Numerical Simulation of Micro cavity Flow Using Perturbation Theory

A new method of modeling micro flows is presented in thisresearch. First, the continuum equations of the fluiddynamics are developed by using perturbation expansionsof the velocity, pressure and density and temperature fields.Subsequently, different orders of equations in dependenceof Knudsen number are obtained. Required boundaryconditions for solving each order of these equations isobtained by substitution of the perturbation expansions intothe general boundary conditions for velocity slip andtemperature jump. We use three-therm perturbationexpansions and reach to three orders of equations and theirboundary conditions. A three-part computer program hasbeen produced for solving the set of discretized equations.Each part of this code, solve one order of the equations withthe SIMPLE algorithm. A shear-driven microcavity flowwith slip is investigated and its results are compared withthose by the DSMC approach.