摘要:

Developments since the formulation of the Boltzmann equation will be discussed. This includes assumptions in the derivation of the equation that make it valid only asymptotically. Merits of the solution of the equation by various numerical techniques will be outlined including the lattice Boltzmann version. Finally, attempts at extending applicability to higher density and embedding into a continuum will be discussed. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407535

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

For the physically accurate simulation of molecular gases, the CTC-DSMC method is developed by directly coupling classical trajectory calculations (CTC) for rigid and vibrating rotators with the direct simulation Monte Carlo (DSMC) method. Using the CTC-DSMC method for rigid rotators, the rotational relaxation of nitrogen through a normal shock wave is simulated by employing the accurate potential energy surface. The CTC-DSMC results agree well with the experimental results. The CTC-DSMC method for vibrating rotators is used for the simulation of the vibrational relaxation and dissociation of oxygen infinitely dilute in an isothermal heat bath of argon with the model potentials, where the test-particle procedure is efficiently employed. It is shown that the dissociation occurs preferentially from the upper rotational quantum levels over almost all the vibrational quantum levels and that the steady velocity, rotational, and vibrational distributions considerably deviate from the heat-bath equilibrium distributions. The CTC-DSMC calculation reasonably reproduces the experimental results measured in shock-heated dilute oxygen-argon mixtures. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407536

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Alexander, Garcia and Alder [1] introduced the Consistent Boltzmann Algorithm (CBA) as a simple variant of Direct Simulation Monte Carlo (DSMC) for dense gases. In CBA, collisions alter both the positions and velocities of the particles. In the present work the limiting kinetic equation for CBA is derived; the formulation is similar to the proof that the Boltzmann equation is the limiting kinetic equation for DSMC [11]. The relation between this new kinetic equation and the Enskog equation is outlined. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407537

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

The diffusion-slip problem for a binary mixture of gases is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problem is analyzed numerically by the finite-difference method, where the collision integrals are computed by the numerical kernel method first introduced by Sone, Ohwada and Aoki for single-component gases [Sone &etal;, Phys. Fluids A,1, 363 (1989)]. This is the first report in which the method is extended and applied to the case of mixtures. The analysis is carried out for several combinations of the component gases and the behavior of the mixture is clarified at the level of the velocity distribution functions. As a result, the coefficient of the diffusion-slip and the associated Knudsen-layer functions are obtained. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407538

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

To avoid the complexity of the Boltzmann collision operator, the BGK Model Equation is widely used, but it is well known that one of its shortcoming is that it gives a Prandtl number of one in the fluid limit. The ES-BGK was introduced to obtain the correct Prandtl number, but the entropy property for this model was an open problem. In this talk we prove that this model actually verify an H theorem. Moreover we show in a simple case that computations with this model are of the same order of complexity and cost as with the BGK model, so that it appears as a valid alternative of the BGK model. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407539

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

We consider two species of light test particles interacting with a medium constituted by two species of much heavier field particles. A reversible bimolecular chemical reaction is assumed to occur, with conservation of mass, momentum and total energy. In the Lorentz gas limit, the resulting model is described by a system of two extended linear Boltzmann equations for the light test particles. The main properties of the collision operators are discussed and collision invariants are properly introduced. Equilibria are determined and turn out to be defined up to an arbitrary isotropic shape function. Stability and uniqueness of the equilibrium associated to any given initial datum are investigated in the space homogeneous case. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407540

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

The behavior of a gas may be quite atypical if the velocity distribution function is significantly distorted by the presence of large gradients. Under such circumstances phenomena like shear thinning or negative effective thermal conductivity may be present. Hydrodynamic equations derived directly from Boltzmann’s equation using a moment expansion method yield predictions which are sensitive to the value of Knudsen numbers associated to the macroscopic fields themselves and provide a rational for the peculiar behavior. In the case of sheared laminar flows the law of viscous flow predicts non-Newtonian effects including shear thinning and the law of energy transport (associated to what is usually called heat flux) is more general than Fourier’s law: it is not linear and it implies a flux with a nontrivial component parallel to the isotherms. These nonlinear transport laws are well corroborated by molecular dynamic simulations based on straightforward Newtonian dynamics. More in general it is shown that the energy flux is naturally split in a component that removes heat from the system and a divergenceless component which represents a flux of energy which does not leave the system. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407541

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407542

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Investigations in the field of quantum optics very often requires a molecular simulation of transport phenomena. This paper presents a discrete kinetic model to deal with the quantum optical problem of hole burning. Based on a full discretization of the velocity space, Boltzmann-like equations are established to govern the temporal evolution of heavily disturbed Maxwell distributions of optically excited particles diffusing in a buffer gas. These model equations involve elastic collisions and the interaction of photons with three-level atoms by taking into account the Doppler effect. Important features of the developed model are the realistic simulation of the relaxation process and the existence of a stable and unique equilibrium solution. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407543

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Moment equations derived from the Boltzmann equation were applyed to the Riemann problem. A new closure method of the moment equations were proposed. It was demonstrated that supplemented moment equations were applicable to the analysis of moderately strong shock waves. Various higher order moments of the distribution function in the shock wave were obtained. Present result suggested that these higher order moments would not be simply expressed in terms of higher order derivatives of velocity, temperature, and pressure. If we include more higher moment equations present results may be considerablly improved. Present method is expected for the analysis of nonequilibrium rarefied flow connecting with higher order moments demonstrated in this paper. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1407544

出版商:AIP    

年代:1901

数据来源: AIP