Theory and simulation of micronolar fluid dynamics

This paper reviews the fundamentals of micropolar fluid dynamics (MFD), and proposes a numerical scheme integrating Chorin's projection method and time-centred split method (TCSM) for solving unsteady forms of MFD equations. It has been known that Navier-Stokes equations are incapable of explaining the phenomena at micro and nano scales. On the contrary, MFD can naturally pick up the physical phenomena at micro and nano scales owingto its additional degrees of freedom for gyration. In this study, the analytical and exact solutions of Couette and Hagen-Poiseuille flow are provided. Though this study is limited to the steady flow cases, the unsteady term in the MFD has been taken into account. This present work initiates the development of a general-purpose code of computational micropolar fluid dynamics (CMFD). The discretization scheme in space is demonstrated with nearly second-order accuracy on multiple meshes.