Direct-Forcing Immersed Boundary Method for Mixed Heat Transfer (Communications in Computational Physics, 2020)
A direct-forcing immersed boundary method (DFIB) with both virtual forceand heat source is developed here to solve Navier-Stokes and the associated energytransport equations to study some thermal flow problems caused by a moving rigidsolid object within. The key point of this novel numerical method is that the solid object,stationary or moving, is first treated as fluid governed by Navier-Stokes equationsfor velocity and pressure, and by energy transport equation for temperature in everytime step. An additional virtual force term is then introduced on the right hand sideof momentum equations in the solid object region to make it act exactly as if it werea solid rigid body immersed in the fluid. Likewise, an additional virtual heat sourceterm is applied to the right hand side of energy equation at the solid object regionto maintain the solid object at the prescribed temperature all the time. The currentmethod was validated by some benchmark forced and natural convection problemssuch as a uniform flow past a heated circular cylinder, and a heated circular cylinderinside a square enclosure. We further demonstrated this method by studying a mixedconvection problem involving a heated circular cylinder moving inside a square enclosure.Our current method avoids the otherwise requested dynamic grid generation intraditional method and shows great efficiency in the computation of thermal and flowfields caused by fluid-structure interaction.