Unified solver for thermobuoyant flows on unstructured meshes

We propose an unified formulation for thermobuoyant flows an arbitrary mesh topologies. Unlike incompressible flow, the pressure correction equation is derived from the energy equation. The resulting Poisson’s equation reduces to continuity constraint ∇ · u = 0, only in absence of thermal gradient and compressibility effects. Investigations are carried out for flows with small and large temperature differences in a differentially heated square enclosure. Studies using Cartesian and triangular grids show that the proposed approach can successfully simulate non-Boussinesq convection with extreme density variation.