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

Abstract

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 equations and Navier–Stokes equations with the Boussinesq approximation, respectively. The governing equations are solved by a conventional finite difference scheme on a 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 seven numerical examples over a wide range of governing parameters, including that with the 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 a 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; and (7) flow over a heated circular cylinder. The excellent agreement 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 the high Prandtl number.