An additional potential energy distribution function is introduced on the basis of previous D3Q25 model,and the equilibrium distribution function of D3Q25 is obtained by spherical function.A novel three-dimensional(3D...An additional potential energy distribution function is introduced on the basis of previous D3Q25 model,and the equilibrium distribution function of D3Q25 is obtained by spherical function.A novel three-dimensional(3D)shifted lattice model is proposed,therefore a shifted lattice model is introduced into D3Q25.Under the finite volume scheme,several typical compressible calculation examples are used to verify whether the numerical stability of the D3Q25 model can be improved by adding the shifted lattice model.The simulation results show that the numerical stability is indeed improved after adding the shifted lattice model.展开更多
A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, su...A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, surface tension,wetting properties, and rheological characteristics of the fluid on the two-phase flow are analyzed. The results indicate that the flow pattern transfers from slug flow to dry-plug flow with a sufficiently small capillary number. Due to the presence of three-phase contact lines, the contact angle has a more significant effect on the dry-plug flow pattern than on the slug flow pattern. The deformation of the front and rear meniscus of a bubble in the shear-thinning fluid can be explained by the variation of the capillary number. The reduced viscosity and increased contact angle are beneficial for the drag reduction in a microchannel. It also demonstrates the effectiveness of the current method to simulate the gas–liquid two-phase flow in a microchannel.展开更多
Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finel...Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.展开更多
Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical per...Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.展开更多
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio...For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.展开更多
For present solid oxide fuel cells(SOFCs),rapid performance degradation is observed in the initial aging process,and the dis-cussion of the degradation mechanism necessitates quantitative analysis.Herein,focused ion b...For present solid oxide fuel cells(SOFCs),rapid performance degradation is observed in the initial aging process,and the dis-cussion of the degradation mechanism necessitates quantitative analysis.Herein,focused ion beam-scanning electron microscopy was em-ployed to characterize and reconstruct the ceramic microstructures of SOFC anodes.The lattice Boltzmann method(LBM)simulation of multiphysical and electrochemical processes in the reconstructed models was performed.Two samples collected from industrial-size cells were characterized,including a reduced reference cell and a cell with an initial aging process.Statistical parameters of the reconstructed microstructures revealed a significant decrease in the active triple-phase boundary and Ni connectivity in the aged cell compared with the reference cell.The LBM simulation revealed that activity degradation is dominant compared with microstructural degradation during the initial aging process,and the electrochemical reactions spread to the support layer in the aged cell.The microstructural and activity de-gradations are attributed to Ni migration and coarsening.展开更多
The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanopart...The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles: TiO2 , Ag, Cu, and Al2O3 . The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical methods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ = 2.5 when Ra = 106 while at λ = 1.5 for other Rayleigh numbers.展开更多
The bubbles rise up and burst at the free surface is a complex two-phase process.A free energy lattice Boltzmann method(LBM)model is adopted in this paper to study this phenomenon.The interface capturing technique[Zhe...The bubbles rise up and burst at the free surface is a complex two-phase process.A free energy lattice Boltzmann method(LBM)model is adopted in this paper to study this phenomenon.The interface capturing technique[Zheng et al.,2006]is used to deal with the high density ratio problem.The Laplace law and the air-water interface capturing ability are validated for the multiphase model.The interaction between the single bubble or multiple bubbles and the free surface are studied by the multiphase model.The force acting on the bubble and the evolution of the free surface is studied.Meanwhile,effect of the initial distance between two adjacent bubbles on interaction effects of multiple bubbles is investigated as well.展开更多
In this paper, a novel model is proposed to investigate the neutron transport in scattering and absorbing medium. This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method(LB...In this paper, a novel model is proposed to investigate the neutron transport in scattering and absorbing medium. This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method(LBM) with the collision and streaming process. The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability, and relaxation time and equilibrium particle distribution function are obtained. To validate the new lattice Boltzmann model, the LBM formulation is tested for a homogenous media with different sources, and both transient and steady-state LBM results get a good agreement with the benchmark solutions.展开更多
By using the interaction of particles,such as the physical principle of the same attract each other and the different repulse each other,a new model of Lattice Boltzmann to simulate the two-phase driven in porous medi...By using the interaction of particles,such as the physical principle of the same attract each other and the different repulse each other,a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore,the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.展开更多
We consider a pressure (density) in a square flume solid boundaries and no-slip format condition formulation are introduced to investigate cavitation bubble for the two-dimensional lattice Boltz- mann method (LBM). Us...We consider a pressure (density) in a square flume solid boundaries and no-slip format condition formulation are introduced to investigate cavitation bubble for the two-dimensional lattice Boltz- mann method (LBM). Using the coupling Carnahan-Starling equation of state (C-S EOS) and exact difference method (EDM) based on modified Shan-Chen model, the whole process of bubble collapse was observed complete and visual with equilibrium distribution function and rebound format. This paper analyzes the bubble form evolution, collapse time and dynamic character under the two dimensional press fields.展开更多
Oxygen transfer presents a serious challenge in the application of liquid lead as a nuclear coolant in advanced reactors.To mitigate corrosion by liquid lead in contact with steel,carefully controlling the oxygen conc...Oxygen transfer presents a serious challenge in the application of liquid lead as a nuclear coolant in advanced reactors.To mitigate corrosion by liquid lead in contact with steel,carefully controlling the oxygen concentration has been used as an effective way.Oxygen needs to mix in liquid lead uniformly and quickly.To enhance oxygen transport in liquid lead,nanoparticles are added to the liquid metal.In the current study,a lattice Boltzmann method is applied to investigate natural convection of copper/lead and aluminum oxide/lead in two-dimensional simplified container.Two thermal boundary cases are evaluated in order to check the effect of different natural convection flow patterns on oxygen transport.Some useful information are obtained such as improvement in natural convection and reduction in oxygen equilibrium time.展开更多
A method combining the immersed boundary technique and a multirelaxation-time(MRT) lattice Boltzmann flux solver(LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders...A method combining the immersed boundary technique and a multirelaxation-time(MRT) lattice Boltzmann flux solver(LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations(LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution.The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.展开更多
For the growth and departure of bubbles from an orifice, a free energy lattice Boltzmann model is adopted to deal with this complex multiphase flow phenomenon. A virtual layer is set at the boundary of the flow domain...For the growth and departure of bubbles from an orifice, a free energy lattice Boltzmann model is adopted to deal with this complex multiphase flow phenomenon. A virtual layer is set at the boundary of the flow domain to deal with the no-slip boundary condition. Effects of the viscosity, surface tension, gas inertial force and buoyancy on the characteristics of bubbles when they grow and departure from an orifice in quiescent liquid are studied. The releasing period and departure diameter of the bubble are influenced by the residual gas at the orifice, and the interaction between bubbles is taken into consideration. The relations between the releasing period or departure diameter and the gravity acceleration show fair agreements with previous numerical and theoretical results. And the influence of the gas outflow velocity on bubble formation is discussed as well. For the bubbles growing in cross-flow field, effects of the cross-flow speed and the gas outflow velocity on the bubble formation are discussed, which is related to the application in ship resistance reduction. And optimal choice of the ship speed and gas outflow velocity is studied. Cases in this paper also prove that this high density ratio LBM model has its flexibility and effectiveness on multiphase flow simulations.展开更多
The phase-change problem is solved by the migration-collision scheme of lattice Boltzmann method.After formula derivation,we find that this method can give a rigorous numerical value for the phase-change temperature,w...The phase-change problem is solved by the migration-collision scheme of lattice Boltzmann method.After formula derivation,we find that this method can give a rigorous numerical value for the phase-change temperature,which is of crucial importance.One-dimensional solidification in half-space and two-dimensional solidification in a corner are simulated.The phase change temperature and the liquid-solid interface are both obtained,and the results conform to the analytical solution.展开更多
We present an improvement of the finite temperature Lanczos method in order to apply this method to systems at very low temperature. One proposal is to introduce two steps in this method. In the first step, we use the...We present an improvement of the finite temperature Lanczos method in order to apply this method to systems at very low temperature. One proposal is to introduce two steps in this method. In the first step, we use the Chebyshev polynomial expansion to calculate exp(-H/T1) random vector>?at moderate temperature T1. In the second step, we apply the ordinary finite temperature Lanczos method using the calculated state as the initial state of the Lanczos method. Another proposal is to employ a sampling method for selecting a random vector. By this sampling, we can improve an efficiency of calculations. Using the improved finite temperature Lanczos method, we calculate the specific heat of the spin-1/2 Heisenberg model on the kagome lattices of 27 and 30 sites.展开更多
This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods.The whole work focuses on investigating some...This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods.The whole work focuses on investigating some indices including the number of failed edges,dynamic edge tolerance capacity and the perturbation of edge.In general,it assumes that the perturbation is attributed to the normal distribution in adopted simulations.By investigating the effiectiveness of edge tolerance in scale-free and random networks,it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks.These results indicate that the cascading failure process can be effiectively controlled by increasing the tolerance parameter λ.Moreover,the simulations also show that,larger variance of perturbation can easily trigger the cascading failures than the smaller one.This study may be useful for evaluating efficiency of whole traffic systems,and for alleviating cascading failure in such systems.展开更多
In this study,a two-dimensional approach is elaborated to study with the lattice Boltzmann method(LBM)the seepage of water in the pores of a soil.Firstly,the D2Q9 model is selected to account for the discrete velocity...In this study,a two-dimensional approach is elaborated to study with the lattice Boltzmann method(LBM)the seepage of water in the pores of a soil.Firstly,the D2Q9 model is selected to account for the discrete velocity distribution of water flow.In particular,impermeability is considered as macroscopic boundary condition for the left and right domain sides,while the upper and lower boundaries are assumed to behave as pressure boundaries controlled by different densities.The micro-boundary conditions are implemented through the standard rebound strategy and a non-equilibrium extrapolation scheme.Matlab is used for the development of the related algorithm.Finally,the influence of porosity,permeability,osmotic pressure and other factors is assessed with regard to seepage characteristics and the ensuing results are compared with Darcy’s law.The computations show that,for fixed initial conditions,the pore structure has a certain influence on the local velocity of seepage,but the overall state is stable,and the average velocity of each layer is the same.The larger the pore passage is,the faster the flow velocity is,and vice versa.For low permeability,the numerical results are consistent with the Darcy's law.The greater the pressure difference between the inlet and outlet of seepage,the greater the seepage rate.The relationship between them is linear(yet in good agreement with Darcy’s law).展开更多
In the present study,the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multicomponent multi-phase lattice Boltzmann model.The results indicate that three typical nucleation modes ...In the present study,the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multicomponent multi-phase lattice Boltzmann model.The results indicate that three typical nucleation modes of condensate droplets are produced by changing the geometrical parameters of nanoarrays.Droplets nucleated at the top(top-nucleation mode),or in the upside interpillar space of nanoarrays(side-nucleation mode),generate the non-wetting Cassie state,whereas the ones nucleated at the bottom corners between the nanoarrays(bottom-nucleation mode) present the wetting Wenzel state.Time evolutions of droplet pressures at the upside and downside of the liquid phase are analyzed to understand the wetting behaviors of the droplets condensed from different nucleation modes.The phenomena of droplet condensation on nanoarrays patterned with different hydrophilic and hydrophobic regions are simulated,indicating that the nucleation mode of condensate droplets can also be manipulated by modifying the local intrinsic wettability of nanoarray surface.The simulation results are compared well with the experimental observations reported in the literature.展开更多
Applying the parametric derivation method,Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory,while the results obtained by the power-series expansion according to si...Applying the parametric derivation method,Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory,while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law.The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow.Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law.Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.展开更多
基金the Youth Program of the National Natural Science Foundation of China(Grant Nos.11972272,12072246,and 12202331)the National Key Project,China(Grant No.GJXM92579)the Natural Science Basic Research Program of Shaanxi Province,China(Program No.2022JQ-028)。
文摘An additional potential energy distribution function is introduced on the basis of previous D3Q25 model,and the equilibrium distribution function of D3Q25 is obtained by spherical function.A novel three-dimensional(3D)shifted lattice model is proposed,therefore a shifted lattice model is introduced into D3Q25.Under the finite volume scheme,several typical compressible calculation examples are used to verify whether the numerical stability of the D3Q25 model can be improved by adding the shifted lattice model.The simulation results show that the numerical stability is indeed improved after adding the shifted lattice model.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51775077)。
文摘A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, surface tension,wetting properties, and rheological characteristics of the fluid on the two-phase flow are analyzed. The results indicate that the flow pattern transfers from slug flow to dry-plug flow with a sufficiently small capillary number. Due to the presence of three-phase contact lines, the contact angle has a more significant effect on the dry-plug flow pattern than on the slug flow pattern. The deformation of the front and rear meniscus of a bubble in the shear-thinning fluid can be explained by the variation of the capillary number. The reduced viscosity and increased contact angle are beneficial for the drag reduction in a microchannel. It also demonstrates the effectiveness of the current method to simulate the gas–liquid two-phase flow in a microchannel.
基金This work is supported in part by the National Natural Science Foundation of China(U19B6003-04-01,42204132,41874130)R&D Department of CNPC(2022DQ0604-01)China Postdoctoral Science Foundation(2020M680667,2021T140661).
文摘Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.
基金the National Natural Science Foundation of China(Nos.12172017 and 12202021)。
文摘Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.
基金supported by the National Key R and D Program of China(2020YFA0713100).
文摘For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.
基金the National Key R&D Program of China(No.2018YFB1502201)the Guangdong Basic and Applied Basic Research Foundation,China(No.2020A1515010551).
文摘For present solid oxide fuel cells(SOFCs),rapid performance degradation is observed in the initial aging process,and the dis-cussion of the degradation mechanism necessitates quantitative analysis.Herein,focused ion beam-scanning electron microscopy was em-ployed to characterize and reconstruct the ceramic microstructures of SOFC anodes.The lattice Boltzmann method(LBM)simulation of multiphysical and electrochemical processes in the reconstructed models was performed.Two samples collected from industrial-size cells were characterized,including a reduced reference cell and a cell with an initial aging process.Statistical parameters of the reconstructed microstructures revealed a significant decrease in the active triple-phase boundary and Ni connectivity in the aged cell compared with the reference cell.The LBM simulation revealed that activity degradation is dominant compared with microstructural degradation during the initial aging process,and the electrochemical reactions spread to the support layer in the aged cell.The microstructural and activity de-gradations are attributed to Ni migration and coarsening.
文摘The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles: TiO2 , Ag, Cu, and Al2O3 . The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical methods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ = 2.5 when Ra = 106 while at λ = 1.5 for other Rayleigh numbers.
基金supported by the National Natural Science Foundation of China (11672081)
文摘The bubbles rise up and burst at the free surface is a complex two-phase process.A free energy lattice Boltzmann method(LBM)model is adopted in this paper to study this phenomenon.The interface capturing technique[Zheng et al.,2006]is used to deal with the high density ratio problem.The Laplace law and the air-water interface capturing ability are validated for the multiphase model.The interaction between the single bubble or multiple bubbles and the free surface are studied by the multiphase model.The force acting on the bubble and the evolution of the free surface is studied.Meanwhile,effect of the initial distance between two adjacent bubbles on interaction effects of multiple bubbles is investigated as well.
基金supported by the Foundation of National Key Laboratory of Reactor System Design Technology(No.HT-LW-02-2014003)the State Key Program of National Natural Science of China(No.51436009)
文摘In this paper, a novel model is proposed to investigate the neutron transport in scattering and absorbing medium. This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method(LBM) with the collision and streaming process. The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability, and relaxation time and equilibrium particle distribution function are obtained. To validate the new lattice Boltzmann model, the LBM formulation is tested for a homogenous media with different sources, and both transient and steady-state LBM results get a good agreement with the benchmark solutions.
文摘By using the interaction of particles,such as the physical principle of the same attract each other and the different repulse each other,a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore,the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.
文摘We consider a pressure (density) in a square flume solid boundaries and no-slip format condition formulation are introduced to investigate cavitation bubble for the two-dimensional lattice Boltz- mann method (LBM). Using the coupling Carnahan-Starling equation of state (C-S EOS) and exact difference method (EDM) based on modified Shan-Chen model, the whole process of bubble collapse was observed complete and visual with equilibrium distribution function and rebound format. This paper analyzes the bubble form evolution, collapse time and dynamic character under the two dimensional press fields.
基金the financial support from the office of Vice-President for Research at University of Nevada-Las Vegas
文摘Oxygen transfer presents a serious challenge in the application of liquid lead as a nuclear coolant in advanced reactors.To mitigate corrosion by liquid lead in contact with steel,carefully controlling the oxygen concentration has been used as an effective way.Oxygen needs to mix in liquid lead uniformly and quickly.To enhance oxygen transport in liquid lead,nanoparticles are added to the liquid metal.In the current study,a lattice Boltzmann method is applied to investigate natural convection of copper/lead and aluminum oxide/lead in two-dimensional simplified container.Two thermal boundary cases are evaluated in order to check the effect of different natural convection flow patterns on oxygen transport.Some useful information are obtained such as improvement in natural convection and reduction in oxygen equilibrium time.
文摘A method combining the immersed boundary technique and a multirelaxation-time(MRT) lattice Boltzmann flux solver(LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations(LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution.The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.
基金financially supported by the National Key R&D Program of China(Grant No.2018YFC0308900)the Industrial Technology Development Program(Grant No.JCKY2018604C010)Shenzhen Special Fund for Future Industries(Grant No.JCYJ20160331163751413)
文摘For the growth and departure of bubbles from an orifice, a free energy lattice Boltzmann model is adopted to deal with this complex multiphase flow phenomenon. A virtual layer is set at the boundary of the flow domain to deal with the no-slip boundary condition. Effects of the viscosity, surface tension, gas inertial force and buoyancy on the characteristics of bubbles when they grow and departure from an orifice in quiescent liquid are studied. The releasing period and departure diameter of the bubble are influenced by the residual gas at the orifice, and the interaction between bubbles is taken into consideration. The relations between the releasing period or departure diameter and the gravity acceleration show fair agreements with previous numerical and theoretical results. And the influence of the gas outflow velocity on bubble formation is discussed as well. For the bubbles growing in cross-flow field, effects of the cross-flow speed and the gas outflow velocity on the bubble formation are discussed, which is related to the application in ship resistance reduction. And optimal choice of the ship speed and gas outflow velocity is studied. Cases in this paper also prove that this high density ratio LBM model has its flexibility and effectiveness on multiphase flow simulations.
基金supported by the National Natural Science Foundation of China(10932010,11072220)the Natural Science Foundation of Zhejiang Province(Y607425, Z6090556 )
文摘The phase-change problem is solved by the migration-collision scheme of lattice Boltzmann method.After formula derivation,we find that this method can give a rigorous numerical value for the phase-change temperature,which is of crucial importance.One-dimensional solidification in half-space and two-dimensional solidification in a corner are simulated.The phase change temperature and the liquid-solid interface are both obtained,and the results conform to the analytical solution.
文摘We present an improvement of the finite temperature Lanczos method in order to apply this method to systems at very low temperature. One proposal is to introduce two steps in this method. In the first step, we use the Chebyshev polynomial expansion to calculate exp(-H/T1) random vector>?at moderate temperature T1. In the second step, we apply the ordinary finite temperature Lanczos method using the calculated state as the initial state of the Lanczos method. Another proposal is to employ a sampling method for selecting a random vector. By this sampling, we can improve an efficiency of calculations. Using the improved finite temperature Lanczos method, we calculate the specific heat of the spin-1/2 Heisenberg model on the kagome lattices of 27 and 30 sites.
基金supported by National Basic Research Program of China (Grant No 2006CB705500)Chang-Jiang Scholars and Innovative Research Team in University of China (Grant No IRT0605)the National Natural Science Foundation of China (Grant No70631001)
文摘This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods.The whole work focuses on investigating some indices including the number of failed edges,dynamic edge tolerance capacity and the perturbation of edge.In general,it assumes that the perturbation is attributed to the normal distribution in adopted simulations.By investigating the effiectiveness of edge tolerance in scale-free and random networks,it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks.These results indicate that the cascading failure process can be effiectively controlled by increasing the tolerance parameter λ.Moreover,the simulations also show that,larger variance of perturbation can easily trigger the cascading failures than the smaller one.This study may be useful for evaluating efficiency of whole traffic systems,and for alleviating cascading failure in such systems.
文摘In this study,a two-dimensional approach is elaborated to study with the lattice Boltzmann method(LBM)the seepage of water in the pores of a soil.Firstly,the D2Q9 model is selected to account for the discrete velocity distribution of water flow.In particular,impermeability is considered as macroscopic boundary condition for the left and right domain sides,while the upper and lower boundaries are assumed to behave as pressure boundaries controlled by different densities.The micro-boundary conditions are implemented through the standard rebound strategy and a non-equilibrium extrapolation scheme.Matlab is used for the development of the related algorithm.Finally,the influence of porosity,permeability,osmotic pressure and other factors is assessed with regard to seepage characteristics and the ensuing results are compared with Darcy’s law.The computations show that,for fixed initial conditions,the pore structure has a certain influence on the local velocity of seepage,but the overall state is stable,and the average velocity of each layer is the same.The larger the pore passage is,the faster the flow velocity is,and vice versa.For low permeability,the numerical results are consistent with the Darcy's law.The greater the pressure difference between the inlet and outlet of seepage,the greater the seepage rate.The relationship between them is linear(yet in good agreement with Darcy’s law).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51101035,51371051,and 51306037)
文摘In the present study,the process of droplet condensation on superhydrophobic nanoarrays is simulated using a multicomponent multi-phase lattice Boltzmann model.The results indicate that three typical nucleation modes of condensate droplets are produced by changing the geometrical parameters of nanoarrays.Droplets nucleated at the top(top-nucleation mode),or in the upside interpillar space of nanoarrays(side-nucleation mode),generate the non-wetting Cassie state,whereas the ones nucleated at the bottom corners between the nanoarrays(bottom-nucleation mode) present the wetting Wenzel state.Time evolutions of droplet pressures at the upside and downside of the liquid phase are analyzed to understand the wetting behaviors of the droplets condensed from different nucleation modes.The phenomena of droplet condensation on nanoarrays patterned with different hydrophilic and hydrophobic regions are simulated,indicating that the nucleation mode of condensate droplets can also be manipulated by modifying the local intrinsic wettability of nanoarray surface.The simulation results are compared well with the experimental observations reported in the literature.
基金Project supported by the National Natural Science Foundation of China (No.10774196)the Science Foundation Project of CQ CSTC (No.2006BB4156)Chongqing University Postgraduates'Science and Innovation Fund (No.2007A1A0030240).
文摘Applying the parametric derivation method,Peierls energy and Peierls stress are calculated with a non-sinusoidal force law in the lattice theory,while the results obtained by the power-series expansion according to sinusoidal law can be deduced as a limiting case of non- sinusoidal law.The simplified expressions of Peierls energy and Peierls stress are obtained for the limit of wide and narrow.Peierls energy and Peierls stress decrease monotonically with the factor of modification of force law.Present results can be used expediently for prediction of the correct order of magnitude of Peierls stress for materials.
