A Semi-Implicit Fractional Step Method Immersed Boundary Method for the Numerical Simulation of Natural Convection Non-Boussinesq Flows (Communications in Computational Physics, 2022)
The paper presents a novel pressure-corrected formulation of the immersedboundary 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 immersedbody characterized by a complex geometry. Here, we first present extensive grid independence and verification studies addressing incompressible pressure-driven flowin an extended channel and non-Boussinesq natural convection flow in a differentiallyheated cavity. Next, the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold squarecavity is thoroughly investigated. The obtained results are presented and analyzed interms of the spatial distribution of path lines and temperature fields and of heat fluxvalues typical of the hot cylinder and the cold cavity surfaces. Flow characteristicsof multiple steady-state solutions discovered for several configurations are presentedand discussed in detail.
Keywords: Natural convection non-Boussinesq flows; pressure-corrected immersed boundary method; multiple steady state solutions.