This Element presents a unified computational fluid dynamics
framework from rarefied to continuum regimes. The 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. With the
variation-of-cell Knudsen number, continuous modelling equations in
different regimes have been obtained, and the Boltzmann and
Navier-Stokes equations become two limiting equations in the
kinetic and hydrodynamic scales. The unified algorithms include the
discrete velocity method (DVM)-based unified gas-kinetic scheme
(UGKS), the particlebased unified gas-kinetic particle method
(UGKP), and the wave and particle-based unified gas-kinetic
wave-particle method (UGKWP). The UGKWP is a multi-scale method
with the particle for non-equilibrium transport and wave for
equilibrium evolution. The particle dynamics in the rarefied regime
and the hydrodynamic flow solver in the continuum regime have been
unified according to the cell's Knudsen number.
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