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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.
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B. R. Wienke (1974) studied this question.
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