Stability analysis of numerical interface boundary conditions for parabolic equations

Abstract

This paper analyses the numerical stability of coupling procedures in modelling the thermal diffusion in a solid and fluid with continuity of temperature and heat flux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of different explicit and implicit algorithms are considered for both the interior equations and the boundary conditions. The analysis shows that, in general, these are stable provided Dirichlet boundary conditions are imposed on the fluid and Neumann boundary conditions are imposed on the solid; in each case, the imposed values are obtained from the other domain.