Modeling of diffusion processes: Numerical solutions to the diffusion equation
A. D. Romig, N.Y. Pehlivanturk, Osman Tugay Inal · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1988
Many phenomena in materials science are controlled by volume diffusion. To model these phenomena it is often necessary to solve the diffusion equation under initial and boundary conditions for which analytical solutions do not exist. Specific examples requiring numerical solutions include cases where the initial composition profile is neither constant nor a simple error function, where the boundary compositions are constant nor a simple error function, where the boundary compositions are not fixed and vary as impingement occurs, and where diffusion occurs under non-iosthermal conditions. Several numerical algorithms have been used to solve these problems including explicit finite differences, implicit finite differences (Crank-Nicholson), method of lines, and finite elements. The advantages and disadvantages of each technique will be described. In a tutorial fashion, a simple fixed boundary diffusion problem and a two-phase moving boundary problem will be solved analytically and numerically and the results compared. A more complex example of a diffusion problem requiring a numerical solution will also be given. 34 refs., 11 figs., 1 tab.