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
In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excita...In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.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
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
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
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
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 the Project of manned space engineering technology(2018-14)“Large-scale parallel computation of aerodynamic problems of irregular spacecraft reentry covering various flow regimes”the National Natural Science Foundation of China(91530319).
文摘In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.
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(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 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 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.
