Nonlinear filtering for low-velocity gaseous microflows

Gaseous flows in microfluidic devices are often characterized by relatively high Knudsen numbers. For such flows, the continuum approximation is not valid, and direct simulation Monte Carlo (DSMC) may be used to find an appropriate solution. For low-velocity flows, where the fluid velocity is much smaller than the mean molecular velocity, large statistical fluctuations in the solution mean that the features of the flow may be obscured by noise in the solution. The use of a high-order, nonlinear monotone convection algorithm, flux-corrected transport (FCT), as a filter to extract the solution from the noisy DSMC calculation is described. The diffusion, antidiffusion, and flux-limiting properties of FCT are discussed in terms of their filtering properties. The effects of filtering with FCT are demonstrated for a series of test problems, including a square wave with superimposed random noise, and low-and high-velocity and low- and high-Knudsen-number microchannel flows. It is shown that FCT filtering removes high-frequency statistical fluctuations and can extract a solution from a noisy DSMC calculation when the flow velocity is much less than the molecular thermal velocity and when the ratio of real to simulated particles is relatively high. Although the application described has been limited to microflows, this filter has significant potential for a wide variety of DSMC problems used in physical regimes where statistical noise must be eliminated. Because it is a postprocessing operation and does not affect the DSMC calculation as it is running, filtering can be applied to any DSMC solution. This includes calculations with complex geometries, the presence of many interacting species with chemical reactions, varied and complicated boundary conditions, and time-dependent solutions.