A General Scheme for the Boundary Conditions in Convective and Diffusive Heat Transfer With Immersed Boundary Methods

Abstract

We describe the implementation of an interpolation technique, which allows the accurate imposition of the Dirichlet, Neumann, and mixed (Robin) boundary conditions on complex geometries using the immersed-boundary technique on Cartesian grids, where the interface effects are transmitted through forcing functions. 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 several two- and three-dimensional heat transfer problems: (1) forced convection over cylinders placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, (3) heat diffusion inside an annulus, and (4) forced convection around a stationary sphere. The results show that the scheme preserves the second-order accuracy of the equations solver and are in agreement with analytical and/or numerical data.