This paper proposes a double Markov model of the double continuous auction for describing intra-day price changes. The model splits intra-day price changes as the repetition of one tick price moves and assumes order a...This paper proposes a double Markov model of the double continuous auction for describing intra-day price changes. The model splits intra-day price changes as the repetition of one tick price moves and assumes order arrivals are independent Poisson random processes. The dynamic process of price formation is described by a birth-death process of the double M/M/1 server queue corresponding to the best bid/ask. The initial depths of the best bid and ask are defined as different constants depending on the last price change. Thus, the price changes in the model follow a first-order Markov process. As the initial depth of the best bid/ask is originally larger than that of the opposite side when the last price is down/up, the model may explain the negative autocorrelations of the price of the best bid/ask. The estimated parameters are based on the real tick-by-tick data of the Nikkei 225 futures listed in Osaka Stock Exchanges. The authors find the model accurately predicts the returns of Osaka Stock Exchange average.展开更多
This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been...This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.展开更多
The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and ...The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.展开更多
In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material ...In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.展开更多
A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale flu...A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.展开更多
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reyn...The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.展开更多
It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study seco...It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analyticalsolution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second orderfluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.展开更多
The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equation...The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.展开更多
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 appr...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.展开更多
A Non-Intrusive Reduced-Order Model(NIROM)based on Proper Orthogonal Decomposition(POD)has been proposed for predicting the flow fields of transonic airfoils with geometry parameters.To provide a better reduced-order ...A Non-Intrusive Reduced-Order Model(NIROM)based on Proper Orthogonal Decomposition(POD)has been proposed for predicting the flow fields of transonic airfoils with geometry parameters.To provide a better reduced-order subspace to approximate the real flow field,a domain decomposition method has been used to separate the hard-to-predict regions from the full field and POD has been adopted in the regions individually.An Artificial Neural Network(ANN)has replaced the Radial Basis Function(RBF)to interpolate the coefficients of the POD modes,aiming at improving the approximation accuracy of the NIROM for non-samples.When predicting the flow fields of transonic airfoils,the proposed NIROM has demonstrated a high performance.展开更多
We investigated the influence of hall, heat and mass transfer on the peristaltic flow of MHD third order fluid under long-wavelength and low Reynolds number approximation. The governing equations are solved analytical...We investigated the influence of hall, heat and mass transfer on the peristaltic flow of MHD third order fluid under long-wavelength and low Reynolds number approximation. The governing equations are solved analytically with the appropriate boundary conditions by using perturbation technique. The formula of velocity with temperature and concentration is obtained analytically as a function of the physical parameters of the problem.展开更多
The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collisi...The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.展开更多
In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an invest...In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.展开更多
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 ...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.展开更多
The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scal...The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.展开更多
Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme...Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.展开更多
A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A nume...A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.展开更多
A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simp...A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71173060,71031003the Fundamental Research Funds for the Central Universities under Grant No.HIT.HSS.201120partially supported by JSPS KAKENHI under Grant No.22560059
文摘This paper proposes a double Markov model of the double continuous auction for describing intra-day price changes. The model splits intra-day price changes as the repetition of one tick price moves and assumes order arrivals are independent Poisson random processes. The dynamic process of price formation is described by a birth-death process of the double M/M/1 server queue corresponding to the best bid/ask. The initial depths of the best bid and ask are defined as different constants depending on the last price change. Thus, the price changes in the model follow a first-order Markov process. As the initial depth of the best bid/ask is originally larger than that of the opposite side when the last price is down/up, the model may explain the negative autocorrelations of the price of the best bid/ask. The estimated parameters are based on the real tick-by-tick data of the Nikkei 225 futures listed in Osaka Stock Exchanges. The authors find the model accurately predicts the returns of Osaka Stock Exchange average.
基金supported by an Early Career Faculty grant from NASA's Space Technology Research Grants Programprovided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center
文摘This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.
基金Project supported by the National Natural Science Foundation of China(No.11602128)the Natural Science Foundation of Fujian Province of China(No.2016J01679)
文摘The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.
文摘In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.
基金The project supported by the Special Funds for Major State Basic Research,China(G-1999-0222-08)the Postdoctoral Science Foundation(2004036239)
文摘A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.
文摘The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.
文摘It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analyticalsolution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second orderfluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.
文摘The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.
基金supported by the National Natural Science Foundation of China(Nos.11072141 and11272199)the National Basic Research Program of China(No.2012CB725404)+2 种基金the Shanghai Program for Innovative Research Team in Universitiesthe Research Grants Council of the Hong KongSpecial Administrative Region,China(No.HKU7184/10E)the National Research Foundationof Korea(MEST)(No.NRF-2010-0029446)
文摘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.
基金supported by the National Natural Science Foundation of China(No.11802245).
文摘A Non-Intrusive Reduced-Order Model(NIROM)based on Proper Orthogonal Decomposition(POD)has been proposed for predicting the flow fields of transonic airfoils with geometry parameters.To provide a better reduced-order subspace to approximate the real flow field,a domain decomposition method has been used to separate the hard-to-predict regions from the full field and POD has been adopted in the regions individually.An Artificial Neural Network(ANN)has replaced the Radial Basis Function(RBF)to interpolate the coefficients of the POD modes,aiming at improving the approximation accuracy of the NIROM for non-samples.When predicting the flow fields of transonic airfoils,the proposed NIROM has demonstrated a high performance.
文摘We investigated the influence of hall, heat and mass transfer on the peristaltic flow of MHD third order fluid under long-wavelength and low Reynolds number approximation. The governing equations are solved analytically with the appropriate boundary conditions by using perturbation technique. The formula of velocity with temperature and concentration is obtained analytically as a function of the physical parameters of the problem.
基金Project supported by the National Key Basic Research and Development Program of China(No.G1999-0222-08)
文摘The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.
基金Supported by the National Natural Science Foundations of China under Grant Nos.21576023,51406008the National Key Research Program of China under Grant Nos.2016YFC0700601,2016YFC0700603,and 2016YFE0115500
文摘In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.
文摘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.
基金Project supported by the Science Challenge Program(No.TZ2016001)the National Natural Science Foundation of China(Nos.11472277,11572331,11232011,and 11772337)+2 种基金the Strategic Priority Research Program,Chinese Academy of Sciences(CAS)(No.XDB22040104)the Key Research Program of Frontier Sciences,CAS(No.QYZDJ-SSW-SYS002)the National Basic Research Program of China(973 Program)(No.2013CB834100)
文摘The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.
文摘Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.
基金Project supported by the National Natural Science Foundation of China (Nos. 11072141 and 11272199)the National Basic Research Program of China (No. 2012CB725404)+1 种基金the University Research Committee, HKU SPACE Research FundFaculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)
文摘A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.
文摘A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed. Using the Chapman-Enskog expansion and multi-scale technique, we obtain the higher-order moments of equilibrium distribution function. A simple traffic light problem is simulated by using the present lattice Boltzmann model, and the result agrees well with analytical solution.
