Summary and Outlook

Abstract

It is our hope that this book has provided a concise but self-contained introduction to the theories of describing various flow problems at different scales, and the difference as well as correlation between different theories. We focused on the kinetic theory of using the Boltzmann equation, which is valid for modeling flows of different regimes from continuum to free molecular flow. Then, various fluid behaviors can be modeled by different simulation methods developed based on the same framework of Boltzmann equation. As summarized in Fig. 5.1, four simulation methods are introduced and they are the DSMC method, DSBGK method, DVM and LBM. The algorithm differences among those simulation methods are noticeable and their performance comparisons are detailed in several benchmark problems of the preceding chapters, which provides some guidelines for those interested in using appropriate methods for their particular applications.