A Semi-Implicit Fractional Step Method Immersed Boundary Method for the Numerical Simulation of Natural Convection Non-Boussinesq Flows

The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection flows.The formulation incorporated into the pressure-based fractional step approach facilitates simulation of the flows in the presence of an immersed body characterized by a complex geometry.Here,we first present extensive grid independence and verification studies addressing incompressible pressure-driven flow in an extended channel and non-Boussinesq natural convection flow in a differentially heated cavity.Next,the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold square cavity is thoroughly investigated.The obtained results are presented and analyzed in terms of the spatial distribution of path lines and temperature fields and of heat flux values typical of the hot cylinder and the cold cavity surfaces.Flow characteristics of multiple steady-state solutions discovered for several configurations are presented and discussed in detail.

The Immersed Boundary Method: Application to Two-Phase Immiscible Flows

In this paper we present an extended formulation of the immersed boundary(IB)method that facilitates simulation of incompressible immiscible two-phase flows.In the developed formulation the pressure field and the surface tension forces associated with interface curvature are implicitly introduced in the form of distributed Lagrange multipliers.The approach provides for impermeability between both phases and exhibits accurate mass conservation without the need for additional correction procedures.Further,we present a grid independence study and extensive verification of the developed method for representative 2D two-phase flows dominated by buoyancy,shear stress,and surface tension forces.