A kinetic transport and reaction model and simulator for rarefied gas flow in the transition regime

We present a model for rarefied gas flows that are characterized by reactive species as minor constituents in a dominant inert carrier species. The kinetic transport and reaction model consists of a system of transient linear Boltzmann equations for the reactive species in the flow. This model applies to a wide range of transport regimes, including the transition regime in which both transport and collisions between molecules must be taken into account, characterized by Knudsen numbers on the order of unity. A numerical simulator based on a spectral Galerkin method in velocity space approximates each linear Boltzmann equation by a system of transient conservation laws in space and time with diagonal coefficient matrices, which are solved using the discontinuous Galerkin method. This deterministic solver gives direct access to the kinetic density that is the solution to the Boltzmann equation, as a function of position, velocity, and time. It is valuable to have direct access to the velocity dependence in order to analyze the underlying kinetic causes of macroscopic observeables. Using chemical vapor deposition as an important application example, the influence of process parameters is studied in two-dimensional reference studies and transient studies for a three-dimensional domain that represents structures seen during integrated circuit fabrication.