Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. ...Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo （DSMC） simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.展开更多
This paper extends the previous work[1]for the three-temperature gray radiative transfer equations to the frequency-dependent case.Since the additional frequency variable is considered,the equations are more complicat...This paper extends the previous work[1]for the three-temperature gray radiative transfer equations to the frequency-dependent case.Since the additional frequency variable is considered,the equations are more complicated than those in the gray case.Moreover,opacity may be typically a decreasing function of the frequency variable in applications.At the same spatial location,the equations can be in the optically thick case for low frequency photons,while in the optically thin case for high frequency ones.Thus,the resulting discrete equations can significantly increase the computational cost for opacity having the multi-scale property in multiple frequency radiation.Due to the presence of the radiation-electron coupling,electronion coupling,and electron-ion diffusion terms,the model under consideration exhibits strong nonlinearity and strong coupling properties.In this paper,the multigroup method is used to discretize the frequency variable and the H_(N)^(T)method to discretize the angular variable first.Then,within the framework of a unified gas kinetic scheme(UGKS),a multigroup H_(N)^(T)-UGKS method is constructed to solve this complex model iteratively.Furthermore,it can be shown that as the Knudsen number tends to zero,with variations in the electron-ion coupling,absorption,and scattering coefficients,the multigroup H_(N)^(T)-UGKS scheme can converge to numerical schemes for the single-temperature,two-temperature,and the frequency-dependent three-temperature,two-temperature diffusion limit equations,respectively.Finally,several numerical examples are provided to validate the effectiveness and stability of the proposed scheme.展开更多
The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. ...The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. After valida- tion, the UGKS is used to study the air-bearing problem under different non- equilibrium conditions. On the surface of the slider, the dependency of the gas pressure and normal force on the Mach and Knudsen numbers are fully evaluated. The non-equilibrium effect on the force loading in the whole transition regime up to the free molecular limit is also studied.展开更多
An implicit discrete unified gas kinetic scheme(DUGKS)is developed for multiscale steady flows of binary gas mixtures by solving the Andries-Aoki-Perthame kinetic model(AAP).To ensure the high convergence efficiency f...An implicit discrete unified gas kinetic scheme(DUGKS)is developed for multiscale steady flows of binary gas mixtures by solving the Andries-Aoki-Perthame kinetic model(AAP).To ensure the high convergence efficiency for all flow regimes,the microscopic and macroscopic asynchronous iterative strategies are used,where both the macroscopic and microscopic equations are solved iteratively by the LowerUpper Symmetric Gauss-Seidel(LU-SGS)method.The macroscopic iteration is conducted to solve the macroscopic governing equations containing source terms as an implicit prediction step to evaluate the local equilibrium state of the microscopic evolution,and the macroscopic flux used in the macroscopic iteration is obtained by taking moments of the distribution function.Besides,to keep the asymptotic preserving properties,the numerical flux across the cell interface is reconstructed by the characteristic solution of the kinetic governing equations for both species like the explicit DUGKS for a single gas.Several numerical tests,including the Couette flow,the lid-driven cavity flow,and the flows through a slit of different mixtures,are simulated to verify the accuracy and efficiency of the present scheme for binary mixtures.Furthermore,compared to the explicit DUGKS,the implicit scheme improves the computational efficiency by 1-2 orders of magnitude.展开更多
With discretized particle velocity space,a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case[J.Comput.Phys.,vol.229(2010),pp...With discretized particle velocity space,a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case[J.Comput.Phys.,vol.229(2010),pp.7747-7764].For the kinetic equation,to extend a one-dimensional scheme to multidimensional flow is not so straightforward.The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional,rather than axially symmetric,in velocity space.In this paper,a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented.Instead of particle-based modeling for the rarefied flow,such as the direct simulation Monte Carlo(DSMC)method,the philosophical principal underlying the current study is a partial-differential-equation(PDE)-based modeling.Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different,the gas evolution in a discretized space is modeled with the help of kinetic equation,instead of directly solving the partial differential equation.Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface,the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions.In comparison with the DSMC and Navier-Stokes flow solvers,the current method is much more efficient than DSMC in low speed transition and continuum flow regimes,and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes.As a result,the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation.This paper will extensively evaluate the performance of the unified scheme fromfreemolecule to continuum NS solutions,and fromlow speedmicro-flow to high speed non-equilibrium aerodynamics.The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations,and the scheme provides an important tool in the study of non-equilibrium flow.展开更多
Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied ...Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied flow computation,even though these methods face statistical scattering problem in the low speed limit.With discretized particle velocity space,a unified gas-kinetic scheme(UGKS)for entire Knudsen number flow has been constructed recently for flow computation.Contrary to the particle-based direct simulation Monte Carlo(DSMC)method,the unified scheme is a partial differential equation-based modeling method,where the statistical noise is totally removed.But,the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space.Due to the multiscale modeling in the unified method,i.e.,the update of both macroscopic flow variables and microscopic gas distribution function,the conventional constraint of time step being less than the particle collision time inmany direct Boltzmann solvers is released here.The numerical tests show that the unified scheme is more efficient than the particle-basedmethods in the low speed rarefied flow computation.Themain purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena.In the continuum and free molecular limits,the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions.In the transition regime,the DSMC solution will be used for the validation of UGKS results.This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows.It not only recovers the DSMC results whenever available,but also provides high resolution results in cases where the DSMC can hardly afford the computational cost.In thermal creep flow simulation,surprising solution,such as the gas flowing from hot to cold regions along the wall surface,is observed for the first time by the unified scheme,which is confirmed later through intensive DSMC computation.展开更多
In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys....In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.展开更多
A discrete unified gas kinetic scheme(DUGKS)is developed for multi-species flow in all flow regimes based on the Andries-Aoki-Perthame(AAP)kinetic model.Although the species collision operator in the AAP model conserv...A discrete unified gas kinetic scheme(DUGKS)is developed for multi-species flow in all flow regimes based on the Andries-Aoki-Perthame(AAP)kinetic model.Although the species collision operator in the AAP model conserves fully the mass,momentum,and energy for the mixture,it does not conserve the momentum and energy for each species due to the inter-species collisions.In this work,the species collision operator is decomposed into two parts:one part is fully conservative for the species and the other represents the excess part.With this decomposition,the kinetic equation is solved using the Strang-splitting method,in which the excess part of the collision operator is treated as a source,while the kinetic equation with the species conservative part is solved by the standard DUGKS.Particularly,the time integration of the source term is realized by either explicit or implicit Euler scheme.By this means,it is easy to extend the scheme to gas mixtures composed of Maxwell or hard-sphere molecules,while the previous DUGKS[Zhang Y,Zhu L,Wang R et al,Phys Rev E 97(5):053306,2018]of binary gases was only designed for Maxwell molecules.Several tests are performed to validate the scheme,including the shock structure under different Mach numbers and molar concentrations,the Couette flow under different mass ratios,and the pressure-driven Poiseuille flow in different flow regimes.The results are compared with those from other reliable numerical methods based on different models.And the influence of molecular model on the flow characteristics is studied.The results also show that the present DUGKS with implicit source discretization is more stable and preferable for gas mixture problems involving different flow regimes.展开更多
To improve the efficiency of the discrete unified gas kinetic scheme(DUGKS)in capturing cross-scale flow physics,an adaptive partitioning-based discrete unified gas kinetic scheme(ADUGKS)is developed in this work.The ...To improve the efficiency of the discrete unified gas kinetic scheme(DUGKS)in capturing cross-scale flow physics,an adaptive partitioning-based discrete unified gas kinetic scheme(ADUGKS)is developed in this work.The ADUGKS is designed from the discrete characteristic solution to the Boltzmann-BGK equation,which contains the initial distribution function and the local equilibrium state.The initial distribution function contributes to the calculation of free streaming fluxes and the local equilibrium state contributes to the calculation of equilibrium fluxes.When the contribution of the initial distribution function is negative,the local flow field can be regarded as the continuous flow and the Navier-Stokes(N-S)equations can be used to obtain the solution directly.Otherwise,the discrete distribution functions should be updated by the Boltzmann equation to capture the rarefaction effect.Given this,in the ADUGKS,the computational domain is divided into the DUGKS cell and the N-S cell based on the contribu-tion of the initial distribution function to the calculation of free streaming fluxes.In the N-S cell,the local flow field is evolved by solving the N-S equations,while in the DUGKS cell,both the discrete velocity Boltzmann equation and the correspond-ing macroscopic governing equations are solved by a modified DUGKS.Since more and more cells turn into the N-S cell with the decrease of the Knudsen number,a significant acceleration can be achieved for the ADUGKS in the continuum flow regime as compared with the DUGKS.展开更多
Sentiment analysis has been widely used to mine users'opinions on products,product attributes and merchants'response attitudes from online product reviews.One of the key challenges is that the opinion words in...Sentiment analysis has been widely used to mine users'opinions on products,product attributes and merchants'response attitudes from online product reviews.One of the key challenges is that the opinion words in some reviews lack obvious evaluation objects(product attributes).This paper aims to identify implicit attributes from online clothing reviews,and presents a unified model which applies a unified tagging scheme.Our model integrates the indicator consistency(IC)module on the basis of bidirectional gated recurrent unit(BiGRU)with a conditional random fields(CRF)layer(BiGRU-CRF),which denoted as BiGRU-IC-CRF.On the 9640 comments data set of a certain clothing brand,the comparative experiment is carried out by BiGRU,BiGRU with an IC layer(BiGRU-IC)and BiGRU-CRF.The results show that this method has a higher recognition rate,and the F1 value reaches 85.48%.The method proposed in this paper is based on character labeling,which effectively avoids the inaccuracy of word segmentation in natural language processing.The IC module proposed in this paper can maintain the consistency of the product attributes corresponding to the opinion words,thereby enhancing the recognition ability of the original BiGRU-CRF method.This method is not only applicable to the implicit attributes recognition in clothing reviews,but also helpful to other fields implicit attribute recognition of product reviews.展开更多
In this paper,the discrete unified gas-kinetic scheme(DUGKS)is extended to the convection heat transfer in porous media at representative elementary volume(REV)scale,where the changes of velocity and temperature field...In this paper,the discrete unified gas-kinetic scheme(DUGKS)is extended to the convection heat transfer in porous media at representative elementary volume(REV)scale,where the changes of velocity and temperature fields are described by two kinetic equations.The effects from the porous medium are incorporated into the method by including the porosity into the equilibrium distribution function,and adding a resistance force in the kinetic equation for the velocity field.The proposed method is systematically validated by several canonical cases,including the mixed convection in porous channel,the natural convection in porous cavity,and the natural convection in a cavity partially filled with porous media.The numerical results are in good agreement with the benchmark solutions and the available experimental data.It is also shown that the coupled DUGKS yields a second-order accuracy in both temporal and spatial spaces.展开更多
To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pse...To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS.Due to the flux reconstruction procedure,additional terms that break the isotropic requirements of the pseudopotential model will be introduced.To eliminate the influences of nonisotropic terms,the expression of equilibrium distribution functions is reformulated in a moment-based form.With the isotropy-preserving parameter appropriately tuned,the nonisotropic effects can be properly canceled out.The fundamental capabilities are validated by the flat interface test and the quiescent droplet test.It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces.The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition.Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state.By directly incorporating the intermolecular interactions,the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors,which could help gain fresh insights into multiphase fluid flow.展开更多
The gas separation phenomenon of the pressure-driven binary mixture(helium–argon)flows in a microchannel is investigated numerically over a wide range of Knudsen numbers using the discrete unified gas kinetic scheme....The gas separation phenomenon of the pressure-driven binary mixture(helium–argon)flows in a microchannel is investigated numerically over a wide range of Knudsen numbers using the discrete unified gas kinetic scheme.The effects of inlet/outlet pressure ratio and Knudsen number on gas separation are studied numerically.It is found that the separation is strengthened with the increase of pressure ratio,and exhibits different trends under different rarefied conditions.The degree of gas separation changes nonlinearly with the outlet Knudsen number and exhibits a maximum in the transitional regime.In particular,we find that the relative pressure deviation and the velocity ratio between light species helium and heavy species argon can be served as indicators for gas separation under different working conditions.Finally,the phenomenon of Knudsen minimum is observed for the light species and gas mixture in the transition regime,but it does not appear for the heavy species within the considered Knudsen number range(≤10).展开更多
This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,...This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.展开更多
基金supported by Hong Kong Research Grant Council(621709,621011)HKUST grants SRFI11SC05 and RPC10SC11the Nanoscience and Nanotechnology Program at HKUST
文摘Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo （DSMC） simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.
基金supported by the Beijing Natural Science Foundation(Z230003)for Sunby the National Key R&D Program(2020YFA0712200)+1 种基金the National Key Project(GJXM92579)the Sino-German Science Center(GZ 1465)for Jiang。
文摘This paper extends the previous work[1]for the three-temperature gray radiative transfer equations to the frequency-dependent case.Since the additional frequency variable is considered,the equations are more complicated than those in the gray case.Moreover,opacity may be typically a decreasing function of the frequency variable in applications.At the same spatial location,the equations can be in the optically thick case for low frequency photons,while in the optically thin case for high frequency ones.Thus,the resulting discrete equations can significantly increase the computational cost for opacity having the multi-scale property in multiple frequency radiation.Due to the presence of the radiation-electron coupling,electronion coupling,and electron-ion diffusion terms,the model under consideration exhibits strong nonlinearity and strong coupling properties.In this paper,the multigroup method is used to discretize the frequency variable and the H_(N)^(T)method to discretize the angular variable first.Then,within the framework of a unified gas kinetic scheme(UGKS),a multigroup H_(N)^(T)-UGKS method is constructed to solve this complex model iteratively.Furthermore,it can be shown that as the Knudsen number tends to zero,with variations in the electron-ion coupling,absorption,and scattering coefficients,the multigroup H_(N)^(T)-UGKS scheme can converge to numerical schemes for the single-temperature,two-temperature,and the frequency-dependent three-temperature,two-temperature diffusion limit equations,respectively.Finally,several numerical examples are provided to validate the effectiveness and stability of the proposed scheme.
基金supported by Hong Kong Research Grant Council(621011 and 620813)HKUST(SRFI11SC05 and FSGRF13SC21)
文摘The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. After valida- tion, the UGKS is used to study the air-bearing problem under different non- equilibrium conditions. On the surface of the slider, the dependency of the gas pressure and normal force on the Mach and Knudsen numbers are fully evaluated. The non-equilibrium effect on the force loading in the whole transition regime up to the free molecular limit is also studied.
基金supported by the National Natural Science Foundation of China(Grants No.12002131 and No.11872024)Project funded by China Postdoctoral Science Foundation(No.2020M672347 and No.2021M701565).
文摘An implicit discrete unified gas kinetic scheme(DUGKS)is developed for multiscale steady flows of binary gas mixtures by solving the Andries-Aoki-Perthame kinetic model(AAP).To ensure the high convergence efficiency for all flow regimes,the microscopic and macroscopic asynchronous iterative strategies are used,where both the macroscopic and microscopic equations are solved iteratively by the LowerUpper Symmetric Gauss-Seidel(LU-SGS)method.The macroscopic iteration is conducted to solve the macroscopic governing equations containing source terms as an implicit prediction step to evaluate the local equilibrium state of the microscopic evolution,and the macroscopic flux used in the macroscopic iteration is obtained by taking moments of the distribution function.Besides,to keep the asymptotic preserving properties,the numerical flux across the cell interface is reconstructed by the characteristic solution of the kinetic governing equations for both species like the explicit DUGKS for a single gas.Several numerical tests,including the Couette flow,the lid-driven cavity flow,and the flows through a slit of different mixtures,are simulated to verify the accuracy and efficiency of the present scheme for binary mixtures.Furthermore,compared to the explicit DUGKS,the implicit scheme improves the computational efficiency by 1-2 orders of magnitude.
基金supported by Hong Kong Research Grant Council 621709 and 621011,National Natural Science Foundation of China(Project No.10928205)National Key Basic Research Program(2009CB724101)J.C.Huang was supported by National Science Council of Taiwan through grant no.NSC 100-2221-E-019-048-MY3。
文摘With discretized particle velocity space,a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case[J.Comput.Phys.,vol.229(2010),pp.7747-7764].For the kinetic equation,to extend a one-dimensional scheme to multidimensional flow is not so straightforward.The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional,rather than axially symmetric,in velocity space.In this paper,a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented.Instead of particle-based modeling for the rarefied flow,such as the direct simulation Monte Carlo(DSMC)method,the philosophical principal underlying the current study is a partial-differential-equation(PDE)-based modeling.Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different,the gas evolution in a discretized space is modeled with the help of kinetic equation,instead of directly solving the partial differential equation.Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface,the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions.In comparison with the DSMC and Navier-Stokes flow solvers,the current method is much more efficient than DSMC in low speed transition and continuum flow regimes,and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes.As a result,the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation.This paper will extensively evaluate the performance of the unified scheme fromfreemolecule to continuum NS solutions,and fromlow speedmicro-flow to high speed non-equilibrium aerodynamics.The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations,and the scheme provides an important tool in the study of non-equilibrium flow.
基金Hong Kong Research Grant Council(621709,621011)and grants SRFI11SC05 and RPC10SC11 atHKUST.J.C.Huang was supported by National Science Council of Taiwan through grant No.NSC 100-2221-E-019-048-MY3.
文摘Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied flow computation,even though these methods face statistical scattering problem in the low speed limit.With discretized particle velocity space,a unified gas-kinetic scheme(UGKS)for entire Knudsen number flow has been constructed recently for flow computation.Contrary to the particle-based direct simulation Monte Carlo(DSMC)method,the unified scheme is a partial differential equation-based modeling method,where the statistical noise is totally removed.But,the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space.Due to the multiscale modeling in the unified method,i.e.,the update of both macroscopic flow variables and microscopic gas distribution function,the conventional constraint of time step being less than the particle collision time inmany direct Boltzmann solvers is released here.The numerical tests show that the unified scheme is more efficient than the particle-basedmethods in the low speed rarefied flow computation.Themain purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena.In the continuum and free molecular limits,the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions.In the transition regime,the DSMC solution will be used for the validation of UGKS results.This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows.It not only recovers the DSMC results whenever available,but also provides high resolution results in cases where the DSMC can hardly afford the computational cost.In thermal creep flow simulation,surprising solution,such as the gas flowing from hot to cold regions along the wall surface,is observed for the first time by the unified scheme,which is confirmed later through intensive DSMC computation.
基金supported by the Science and Technology Development foundation of China Academy of Engineering Physics(Grant Nos.2015B0202041,2015B0202040)the Science and Technology Development foundation of China Academy of Engineering Physics(Grant 2015B0202040)+2 种基金the Science and Technology Development foundation of China Academy of Engineering Physics(Grant No.2015B0202033)for LiNSFC(Grant No.11371068)for SunNSFC(Grant No.11371068)for Zeng
文摘In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.
基金the National Natural Science Foundation of China(Grant Nos.11872024,and 12002131)the China Postdoctoral Science Foundation(Grant No.2020M672347).
文摘A discrete unified gas kinetic scheme(DUGKS)is developed for multi-species flow in all flow regimes based on the Andries-Aoki-Perthame(AAP)kinetic model.Although the species collision operator in the AAP model conserves fully the mass,momentum,and energy for the mixture,it does not conserve the momentum and energy for each species due to the inter-species collisions.In this work,the species collision operator is decomposed into two parts:one part is fully conservative for the species and the other represents the excess part.With this decomposition,the kinetic equation is solved using the Strang-splitting method,in which the excess part of the collision operator is treated as a source,while the kinetic equation with the species conservative part is solved by the standard DUGKS.Particularly,the time integration of the source term is realized by either explicit or implicit Euler scheme.By this means,it is easy to extend the scheme to gas mixtures composed of Maxwell or hard-sphere molecules,while the previous DUGKS[Zhang Y,Zhu L,Wang R et al,Phys Rev E 97(5):053306,2018]of binary gases was only designed for Maxwell molecules.Several tests are performed to validate the scheme,including the shock structure under different Mach numbers and molar concentrations,the Couette flow under different mass ratios,and the pressure-driven Poiseuille flow in different flow regimes.The results are compared with those from other reliable numerical methods based on different models.And the influence of molecular model on the flow characteristics is studied.The results also show that the present DUGKS with implicit source discretization is more stable and preferable for gas mixture problems involving different flow regimes.
基金the National Natural Science Foundation of China(12202191,92271103)Natural Science Foundation of Jiangsu Province(BK20210273)+1 种基金Fund of Prospective Layout of Scientific Research for NUAA(Nanjing University of Aeronautics and Astronautics)Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘To improve the efficiency of the discrete unified gas kinetic scheme(DUGKS)in capturing cross-scale flow physics,an adaptive partitioning-based discrete unified gas kinetic scheme(ADUGKS)is developed in this work.The ADUGKS is designed from the discrete characteristic solution to the Boltzmann-BGK equation,which contains the initial distribution function and the local equilibrium state.The initial distribution function contributes to the calculation of free streaming fluxes and the local equilibrium state contributes to the calculation of equilibrium fluxes.When the contribution of the initial distribution function is negative,the local flow field can be regarded as the continuous flow and the Navier-Stokes(N-S)equations can be used to obtain the solution directly.Otherwise,the discrete distribution functions should be updated by the Boltzmann equation to capture the rarefaction effect.Given this,in the ADUGKS,the computational domain is divided into the DUGKS cell and the N-S cell based on the contribu-tion of the initial distribution function to the calculation of free streaming fluxes.In the N-S cell,the local flow field is evolved by solving the N-S equations,while in the DUGKS cell,both the discrete velocity Boltzmann equation and the correspond-ing macroscopic governing equations are solved by a modified DUGKS.Since more and more cells turn into the N-S cell with the decrease of the Knudsen number,a significant acceleration can be achieved for the ADUGKS in the continuum flow regime as compared with the DUGKS.
基金National Key Research and Development Program of China(No.2020YFB1707700)。
文摘Sentiment analysis has been widely used to mine users'opinions on products,product attributes and merchants'response attitudes from online product reviews.One of the key challenges is that the opinion words in some reviews lack obvious evaluation objects(product attributes).This paper aims to identify implicit attributes from online clothing reviews,and presents a unified model which applies a unified tagging scheme.Our model integrates the indicator consistency(IC)module on the basis of bidirectional gated recurrent unit(BiGRU)with a conditional random fields(CRF)layer(BiGRU-CRF),which denoted as BiGRU-IC-CRF.On the 9640 comments data set of a certain clothing brand,the comparative experiment is carried out by BiGRU,BiGRU with an IC layer(BiGRU-IC)and BiGRU-CRF.The results show that this method has a higher recognition rate,and the F1 value reaches 85.48%.The method proposed in this paper is based on character labeling,which effectively avoids the inaccuracy of word segmentation in natural language processing.The IC module proposed in this paper can maintain the consistency of the product attributes corresponding to the opinion words,thereby enhancing the recognition ability of the original BiGRU-CRF method.This method is not only applicable to the implicit attributes recognition in clothing reviews,but also helpful to other fields implicit attribute recognition of product reviews.
基金support by the National Natural Science Foundation of China(No.11872024).
文摘In this paper,the discrete unified gas-kinetic scheme(DUGKS)is extended to the convection heat transfer in porous media at representative elementary volume(REV)scale,where the changes of velocity and temperature fields are described by two kinetic equations.The effects from the porous medium are incorporated into the method by including the porosity into the equilibrium distribution function,and adding a resistance force in the kinetic equation for the velocity field.The proposed method is systematically validated by several canonical cases,including the mixed convection in porous channel,the natural convection in porous cavity,and the natural convection in a cavity partially filled with porous media.The numerical results are in good agreement with the benchmark solutions and the available experimental data.It is also shown that the coupled DUGKS yields a second-order accuracy in both temporal and spatial spaces.
基金National Numerical Wind Tunnel Project,the National Natural Science Foundation of China(No.11902266,11902264,12072283)111 Project of China(B17037).
文摘To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS.Due to the flux reconstruction procedure,additional terms that break the isotropic requirements of the pseudopotential model will be introduced.To eliminate the influences of nonisotropic terms,the expression of equilibrium distribution functions is reformulated in a moment-based form.With the isotropy-preserving parameter appropriately tuned,the nonisotropic effects can be properly canceled out.The fundamental capabilities are validated by the flat interface test and the quiescent droplet test.It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces.The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition.Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state.By directly incorporating the intermolecular interactions,the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors,which could help gain fresh insights into multiphase fluid flow.
基金supported by the National Natural Science Foundation of China(Grant Nos.12472290,and 12002131)support of the China Scholarship Council(No.202406160103).
文摘The gas separation phenomenon of the pressure-driven binary mixture(helium–argon)flows in a microchannel is investigated numerically over a wide range of Knudsen numbers using the discrete unified gas kinetic scheme.The effects of inlet/outlet pressure ratio and Knudsen number on gas separation are studied numerically.It is found that the separation is strengthened with the increase of pressure ratio,and exhibits different trends under different rarefied conditions.The degree of gas separation changes nonlinearly with the outlet Knudsen number and exhibits a maximum in the transitional regime.In particular,we find that the relative pressure deviation and the velocity ratio between light species helium and heavy species argon can be served as indicators for gas separation under different working conditions.Finally,the phenomenon of Knudsen minimum is observed for the light species and gas mixture in the transition regime,but it does not appear for the heavy species within the considered Knudsen number range(≤10).
基金This work was supported by the National Natural Science Foundation of China(11402287 and 11372342).
文摘This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.
