NS-DSMC(Navier Stokes-Direct Simulation Monte Carlo)耦合方法是计算连续-稀薄跨流域流动的主要方法,应用过程中如何确定连续流域和稀薄流域的界面是此方法的关键问题之一,界面位置通常通过连续失效参数来判定.为合理选择连续失效参...NS-DSMC(Navier Stokes-Direct Simulation Monte Carlo)耦合方法是计算连续-稀薄跨流域流动的主要方法,应用过程中如何确定连续流域和稀薄流域的界面是此方法的关键问题之一,界面位置通常通过连续失效参数来判定.为合理选择连续失效参数,对目前广泛使用的两种连续失效参数KnQ和B参数进行了理论上的分析和比较,表明虽然他们建立的出发点不同,但在数学形式上具有一定相似性.通过圆柱绕流问题的数值试验进一步验证了两种连续失效参数具有一定对应关系.KnQ和B两种连续失效参数在NS-DSMC耦合方法中应用效果相差不大,但KnQ的阈值0.05适用范围较广,而B参数的阈值对不同流动问题会有变化.展开更多
This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 0. This model...This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.展开更多
In this paper, a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enabl...In this paper, a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enables the study of multicomponent flows with different molecular weights, different viscosities and different Schmidt numbers, but also ensures that the distribution function of each component evolves on the same square lattice without invoking ad- ditional interpolations. Furthermore, the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations, and satisfies the indifferentiability principle. The numerical validation exercises further demonstrate that the favorable performance of the present model.展开更多
The aim of this work is to clarify the new mathematical model describing the mechanics of continuous media and rarefied gas. The present study is associated with the formulation of conservation laws as conditions of e...The aim of this work is to clarify the new mathematical model describing the mechanics of continuous media and rarefied gas. The present study is associated with the formulation of conservation laws as conditions of equilibrium of angular momentums, while usually formulated in terms of balance of force. The equations for gas are found from the modified Boltzmann equation and the phenomenological theory. For a rigid body, the equations used the phenomenological theory, but changed their interpretation. We elucidate the contribution of cross-effects in the conservation laws of continuum mechanics, including the self-diffusion, thermal diffusion, etc., which indicated S. Wallander. The paradox of Hilbert in the solution of the Boltzmann equation by the Chapman-Enskog method was resolved. Refined model of the boundary conditions for rarefied gas flows and transient flow were near the moving surfaces. We establish conditions for the existence of the A. N. Kolmogorov inertial range on the basis of the proposed theory. Based on the theory, derivation of the Prandtl formula for boundary layer was received. Delay in mechanics plays an important role on commensurability of relaxation times and lateness. New accounting delay option is proposed to consider the difference between the time derivative as a limit and end values of the mean free path in a rarefied gas. The role of individual time delay for each particle velocity and the average time is debated. The Boltzmann equation is written with an additional term. This situation is typical for discrete medium. The transition from discrete to continuous environment is a key issue mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The role of the time has similar problems in quantum mechanics. Some examples are suggested.展开更多
文摘NS-DSMC(Navier Stokes-Direct Simulation Monte Carlo)耦合方法是计算连续-稀薄跨流域流动的主要方法,应用过程中如何确定连续流域和稀薄流域的界面是此方法的关键问题之一,界面位置通常通过连续失效参数来判定.为合理选择连续失效参数,对目前广泛使用的两种连续失效参数KnQ和B参数进行了理论上的分析和比较,表明虽然他们建立的出发点不同,但在数学形式上具有一定相似性.通过圆柱绕流问题的数值试验进一步验证了两种连续失效参数具有一定对应关系.KnQ和B两种连续失效参数在NS-DSMC耦合方法中应用效果相差不大,但KnQ的阈值0.05适用范围较广,而B参数的阈值对不同流动问题会有变化.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10661005)Fujian Province Science and Technology Plan Item (Grant No. 2008F5019)
文摘This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (62311)supported by the National Natural Science Foundation of China(51006040)+1 种基金the Hong Kong Scholar Programthe National Science Fund for Distinguished Young Scholars of China (51125024)
文摘In this paper, a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems. Unlike previous models in the literature, the present model not only enables the study of multicomponent flows with different molecular weights, different viscosities and different Schmidt numbers, but also ensures that the distribution function of each component evolves on the same square lattice without invoking ad- ditional interpolations. Furthermore, the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations, and satisfies the indifferentiability principle. The numerical validation exercises further demonstrate that the favorable performance of the present model.
文摘The aim of this work is to clarify the new mathematical model describing the mechanics of continuous media and rarefied gas. The present study is associated with the formulation of conservation laws as conditions of equilibrium of angular momentums, while usually formulated in terms of balance of force. The equations for gas are found from the modified Boltzmann equation and the phenomenological theory. For a rigid body, the equations used the phenomenological theory, but changed their interpretation. We elucidate the contribution of cross-effects in the conservation laws of continuum mechanics, including the self-diffusion, thermal diffusion, etc., which indicated S. Wallander. The paradox of Hilbert in the solution of the Boltzmann equation by the Chapman-Enskog method was resolved. Refined model of the boundary conditions for rarefied gas flows and transient flow were near the moving surfaces. We establish conditions for the existence of the A. N. Kolmogorov inertial range on the basis of the proposed theory. Based on the theory, derivation of the Prandtl formula for boundary layer was received. Delay in mechanics plays an important role on commensurability of relaxation times and lateness. New accounting delay option is proposed to consider the difference between the time derivative as a limit and end values of the mean free path in a rarefied gas. The role of individual time delay for each particle velocity and the average time is debated. The Boltzmann equation is written with an additional term. This situation is typical for discrete medium. The transition from discrete to continuous environment is a key issue mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The role of the time has similar problems in quantum mechanics. Some examples are suggested.
