Acceleration Schemes of the Discrete Velocity Method: Gaseous Flows in Rectangular Microchannels

The convergence rate of the discrete velocity method (DVM), which has been applied extensively in the area of rarefied gas dynamics, is studied via a Fourier stability analysis. The spectral radius of the continuum form of the iteration map is found to be equal to one, which justifies the slow convergence rate of the method. Next the efficiency of the DVM is improved by introducing various acceleration schemes. The new synthetic-type schemes speed up significantly the iterative convergence rate. The spectral radius of the acceleration schemes is also studied and the so-called H1 acceleration method is found to be the optimum one. Finally, the two-dimensional flow problem of a gas through a rectangular microchannel is solved using the new fast iterative DVM. The number of required iterations and the overall computational time are significantly reduced, providing experimental evidence of the analytic formulation. The whole approach is demonstrated using the BGK and S kinetic models.