Numerical Solution for the Nonlinear Diffusion Equation Describing the Transport of Volatile Fission Products in Nuclear Fuels

Abstract

To describe the transport of volatile fission products along grain boundaries in nuclear fuels, a nonlinear diffusion equation must be used. Analytic solutions exist for the steady-state case, but the equation seems to be intractable when time dependence is included. A simple implicit numerical method has been developed that can guarantee a convergent stable solution when there is a central void. If there is no void, the method always yields a solution. There is perfect agreement between the analytic and numerical solutions for the steady state, and the method developed here offers significant advantages over other methods of solution. This basic model can be used in nuclear fuel performance studies.