Denise Kinoshita

In the present paper a general scheme for the three types of thermal boundary conditions is proposed and applied to natural convection and diffusion problems. The numerical algorithm, denominated thermal IMERSPEC, consists of the application of the Fourier pseudospectral method, where Dirichlet, Neumann, or Robin boundary conditions are modeled through immersed boundary method (IBM). The methodology is to impose the boundary conditions on the interface and transmit through distribution functions. Source terms are added to the two-dimensional Navier-Stokes and energy equations on the Cartesian mesh. Manufactured solutions are used for the numerical verification of Dirichlet, Neumann, and Robin boundary conditions, imposed through IBM. The proposed method is applied for solving problems involving thermal energy transfer for natural convection in an annulus between horizontal concentric cylinders. Results for these applications using the thermal IMERSPEC and the traditional finite volume method are compared and a good agreement is obtained for both methodologies.

A novel immersed boundary method (IBM) for flows with thermal effects is proposed, combining high accuracy and low computational cost, provided by the Fourier pseudospectral method (FPSM), for the possibility of handling complex and nonperiodical geometries using the IBM. With focus on incompressible flow problems modeled by Navier-Stokes, mass, and energy equations, the method of manufactured solutions is used for the numerical verification of Dirichlet boundary conditions imposed via the IBM. Then, the proposed method is applied on two different 2-D cases: (1) energy transfer due to natural convection in a square cavity, and (2) an annulus between horizontal concentric cylinders nonuniformly heated. Good agreement with available data in the literature has been achieved.