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
In this paper,we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass,momentum and energy.The new construction holds three distinguished ...In this paper,we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass,momentum and energy.The new construction holds three distinguished features.First,the formulations are more concise as compared with the third-order truncated Hermite polynomial expansion which yields Grad’s 13-moment distribution function;Second,all moments of the present distribution function are determined from conservation laws;Third,these moments are closely linked to the most desirable variables,such as mass,momentum and energy.Then,this new distribution function is applied to construct a new gas kinetic flux solver.Numerical validations show that the proposed method recovers the Navier-Stokes solutions in the continuum regime.In addition,it outperforms Grad’s 13-moment distribution function in the transition regime,especially in the prediction of temperature and heat flux.展开更多
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.
基金supported by the National Natural Science Foundation of China(No.12302376)Natural Science Foundation of Jiangsu Province(No.BK20230905)+2 种基金Fundamental Research Funds for the Central Universities(No.30923011033)National Natural Science Foundation of China(No.52201329)MOE Tier 1 project at National University of Singapore(A-0005235-01-00).
文摘In this paper,we propose a new way to construct the distribution function through the second-order polynomial approximation in terms of particle mass,momentum and energy.The new construction holds three distinguished features.First,the formulations are more concise as compared with the third-order truncated Hermite polynomial expansion which yields Grad’s 13-moment distribution function;Second,all moments of the present distribution function are determined from conservation laws;Third,these moments are closely linked to the most desirable variables,such as mass,momentum and energy.Then,this new distribution function is applied to construct a new gas kinetic flux solver.Numerical validations show that the proposed method recovers the Navier-Stokes solutions in the continuum regime.In addition,it outperforms Grad’s 13-moment distribution function in the transition regime,especially in the prediction of temperature and heat flux.
