An immersed boundary-discrete unified gas-kinetic scheme for non-Oberbeck–Boussinesq thermal convection with curved surfaces

In this paper, an immersed boundary-discrete unified gas-kinetic scheme (IB-DUGKS) is developed for non-Oberbeck–Boussinesq (NOB) natural convection with curved surfaces. A double distribution function model with the Bhatnagar–Gross–Krook (BGK) collision model is employed with the first distribution function representing the density and velocity fields, and the second distribution function determining the total energy. To incorporate the IB force and the heat source/sink, the external forcing term and an extra source term are introduced to the kinetic model. The IB forcing term only contributes to the leading order of the momentum and energy equation. By proper design, the source term plays a dual role, it includes the IB source/sink in the energy equation, and it allows an arbitrary Prandtl number by adjusting the heat flux term, demonstrating a great flexibility of mesoscopic methods particularly in treating thermal coupling. This IB-DUGKS enables the simulation of NOB natural convection flows, governed by the fully compressible Navier–Stokes–Fourier system. Simulations of natural convection between the outer square cavity and inner hot cylinders are performed to investigate the NOB effect. Both OB and NOB flows can be considered with the current scheme by selecting different relative temperature differences. The numerical results are in excellent agreement with the literature results, indicating that the current IB-DUGKS is accurate and robust for NOB thermal flow simulations. Finally, the NOB effects are demonstrated using the temperature field, velocity field, and overall heat transfer by contrasting the NOB solutions with the corresponding OB solutions.