Numerical Simulation of Micro cavity Flow Using Perturbation Theory

A new method of modeling micro flows is presented in this research. First, the continuum equations of the fluid dynamics are developed by using perturbation expansions of the velocity, pressure and density and temperature fields. Subsequently, different orders of equations in dependence of Knudsen number are obtained. Required boundary conditions for solving each order of these equations is obtained by substitution of the perturbation expansions into the general boundary conditions for velocity slip and temperature jump. We use three-therm perturbation expansions and reach to three orders of equations and their boundary conditions. A three-part computer program has been produced for solving the set of discretized equations. Each part of this code, solve one order of the equations with the SIMPLE algorithm. A shear-driven microcavity flow with slip is investigated and its results are compared with those by the DSMC approach.