We describe the implementation of a general interpolation technique which allows the accurate imposition of the Dirichlet, Neumann and mixed boundary conditions on complex geometries when using the immersed boundary technique on Cartesian grids. The scheme is general in that it does not involve any special treatment to handle either one of the three types of boundary conditions. The accuracy of the interpolation algorithm on the boundary is assessed using three heat transfer problems: (1) forced convection over a cylinder placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, and (3) heat diffusion inside an annulus. The results show that the accuracy of the scheme is second order and are in agreement with analytical and/or numerical data.
Volume Subject Area:
Heat Transfer
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