Simulation of micro flows with moving boundaries using high-order upwind FV method on unstructured grids

Abstract

Numerical methods are presented for the simulation of steady and unsteady micro gas¯ows with moving boundaries found in micro scale¯uidic devices. Both steady and unsteady¯ows are calculated by using an implicit real-time discretization and a dual-time stepping scheme implemented in a high-order upwind ®nite-volume unstructured-grid Navier±Stokes solver. For moving boundary problems, a new dynamic mesh method has been developed which is shown to be robust in handling large mesh deformation. Micro-scale¯ows studied with the methods developed include¯ow in micro channels, unsteady¯ow around a micro cylinder in oscillation and transport processes in micro pumps. The simulation is based on the continuum¯uid model (the compressible Navier±Stokes equations) with slip boundary conditions implemented in the context of unstructured grids as the micro¯ows studied are all in the slip¯ow regime. Results are presented to validate the methods and demonstrate their applications to the analysis and design of micrō uidic devices. The implicit dual-time stepping scheme is found to be robust and ef®cient in dealing with both steady and unsteady micro¯ows. The unstructured-grid solver proves to be very¯exible in dealing with complex geometries such as micro pumps. This is the ®rst known report on the use of ®nite-volume unstructured grid solver for studying micro¯ows based on the slip boundary condition with moving boundaries.

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