Application of techniques used in continuum computational fluiddynamics to the Boltzmann equation

摘要

Summary form only given. Detailed determinations of the electronvelocity distribution function are becoming more common due to thegreater availability of computational power. Some of the classicalproblems in ionized gas physics are found to be in need of suchanalysis. Generally, these solutions are derived from statisticaltechniques, such as Monte-Carlo, or from quasi-particle methods, such asPIC, and are essentially time-dependent methods which represent theconvective effects in a very “physical” way. In contrast,the continuum approaches to hyperbolic PDE solutions, which have astrong “mathematical” basis and have experienced significantadvances in recent years, have been difficult to apply to the Boltzmannequation. These methods have several important advantages such as theirability to resolve steep gradients, including discontinuous behavior,and their uniform accuracy across the domain due to theirnon-statistical nature. Furthermore, in situations where simultaneoussolution of several quantities is desired, and some are best describedin the continuum, it is convenient if the same solver can be used forall. Techniques for enabling the application of these methods to theBoltzmann equation will be described