Domain-free discretization method for doubly connected domain and its application to simulate natural convection in eccentric annuli Original Research Article

In this paper, an efficient numerical approach, the domain-free discretization (DFD) method, was presented to solve partial differential equations (PDEs) on a doubly connected domain. For any doubly connected domain, the numerical discretization is always based on the cylindrical coordinate system. No coordinate transformation is involved in the present approach. The mesh points are only distributed along the radial line. So, overall, there is no structure for the mesh point distribution. The proposed method was applied to simulate the natural convection in eccentric annuli. The vorticity-stream function formulation in the cylindrical coordinate system is taken as the governing equation, and the pressure single-value condition is used to update the stream function value on the inner cylinder wall. It was found that the numerical results obtained by the DFD method agree well with available data in the literature.