A novel immersed boundary/Fourier pseudospectral method for flows with thermal effects

ABSTRACTA 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.