The aim of the present work is to produce a general, robust and efficient solver allowing to simulate non-continuum, multi-scale flows for diverse engineering applications. The wide development of MEMS application requires special methods for an investigation of the flow in them, since the rarefaction plays a major role in such flow and the Navier-Stokes equations even provided with slip boundary conditions become invalid in the whole flow field.
The methodology used involves the decomposition of a physical domain into kinetic and hydrodynamic sub-domains by computing appropriate criteria, based on the local Knudsen number and gradients of macroparametrs. The size of sub-domains will change during the evolution depending on the current value of the criterion. The hybrid solver is the combination of a kinetic solver for the S-model of the Boltzmann kinetic equation (based on the discrete velocity method) and a Navier–Stokes solver based on a hybrid finite-difference finite volume scheme. The solution is advanced in time simultaneously in both kinetic and hydrodynamic domains and the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes sub-domains, thus taking care of the conservation of momentum, energy and mass through the coupling interface. Parallelization via MPI (Message Passing Interface) increases the efficiency of the hybrid solver, thus making simulations of complex geometry feasible.
The hybrid solver is validated via the numerical investigation of gas flow through a slit in a wide range of pressure ratio, including flow into vacuum and Knudsen number from slip to transitional regime. The capability of hybrid solver as applied to vacuum science problems is demonstrated. Furthermore, the hybrid solver is applied for the investigation of the effect of the surface roughness. The competition between compressibility, rarefaction and roughness effects is analysed. The improvement in accuracy over Navier-Stokes equations and the computational efficiency of the proposed hybrid solver is assessed via comparison with a pure kinetic solution. Thus, the elaborated hybrid solver demonstrates capabilities to predict numerical results close to kinetic ones up to 10 times quicker.
