A non-iterative direct-forcing immersed boundary method for thermal discrete unified gas kinetic scheme with Dirichlet boundary conditions

Abstract

A non-iterative immersed boundary-thermal discrete unified gas kinetic scheme (IB-TDUGKS) is developed for the simulation of thermal flows. Two sets of distribution functions are applied for the velocity and temperature fields respectively, where the influence of the heat on the fluid is considered by the Boussinesq approximation. The immersed boundary method with the direct-forcing model is used to handle the complex solid boundary, in which it is replaced by the generator of local body force and heat source/sink. However, the explicit force and heat source/sink in the conventional IB methods usually result in the unphysical fluid and heat penetrations. The iterative forcing approach can remove such deficiency, but it increases both the complexity of solutions and the computational load. Therefore, a non-iterative IB method is presented in this study. With the introduction of an adjustment parameter, the present approach evaluates the force and heat source/sink explicitly, and at the same time enforces the boundary conditions for both the velocity and temperature at the fluid-solid interface. Furthermore, the force and heat source/sink are conveniently incorporated into the DUGKS with the Strang-splitting scheme. The accuracy and feasibility of the present IB-TDUGKS is verified in several well-established thermal flow problems. The results agree well the data available in the literature.