In the present study, both dynamic and thermal field with moving rigid boundary are investigated. An immersed boundary method is first applied to simulate two- and three-dimensional viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining ``solid-body forcing'' at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L^1 norm in time and the L^2 norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, simulation of dragonfly flight dynamics, and 3-D simulation of a sphere settling under gravity in a static fluid.

On the other hand, the immersed-boundary method is also adopted to simulate natural and forced convection within a domain with complex geometry. The method is based on the direct momentum and energy forcing on a Cartesian grid, and issues involving the correlation between the internal treatment in solid nodes and external thermal flow are addressed. The accuracy of the method on heat transfer problems was validated by computing flow induced by an heated oscillating cylinder in a stationary square domain. The influence of the solid-body-forcing within the solid nodes is further studied for flow over an isothermal/isoflux circular cylinder with heat convection for two reference frames, where significantly good agreement in the computed Nusselt number distributions are obtained compared with those without a solid-body-forcing strategy when the immersed object moves through a fixed grid. The applicability of the present method for different Prandtl numbers was also considered. Further test problems with heat transfer 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, transversely oscillating cylinder with different excitation frequencies, and 3-D simulation of a heated sphere settling under gravity in a static fluid.

Finally, applications of the method are carried out for natural and forced convection within domains with stationary and rotating complex geometry. The method was first validated with flows induced by natural convection in the annulus between concentric circular and square cylinders, and the grid-function convergence tests were also examined. Natural convection induced by isothermally elliptic cylinder is further investigated for different Rayleigh numbers within the range of 10^{4}-10^{6} and the influence of the outer enclosure was considered as well. The parameters investigated in the study include Rayleigh number, axis ratio and inclined angle of the elliptic cross-section. Local and average heat transfer characteristics are fully studied around the surfaces of both inner cylinder and outer enclosure. Besides, mixed convection in a square enclosure with an active rotating elliptic cylinder is also considered and the heat transfer quantities of the system are obtained for different rotating speeds.

All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.

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