Transport equation in modified Eulerian coordinates

Abstract

The Boltzmann equation is formulated in a hydrodynamic representation (modified Eulerian) in terms of velocities relative to an accelerated medium. Treating the target particles as fixed in moving hydrodynamic zones, or cells, and employing a representation in relative velocities gives a well-defined cross section and permits use of the standard set of velocities and cross sections for computational purposes. Specific one-dimensional forms for the transport equation are also given in plane and spherical geometries.