Abstract:
We present a brief survey of problem formulations related to high-speed beams with emphasis on analytical solutions. Additionally, numerical solutions for some problems of this class are described. Within the framework of kinetic theory, the analytical method is used to consider the interaction of groups of particles (molecules) assuming that the particles' velocities are highly correlated (delta function is used as a distribution density). The problems of beam interaction with and without loss of particles are studied numerically using direct statistical Monte Carlo simulation. For the problem with loss of particles (intersection and interaction of thin beams), good agreement with the analytical solution is obtained. For the problem without loss of particles (collision of flows), we obtain a numerical solution of the type of a traveling shock wave of limiting compression that is formed when the flow collides with a wall. The role of collision transforms at the initial stage of the process is shown. The problem of beam penetration into a stationary gas up to the stage of plume formation is considered, and a similarity of its initial stage with the problem of thin beams is noted. It is emphasized that analytical methods are fruitful as applied to primary analysis of problems and to the verification of numerical solutions.
