A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid flows.The new solver is based on Chapman-Enskog expansion analysis,which is the bridge to link Navie...A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid flows.The new solver is based on Chapman-Enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers.The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.LBFS is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular cylinder.The obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.展开更多
In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from ...In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS[28–31],which is used for simulation of inviscid flows.The first one is its ability to simulate viscous flows by including evaluation of viscous flux.The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock wave.Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.展开更多
A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete se...A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.展开更多
This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock waves.In the FV-LBM,the normal convective flux at the interface of a cell is...This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock waves.In the FV-LBM,the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model,while the tangential flux is calculated using the same way as used in the conventional Euler solvers.The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM.The platform is formed from the conservation forms of moments.Under the platform,both the equilibrium distribution functions and lattice velocities can be determined,and therefore,non-free parameter model can be developed.The paper particularly presents three typical non-free parameter models,D1Q3,D1Q4 and D1Q5.The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems.Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number.From the results,it seems that D1Q4 model could be the best choice for the FVLBM simulation of hypersonic flows.展开更多
A truly three-dimensional(3D)gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work.By local reconstruction of continuous Boltzmann equation,the inviscid and ...A truly three-dimensional(3D)gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work.By local reconstruction of continuous Boltzmann equation,the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver.Different from conventional gaskinetic scheme,in the present work,the distribution function at cell interface is computed in a straightforward way.As an extension of our previous work(Sun et al.,Journal of Computational Physics,300(2015)492–519),the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points.As a result,the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly.To validate the proposed flux solver,several incompressible and compressible viscous flows are simulated.Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.展开更多
In this paper,a simplified lattice Boltzmann method(SLBM)without evolution of the distribution function is developed for simulating incompressible viscous flows.This method is developed from the application of fractio...In this paper,a simplified lattice Boltzmann method(SLBM)without evolution of the distribution function is developed for simulating incompressible viscous flows.This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes(N-S)equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis.In SLBM,the equilibrium distribution function is calculated from the macroscopic variables,while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions.Therefore,SLBM tracks the evolution of the macroscopic variables rather than the distribution function.As a result,lower virtual memories are required and physical boundary conditions could be directly implemented.Through numerical test at high Reynolds number,the method shows very nice performance in numerical stability.An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space.More benchmark tests,including the Couette flow,the Poiseuille flow as well as the 2D lid-driven cavity flow,are conducted to further validate the present method;and the simulation results are in good agreement with available data in literatures.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
A boundary condition-implemented immersed boundary-lattice Boltzmann method(IB-LBM)is presented in this work.The present approach is an improvement to the conventional IB-LBM.In the conventional IB-LBM,the no-slip bou...A boundary condition-implemented immersed boundary-lattice Boltzmann method(IB-LBM)is presented in this work.The present approach is an improvement to the conventional IB-LBM.In the conventional IB-LBM,the no-slip boundary condition is only approximately satisfied.As a result,there is flow penetration to the solid boundary.Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation,which only has the first order of accuracy.In this work,the no-slip boundary condition is directly implemented,and used to correct the velocity at two adjacent mesh points from both sides of the boundary point.The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation.Obviously,the two drawbacks of conventional IB-LBM are removed in the present study.Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law.To validate the proposed method,the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated.As shown in the present results,the flow penetration problem is eliminated,and the obtained results compare very well with available data in the literature.展开更多
Gas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale.In the presence of non-equilibrium flow,the distribution function loses its rotational symmetricity,making the mat...Gas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale.In the presence of non-equilibrium flow,the distribution function loses its rotational symmetricity,making the mathematical derivation difficult.From both the Chapman-Enskog expansion and the Hermite polynomial expansion(Grad’s method),we observe that the non-equilibrium effect is closely related to the peculiar velocity space(C).Based on this recognition,we propose a new methodology to construct the non-equilibrium distribution function from the perspective of polynomial expansion in the peculiar velocity space of molecules.The coefficients involved in the non-equilibrium distribution function can be exactly determined by the compatibility conditions and the moment relationships.This new framework allows constructing non-equilibrium distribution functions at any order of truncation,and the ones at the third and the fourth order have been presented in this paper for illustration purposes.Numerical validations demonstrate that the new method is more accurate than the Grad’s method at the same truncation error for describing non-equilibrium effects.Two-dimensional benchmark tests are performed to shed light on the applicability of the new method to practical engineering problems.展开更多
An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed.The data structure,the directional refinement and coarsening,including the method for init...An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed.The data structure,the directional refinement and coarsening,including the method for initializing the refined new cells,for the anisotropic adaptive method are described.It provides efficient high resolution of flow features,which are aligned with the original quadrilateral mesh structures.Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.展开更多
In this paper,the three-dimensional lattice kinetic scheme is presented to simulate incompressible viscous thermal flows.As compared with the standard LBM,the present scheme has the following good features.It can save...In this paper,the three-dimensional lattice kinetic scheme is presented to simulate incompressible viscous thermal flows.As compared with the standard LBM,the present scheme has the following good features.It can save the computer memory since there is no need to store the density distributions.Like the conventional NS solvers,the implementation of boundary conditions is straightforward since the dependent variables are the macroscopic flow parameters.The easy implementation of boundary conditions is a good property for solving three-dimensional flow problems.The present scheme is validated by simulating the three-dimensional natural convection in an air-filled cubical enclosure,which is heated differentially at two vertical side walls.The obtained numerical results compare very well with available data in the literature.展开更多
A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary meth...A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary method(IBM),the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object.The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points.To be specific,the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity.As compared to the conventional IBM,the present approach accurately implements the non-slip boundary condition.As a result,there is no flow penetration,which is often appeared in the conventional IBM results.The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder.The obtained numerical results agree very well with the data in the literature.展开更多
文摘A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid flows.The new solver is based on Chapman-Enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers.The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.LBFS is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular cylinder.The obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.
基金supported by the State Key Laboratory of Aerodynamics of China(No.SKLA201401).
文摘In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS[28–31],which is used for simulation of inviscid flows.The first one is its ability to simulate viscous flows by including evaluation of viscous flux.The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock wave.Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.
文摘A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.
文摘This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock waves.In the FV-LBM,the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model,while the tangential flux is calculated using the same way as used in the conventional Euler solvers.The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM.The platform is formed from the conservation forms of moments.Under the platform,both the equilibrium distribution functions and lattice velocities can be determined,and therefore,non-free parameter model can be developed.The paper particularly presents three typical non-free parameter models,D1Q3,D1Q4 and D1Q5.The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems.Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number.From the results,it seems that D1Q4 model could be the best choice for the FVLBM simulation of hypersonic flows.
基金National Natural Science Foundation of China(Grant Nos.11772157 and 11832012).
文摘A truly three-dimensional(3D)gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work.By local reconstruction of continuous Boltzmann equation,the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver.Different from conventional gaskinetic scheme,in the present work,the distribution function at cell interface is computed in a straightforward way.As an extension of our previous work(Sun et al.,Journal of Computational Physics,300(2015)492–519),the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points.As a result,the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly.To validate the proposed flux solver,several incompressible and compressible viscous flows are simulated.Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.
文摘In this paper,a simplified lattice Boltzmann method(SLBM)without evolution of the distribution function is developed for simulating incompressible viscous flows.This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes(N-S)equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis.In SLBM,the equilibrium distribution function is calculated from the macroscopic variables,while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions.Therefore,SLBM tracks the evolution of the macroscopic variables rather than the distribution function.As a result,lower virtual memories are required and physical boundary conditions could be directly implemented.Through numerical test at high Reynolds number,the method shows very nice performance in numerical stability.An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space.More benchmark tests,including the Couette flow,the Poiseuille flow as well as the 2D lid-driven cavity flow,are conducted to further validate the present method;and the simulation results are in good agreement with available data in literatures.
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supported by the National Natural Science Foundation of China(11272153).
文摘A boundary condition-implemented immersed boundary-lattice Boltzmann method(IB-LBM)is presented in this work.The present approach is an improvement to the conventional IB-LBM.In the conventional IB-LBM,the no-slip boundary condition is only approximately satisfied.As a result,there is flow penetration to the solid boundary.Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation,which only has the first order of accuracy.In this work,the no-slip boundary condition is directly implemented,and used to correct the velocity at two adjacent mesh points from both sides of the boundary point.The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation.Obviously,the two drawbacks of conventional IB-LBM are removed in the present study.Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law.To validate the proposed method,the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated.As shown in the present results,the flow penetration problem is eliminated,and the obtained results compare very well with available data in the literature.
基金supported by MOE Tier 1 project at National University of Singapore(No.A-0005235-01-00).
文摘Gas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale.In the presence of non-equilibrium flow,the distribution function loses its rotational symmetricity,making the mathematical derivation difficult.From both the Chapman-Enskog expansion and the Hermite polynomial expansion(Grad’s method),we observe that the non-equilibrium effect is closely related to the peculiar velocity space(C).Based on this recognition,we propose a new methodology to construct the non-equilibrium distribution function from the perspective of polynomial expansion in the peculiar velocity space of molecules.The coefficients involved in the non-equilibrium distribution function can be exactly determined by the compatibility conditions and the moment relationships.This new framework allows constructing non-equilibrium distribution functions at any order of truncation,and the ones at the third and the fourth order have been presented in this paper for illustration purposes.Numerical validations demonstrate that the new method is more accurate than the Grad’s method at the same truncation error for describing non-equilibrium effects.Two-dimensional benchmark tests are performed to shed light on the applicability of the new method to practical engineering problems.
文摘An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed.The data structure,the directional refinement and coarsening,including the method for initializing the refined new cells,for the anisotropic adaptive method are described.It provides efficient high resolution of flow features,which are aligned with the original quadrilateral mesh structures.Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.
文摘In this paper,the three-dimensional lattice kinetic scheme is presented to simulate incompressible viscous thermal flows.As compared with the standard LBM,the present scheme has the following good features.It can save the computer memory since there is no need to store the density distributions.Like the conventional NS solvers,the implementation of boundary conditions is straightforward since the dependent variables are the macroscopic flow parameters.The easy implementation of boundary conditions is a good property for solving three-dimensional flow problems.The present scheme is validated by simulating the three-dimensional natural convection in an air-filled cubical enclosure,which is heated differentially at two vertical side walls.The obtained numerical results compare very well with available data in the literature.
文摘A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary method(IBM),the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object.The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points.To be specific,the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity.As compared to the conventional IBM,the present approach accurately implements the non-slip boundary condition.As a result,there is no flow penetration,which is often appeared in the conventional IBM results.The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder.The obtained numerical results agree very well with the data in the literature.
