The model has been developed by viewing agglomeration as a combination of reversible and irreversible pseudo-reaction steps, involving the sub-processes of particle transport, collisions, capture, aggregate rupture, and aggregate cementation.
Theoretically, once the physical process of particle transport and collision is modeled statistically by the kinetic Boltzmann equation, the transport and collision become continuous operators in space and time, and their numerical discretization should be done consistently.
The scheme, being based on a splitting technique between transport and collision, can be easily extended to other collisional operators as the Boltzmann collision integral or to other kinetic equations such as the Vlasov equation.
For these methods which use operator splitting technique to solve the transport and collision separately, it is usually required that the time step is less than the particle collision time.
The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level.
From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood.
The success of the method is due to the un-splitting treatment of the particle transport and collision in the evaluation of local solution of the gas distribution function.
The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled.
Different from operator splitting methods with decoupled treatment of particle transport and collision, for the Navier Stokes solution in the continuum regime the UGKS-AS doesn't have the constraint on the time step being less than the particle collision time.
With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale.
