An immersed boundary-discrete unified gas kinetic scheme for simulating natural convection involving curved surfaces

In this work, an immersed boundary-discrete unified gas kinetic scheme (IB-DUGKS) is proposed and presented for the simulation of natural convection with a curved body surface. In this method, two distribution functions are employed for velocity and temperature field, respectively, and they are coupled under the Boussinesq approximation. The IB-DUGKS provides an effective way for the DUGKS to treat a curved boundary. The Strang-splitting method is used to handle the IB force, and its accuracy is first validated by comparing with another implementation method for the base case of natural convection in a square cavity. The widely used direct-forcing immersed boundary method is adopted due to its simplicity, with an iteration procedure to ensure the accuracy of no-slip condition on the immersed boundary. Natural convection between an outer square and an inner circular cylinder is then simulated under different geometric configurations, including different aspect ratios and locations of the cylinder relative to the cavity. The numerical results are in excellent agreement with the results from the literature, confirming the accuracy and robustness of the proposed method.