Modern methods of numerical investigation of rarefied gas phenomena
Abstract
Analytical techniques for describing the characteristics of a dilute gas are examined, noting their basis in manipulation of terms in the Boltzmann equation. The collisional term in the Boltzmann equation is noted to be too complex to solve using numerical simulation, and attempts to obtain solutions by substituting the BGKmodel for the collisional term have been made. Monte Carlo simulations, employing a loworder approximation in velocity space, have demanded a significant amount of computer time. Direct simulation, involving the sampling of a set number of molecules governed by an initial distribution function, takes into account the number of binary collisions necessary until a stable condition is reached, starting from a point of no collisions. The simulation includes consideration of the Prigogine equation for a multiparticle distribution function. Conservative algorithms are defined for ensuring numerical accuracy in a regular numerical approach, which is demonstrated to be valid when dealing with engineering problems of one and two dimensions where a simple geometry is present.
 Publication:

Indian Academy of Sciences Proceedings: Section C Engineering Sciences
 Pub Date:
 July 1982
 Bibcode:
 1982InES....5..159T
 Keywords:

 Boltzmann Transport Equation;
 Computational Fluid Dynamics;
 Monte Carlo Method;
 Numerical Flow Visualization;
 Rarefied Gas Dynamics;
 Computerized Simulation;
 Molecular Interactions;
 One Dimensional Flow;
 Piston Theory;
 Run Time (Computers);
 Shock Wave Propagation;
 Stochastic Processes;
 Fluid Mechanics and Heat Transfer