Numerical simulation for unsteady compressible Micropolar fluid flow

This paper reports the advancement of computational Micropolar fluid dynamics (CMFD) using the spectral difference (SD) method. The fundamentals, linear constitutive equations and generalized Stokes' hypothesis for Micropolar fluid dynamics are briefly introduced. The additional degrees of freedom in MFD, gyration, can help to understand the coherent structures of vortices from the two-level energy transfer in the balance law of energy. The spectral difference (SD) method is proposed for solving unsteady compressible viscous Micropolar flow problems. The analytical and exact solution of compressible Micropolar Couette flow is solved and used to demonstrate the order of numerical accuracy of the SD method. As a numerical example, a 2D spectral difference solver is developed to simulate flow past a cylinder. The instantaneous gyration contours are plotted for the observation of vortex shedding behind the cylinder. A new physical phenomenon, the coupling effect, is discussed.