A deterministic approach to the numerical solution of the Boltzmann equation becomes viable if the complicated collision integral is replaced by the simpler relaxation term of the BGK model kinetic equation where the term giving the collisional rate of change of the distribution function is simply proportional to the departure from local equilibrium. The BGK model is often more accurate than expected, particularly in problems where momentum transport is the prominent phenomenon and the collision frequency can be adjusted to match the macroscopic viscosity. In this work we address 3D problems and discuss an efficient implementation of the linearized quasi steady BGK model using a discrete velocity ordinate method coupled with a semi-implicit iterative approach with no recourse to time evolution. Finally we demonstrate its applicability to complex 3D MEMS.
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