Simulations of natural and forced convection flows with moving embedded object using immersed boundary method

In the present study, an immersed-boundary method is adopted to simulate natural and forced convection within a domain with complex geometry at low Reynolds numbers. The method is based on the direct momentum and energy forcing on a Cartesian grid, and issues involving the influence of the solid-body-forcing and the implementation of the isothermal and isoflux boundary conditions are addressed. It was shown that the second-order accuracy of global error norms of the method was ascertained only when the solid-body-forcing in velocity is implemented. On the other hand, the solid-body-forcing of the thermal field is not essential. Also, the solid-body-forcing in velocity has negligible influence on the thermal and dynamic field with stationary embedded object. Further test problems are simulated to examine the validity of the present technique: 2-D flows induced by natural convection in the annulus between two horizontal concentric cylinders, moving heated cylinder within a stationary fluid, transversely oscillating cylinder with different excitation frequencies, and 3-D simulation of a heated sphere settling under gravity in a static fluid. All computed results are in general good agreement with previous experimental measurements and numerical simulations.