To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced v...To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.展开更多
A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the gov...A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.展开更多
In this paper,a hybrid Lattice Boltzmann Flux Solver(LBFS)with an improved switch function is proposed for simulation of integrated hypersonic fluid-thermal-structural problems.In the solver,the macroscopic Navier–St...In this paper,a hybrid Lattice Boltzmann Flux Solver(LBFS)with an improved switch function is proposed for simulation of integrated hypersonic fluid-thermal-structural problems.In the solver,the macroscopic Navier–Stokes equations and structural heat transfer equation are discretized by the finite volume method,and the numerical fluxes at the cell interface are reconstructed by the local solution of the Boltzmann equation.To compute the numerical fluxes,two equilibrium distribution functions are introduced.One is the D1Q4 discrete velocity model for calculating the inviscid flux across the cell interface of Navier–Stokes equations,and the other is the D2Q4 model for evaluating the flux of structural energy equation.In this work,a new dual thermal resistance model is proposed to calculate the thermal properties at the fluid–solid interface.The accuracy and stability of the present hybrid solver are validated by simulating several numerical examples,including the fluid-thermal-structural problem of cylindrical leading edge.Numerical results show that the present solver can accurately predict the thermal properties of hypersonic fluid-thermalstructural problems and has the great potential for solving fluid-thermal-structural problems of long-endurance high-speed vehicles.展开更多
In this work,the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional(2D)immersed boundary-multiphase lattice Boltzmann flux solver(...In this work,the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional(2D)immersed boundary-multiphase lattice Boltzmann flux solver(IB-MLBFS).The fluid domain is discretized by finite volume discretization,and the flux on the grid interface is evaluated by lattice Boltzmann equations.Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure.First,the water entry of a circular cylinder is simulated and the results are compared with the experiment,which considered the length-diameter ratio of the circular cylinder.The reliability of 2D simulation is verified and the deformation of the free interface is well investigated.Afterward,the water exit of a circular cylinder with constant velocity is simulated,which is less researched.In addition,the results show the advantage of present IB-MLBFS to some extent.Finally,the water exit and re-entry of a circular cylinder are presented,and the results present the complex deformation of the free interface and the dynamic response of the moving structure.Based on the numerical results,the free interface of the multiphase fluids is well captured,and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS.展开更多
In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretizati...In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretization.The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables.Meanwhile,a switch function is used in LBFS to adjust the magnitude of the numerical viscosity.Thus,it is more beneficial to capture both strong shock waves and thin boundary layers.Moreover,the viscous flux is computed according to the local discontinuous Galerkin method.Some typical compressible viscous problems,including manufactured solution case,lid-driven cavity flow,supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil,are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.展开更多
A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined wit...A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.展开更多
Shock wave/boundary layer interaction(SWBLI)continues to pose a significant chal-lenge in the field of aerospace engineering.This paper aims to address this issue by proposing a novel approach for predicting aerodynam...Shock wave/boundary layer interaction(SWBLI)continues to pose a significant chal-lenge in the field of aerospace engineering.This paper aims to address this issue by proposing a novel approach for predicting aerodynamic coefficients and heat trans-fer in viscous supersonic and hypersonic flows using a high-order flux reconstruction technique.Currently,finite volume methods are extensively employed for the compu-tation of skin aerodynamic coefficients and heat transfer.Nevertheless,these numerical methods exhibit considerable susceptibility to a range of factors,including the inviscid flux function and the computational mesh.The application of high-order flux recon-struction techniques offers promising potential in alleviating these challenges.In contrast to other high-order methods,the flux reconstruction is combined with the lat-tice Boltzmann flux solver in this study.The current method evaluates the common inviscid flux at the cell interface by locally reconstructing the lattice Boltzmann equa-tion solution from macroscopic flow variables at solution points.Consequently,this framework performs a positivity-preserving,entropy-based adaptive filtering method for shock capturing.The present approach is validated by simulating the double Mach reflection,and then simulating some typical viscous problems.The results demonstrate that the current method accurately predicts aerodynamic coefficients and heat trans-fer,providing valuable insights into the application of high-order methods for shock wave/boundary layer interaction.展开更多
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 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
This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volum...This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volume method(FVM)is applied to discretize the Navier-Stokes equations,and the LBFS is utilized to evaluate the numerical flux at the cell interface.In LBFS,the local solution of discrete velocity Boltzmann equation(DVBE)with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface,and the viscous flux is approximated by conventional smooth function approach.In order to improve the robustness and convergence rate of the simulation for hypersonic flows,especially for problems with complex geometry,the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations.A double cone model at Mach number of Ma=9.86 is firstly simulated to validate the proposed scheme,and a hypersonic flight vehicle with wings and rudders at Mach number of Ma=5.56 is then calculated to extend the application in practical engineering problems.Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.展开更多
A discontinuous Galerkin(DG)-based lattice Boltzmann method is employed to solve the Euler and Navier-Stokes equations.Instead of adopting the widely used local Lax-Friedrichs flux and Roe Flux etc.,a hybrid lattice B...A discontinuous Galerkin(DG)-based lattice Boltzmann method is employed to solve the Euler and Navier-Stokes equations.Instead of adopting the widely used local Lax-Friedrichs flux and Roe Flux etc.,a hybrid lattice Boltzmann flux solver(LBFS)is employed to evaluate the inviscid flux across the cell interfaces.The main advantage of the hybrid LBFS is its flexibility for capturing both strong shocks and thin boundary layers through introducing a function which varies from zero to one to control the artificial viscosity.Numerical results indicate that the hybrid lattice Boltzmann flux solver behaves very well combining with the high-order DG method when simulating both inviscid and viscous flows.展开更多
基金Supported by the National Natural Science Foundation of China(52201350,52201394,and 52271301)the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(Grant No.SML2022008).
文摘To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.
基金Supported by the National Natural Science Foundation of China(11272153)
文摘A lattice Boltzmann flux solver(LBFS)is presented for simulation of fluid flows.Like the conventional computational fluid dynamics(CFD)solvers,the new solver also applies the finite volume method to discretize the governing differential equations,but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers.Instead,it is evaluated from local solution of lattice Boltzmann equation(LBE)at cell interface.Two versions of LBFS are presented in this paper.One is to locally apply one-dimensional compressible lattice Boltzmann(LB)model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves.The other is to locally apply multi-dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows.The present solver removes the drawbacks of conventional lattice Boltzmann method(LBM)such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.
基金co-supported by the Postgraduate Research&Practice Innovation Program of Jiangsu Province of China(No.KYCX17_0235)Nanjing University of Aeronautics and Astronautics Ph D Short-term Visiting Scholar Project(No.180602DF01)National Numerical Wind Tunnel Project(Nos.NNW2018-ZT3B08 and NNW2019-ZT7B30)。
文摘In this paper,a hybrid Lattice Boltzmann Flux Solver(LBFS)with an improved switch function is proposed for simulation of integrated hypersonic fluid-thermal-structural problems.In the solver,the macroscopic Navier–Stokes equations and structural heat transfer equation are discretized by the finite volume method,and the numerical fluxes at the cell interface are reconstructed by the local solution of the Boltzmann equation.To compute the numerical fluxes,two equilibrium distribution functions are introduced.One is the D1Q4 discrete velocity model for calculating the inviscid flux across the cell interface of Navier–Stokes equations,and the other is the D2Q4 model for evaluating the flux of structural energy equation.In this work,a new dual thermal resistance model is proposed to calculate the thermal properties at the fluid–solid interface.The accuracy and stability of the present hybrid solver are validated by simulating several numerical examples,including the fluid-thermal-structural problem of cylindrical leading edge.Numerical results show that the present solver can accurately predict the thermal properties of hypersonic fluid-thermalstructural problems and has the great potential for solving fluid-thermal-structural problems of long-endurance high-speed vehicles.
基金Supported by the National Natural Science Foundation of China(52061135107)the Fundamental Research Fund for the Central Universities(DUT20TD108,DUT20LAB308)the Liao Ning Revitalization Talents Program(XLYC1908027),and Dalian Innovation Research Team in Key Areas(2020RT03).
文摘In this work,the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional(2D)immersed boundary-multiphase lattice Boltzmann flux solver(IB-MLBFS).The fluid domain is discretized by finite volume discretization,and the flux on the grid interface is evaluated by lattice Boltzmann equations.Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure.First,the water entry of a circular cylinder is simulated and the results are compared with the experiment,which considered the length-diameter ratio of the circular cylinder.The reliability of 2D simulation is verified and the deformation of the free interface is well investigated.Afterward,the water exit of a circular cylinder with constant velocity is simulated,which is less researched.In addition,the results show the advantage of present IB-MLBFS to some extent.Finally,the water exit and re-entry of a circular cylinder are presented,and the results present the complex deformation of the free interface and the dynamic response of the moving structure.Based on the numerical results,the free interface of the multiphase fluids is well captured,and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS.
基金supported by the National Natural Science Foundation of China(No.12072158)the Natural Science Foundation of Jiangsu Province(No.BK20191271)+1 种基金the Research Fund of Key Laboratory of Computational AerodynamicsAVIC Aerodynamics Research Institute(No.YL2022XFX0402)。
文摘In this paper,a high-order scheme based on the lattice Boltzmann flux solver(LBFS)is proposed to simulate viscous compressible flows.The flux reconstruction(FR)approach is adopted to implement the spatial discretization.The LBFS is employed to compute the inviscid flux by using the local reconstruction of the lattice Boltzmann equation solutions from macroscopic flow variables.Meanwhile,a switch function is used in LBFS to adjust the magnitude of the numerical viscosity.Thus,it is more beneficial to capture both strong shock waves and thin boundary layers.Moreover,the viscous flux is computed according to the local discontinuous Galerkin method.Some typical compressible viscous problems,including manufactured solution case,lid-driven cavity flow,supersonic flow around a cylinder and subsonic flow over a NACA0012 airfoil,are simulated to demonstrate the accuracy and robustness of the proposed FR-LBFS.
基金Project supported by the National Natural Science Foundation of China(No.12072158)。
文摘A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.
基金This study was supported by the National Natural Science Foundation of China(Grant No.12072158)the Natural Science Foundation of Jiangsu Province(Grant No.BK20231437)the Research Fund of Key Laboratory of Computational Aerodynamics,AVIC Aerodynamics Research Institute(Grant No.YL2022XFX0402).
文摘Shock wave/boundary layer interaction(SWBLI)continues to pose a significant chal-lenge in the field of aerospace engineering.This paper aims to address this issue by proposing a novel approach for predicting aerodynamic coefficients and heat trans-fer in viscous supersonic and hypersonic flows using a high-order flux reconstruction technique.Currently,finite volume methods are extensively employed for the compu-tation of skin aerodynamic coefficients and heat transfer.Nevertheless,these numerical methods exhibit considerable susceptibility to a range of factors,including the inviscid flux function and the computational mesh.The application of high-order flux recon-struction techniques offers promising potential in alleviating these challenges.In contrast to other high-order methods,the flux reconstruction is combined with the lat-tice Boltzmann flux solver in this study.The current method evaluates the common inviscid flux at the cell interface by locally reconstructing the lattice Boltzmann equa-tion solution from macroscopic flow variables at solution points.Consequently,this framework performs a positivity-preserving,entropy-based adaptive filtering method for shock capturing.The present approach is validated by simulating the double Mach reflection,and then simulating some typical viscous problems.The results demonstrate that the current method accurately predicts aerodynamic coefficients and heat trans-fer,providing valuable insights into the application of high-order methods for shock wave/boundary layer interaction.
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.
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This paper proposes a stable and efficient implicit block Lower-Upper Symmetric-Gauss-Seidel(LU-SGS)algorithm-based lattice Boltzmann flux solver(LBFS)for simulation of hypersonic flows.In this method,the finite volume method(FVM)is applied to discretize the Navier-Stokes equations,and the LBFS is utilized to evaluate the numerical flux at the cell interface.In LBFS,the local solution of discrete velocity Boltzmann equation(DVBE)with the non-free parameter D1Q4 lattice Boltzmann model is adopted to reconstruct the inviscid flux across the cell interface,and the viscous flux is approximated by conventional smooth function approach.In order to improve the robustness and convergence rate of the simulation for hypersonic flows,especially for problems with complex geometry,the implicit block LU-SGS algorithm is introduced to solve resultant discrete governing equations.A double cone model at Mach number of Ma=9.86 is firstly simulated to validate the proposed scheme,and a hypersonic flight vehicle with wings and rudders at Mach number of Ma=5.56 is then calculated to extend the application in practical engineering problems.Numerical results show that the proposed scheme could offer a more accurate and effective prediction for hypersonic flows.
文摘A discontinuous Galerkin(DG)-based lattice Boltzmann method is employed to solve the Euler and Navier-Stokes equations.Instead of adopting the widely used local Lax-Friedrichs flux and Roe Flux etc.,a hybrid lattice Boltzmann flux solver(LBFS)is employed to evaluate the inviscid flux across the cell interfaces.The main advantage of the hybrid LBFS is its flexibility for capturing both strong shocks and thin boundary layers through introducing a function which varies from zero to one to control the artificial viscosity.Numerical results indicate that the hybrid lattice Boltzmann flux solver behaves very well combining with the high-order DG method when simulating both inviscid and viscous flows.
