An immersed boundary method for restricted diffusion with permeable interfaces

In this note we present an immersed boundary (IB) method for restricted diffusion with permeable interfaces. These problems arise under a variety of circumstances, e.g., in thermal contact problems [7]. Diffusion in a medium consisting of two regimes separated by permeable boundaries is another example. It is well-known that cell boundaries in a living tissue are permeable to oxygen and water molecules [3]. In this case, the cell boundaries can be treated as interfaces permeable to diffusive fluxes. Typically, the conduction of heat and diffusive motion of molecules can be described by the diffusion equation in the bulk ct = ∇ · (D∇c), (1)