A hybrid Cartesian-meshless method for the simulation of thermal flows with complex immersed objects

In this study, a hybrid Cartesian-meshless method is first extended to deal with the thermal flows with complex immersed objects. The temperature and flow fields are governed by energy conservation equation and Navier-Stokes equations with Boussinesq approximation, respectively. The governing equations are solved by conventional finite difference scheme on Cartesian grid and generalized finite-difference (GFD) with singular value decomposition (SVD) approximation on meshless nodes, with second-order accuracy. The present thermal SVD-GFD method is applied to simulate the following six numerical examples over wide ranges of governing parameters, including that with high Prandtl number: (1) Forced convection around a circular cylinder; (2) Mixed convection around a stationary circular cylinder in a lid-driven cavity; (3) Mixed convection involving moving boundary in a cavity with two rotating circular cylinders; (4) Sedimentation of a cold circular particle in a long channel; (5) Freely falling of a sphere in viscous fluid with thermal buoyancy; (6) Sedimentation of a torus with thermal convection; (7) Flow over a heated circular cylinder. The excellent agreements between the published data and the present numerical results demonstrate the good capability of the thermal SVD-GFD method to simulate the thermal flows with complex immersed objects, especially those involving fluid-structure interaction and high Prandtl number.