Fourier pseudospectral method for nonperiodical problems: A general immersed boundary method for three types of thermal boundary conditions

ABSTRACT

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.

Acknowledgments

The authors would like to thank PETROBRAS, CAPES/PROEX, CNPq, FAPEMIG, UFU, UFG for financial and structural support necessary for the development of the present work.