parameters,size of upper outlet D1,size of lower outlet D0,and the height of bar H,are variables here.With varying H we found three regimes:one transition from clogging to a surface flow and another transition from a surface flow to a dense flow.For the dense flow,the flow rate follows Beverloo’s law and there is a saturation of inclination of free surfaceθ.We plotted the velocity field and there is a uniform linear relation between the particle velocity and depth from the free surface.We also found that the required value of D_(1) to guarantee the connectivity of flow is little smaller than D_(0).For the transition from a surface flow to a dense flow,there is a jump of flow rate and the minimumθfor flowing is two degrees larger than the repose angle.

Rate decline analysis of multiple fractured horizontal well in shale reservoir with triple continuum

Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.

Discrete Morse Flow for Yamabe Type Heat Flows

In this paper,we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space.We show that under suitable assumptions on the initial data g one has a weak approxi-mate discrete Morse flow for the Yamabe type heat flow on any time interval.This phenomenon is very different from the smooth Yamabe flow,where the finite time blow up may exist.

Types,Concentration,Diffusion and Spatial Structure Evolution of Natural Gas Resource Flow in China

This paper analyzed the development of different types of natural gas flow zones in China, and then di- vided all provinces into four flow types： non-flow zones, output centers, input centers and exchanging centers. Next, we analyzed the concentration and diffusion characteristics, current spatial pattern and evolution of source and terminal regions of natural gas resource flows. The numbers of non-flow zones, output centers, input centers and exchanging centers all stabilized during the Eleventh Five-Year Plan period. The number of output centers is small but the quantity of flow is large. The number of input centers is large and they are widely distributed. Generally speaking, it presents a significant characteristic of centralized output and dispersed input in geographic space. The current situation for China＇s natural gas output source has random distribution characteristics, but the terminal re- gions of natural gas flow have strong positive spatial correlation, presenting a significant spatial agglomeration pattern. Shandong, Jiangsu, Zhejiang and Shanghai have a high-high agglomeration mode, but Yunnan, Sichuan, Tibet, Qinghai and Gansu have a low-low agglomeration output zones had three different stages： relatively stable mode. Spatial pattern changes in China＇ s natural gas from 2001-2003; moved northwestward, expanded in space, and widely dispersed during 2004-2006; and transferred to the east, spatially contracted and significantly concentrated during 2007-2011. Spatial pattern changes in China＇s natural gas input zones have two stages： ex- panded in east-west direction while contracted in north-south direction during 2001-2005; and relatively stable in spatial structure with intensification from 2006-2011.

Two-stage fourth order: temporal-spatial coupling in computational fluid dynamics (CFD)

With increasing engineering demands,there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct“physics”.There are two families of high order methods:One is the method of line,relying on the Runge-Kutta(R-K)time-stepping.The building block is the Riemann solution labeled as the solution element“1”.Each step in R-K just has first order accuracy.In order to derive a fourth order accuracy scheme in time,one needs four stages labeled as“1111=4”.The other is the one-stage Lax-Wendroff(LW)type method,which is more compact but is complicated to design numerical fluxes and hard to use when applied to highly nonlinear problems.In recent years,the pair of solution element and dynamics element,labeled as“2”,are taken as the building block.The direct adoption of the dynamics implies the inherent temporal-spatial coupling.With this type of building blocks,a family of two-stage fourth order accurate schemes,labeled as“22=4”,are designed for the computation of compressible fluid flows.The resulting schemes are compact,robust and efficient.This paper contributes to elucidate how and why high order accurate schemes should be so designed.To some extent,the“22=4”algorithm extracts the advantages of the method of line and one-stage LW method.As a core part,the pair“2”is expounded and LW solver is revisited.The generalized Riemann problem(GRP)solver,as the discontinuous and nonlinear version of LW flow solver,and the gas kinetic scheme(GKS)solver,the microscopic LW solver,are all reviewed.The compact Hermite-type data reconstruction and high order approximation of boundary conditions are proposed.Besides,the computational performance and prospective discussions are presented.