A unified computational fluid dynamics framework from rarefied to continuum regime is presented in this Element. This framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations.
Focusing on computational fluid dynamics, this book explores the development of CFD algorithms through direct modeling of flow motion in discretized spaces. It introduces the unified gas-kinetic scheme (UGKS), which effectively captures gas evolution across various flow regimes, from rarefied to continuum. The UGKS offers a continuous spectrum of governing equations, enhancing numerical accuracy and providing a comprehensive understanding of fluid dynamics in diverse scenarios.