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 flows with moving boundaries found in micro scale fluidic devices. Both steady and unsteady flows are calculated by using an implicit real-time discretization and a dual-time stepping scheme implemented in a high-order upwind finite-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 flows studied with the methods developed include flow in micro channels, unsteady flow around a micro cylinder in oscillation and transport processes in micro pumps. The simulation is based on the continuum fluid model (the compressible Navier–Stokes equations) with slip boundary conditions implemented in the context of unstructured grids as the micro flows studied are all in the slip flow regime. Results are presented to validate the methods and demonstrate their applications to the analysis and design of micro fluidic devices. The implicit dual-time stepping scheme is found to be robust and efficient in dealing with both steady and unsteady micro flows. The unstructured-grid solver proves to be very flexible in dealing with complex geometries such as micro pumps. This is the first known report on the use of finite-volume unstructured grid solver for studying micro flows based on the slip boundary condition with moving boundaries.