The Hypersonic Double Ellipse in Rarefied Flow Problem 6.4

Abstract

A particle method represents a flow by a large collection of computational molecules whose motions in space are tracked and whose collisions with solid boundaries and intermolecular collisions are modeled. This algorithm represents particle motion and collision modeling independently on each time step. Particle motion occurs in the present method through a network of cells that is overlaid on the computational domain. These cells serve two purposes. Particles that find themselves in a given cell are designated as candidates for possible collision with other particles in the same cell. The cell is also the volume over which the averaging process will occur when statistical information is extracted. It therefore represents the smallest spatial dimension over which flow field features may be resolved. Body fitted coordinates have been used in other particle methods to enhance spatial resolution¹. The approach taken here, however, is to reduce the computational overhead by using simple cubic cells and to reapply this savings in the use of many of them. The use of cubic cells poses a problem in the definition of complex geometries that has been addressed by the development of an algorithm to define the relation of a body surface to the network of cells. This algorithm will be discussed in a subsequent section.