Thermal flows with moving boundaries via adaptive Cartesian grid discrete unified gas kinetic scheme

In recent years, the discrete unified gas kinetic scheme (DUGKS) has attracted considerable attention and demonstrated remarkable potential in the simulation of a wide range of challenging multi-scale flow problems. Nevertheless, the majority of existing studies remain confined to uniform rectangular grids. Although certain recent works have explored static non-uniform grid configurations, their capacity to efficiently handle unsteady problems is still limited. To overcome this limitation, the present work proposes an adaptive Cartesian grid (ACG) strategy within the DUGKS framework. A refinement criterion based on local vortex intensity is employed. The mesh is refined in regions where the local vortex indicator exceeds a prescribed upper threshold, and coarsened in regions where it falls below a prescribed lower threshold. Information transfer between the old and new grids is accomplished through second-order linear or bilinear interpolation, while conservation properties are rigorously maintained throughout the adaptation process. The proposed ACG-DUGKS method is validated through a series of benchmark simulations, including lid-driven cavity flow, natural convection in a square enclosure, mixed convection in a cavity with an eccentrically placed cylinder, non-isothermal flow past a circular cylinder, and the settling of two hot particles in an enclosure. The numerical results demonstrate that the ACG-DUGKS method achieves excellent accuracy, computational efficiency, and geometric flexibility. Furthermore, the simulation of unequal-density dual-particle settling reveals that placing a lighter particle beneath a heavier one promotes faster particle approach and earlier collision, thereby enhancing inter-particle mixing.