Stability Analysis of Numerical Interface Boundary Conditions for Parabolic Equations

This paper analyses the numerical stability of coupling procedures in modelling the thermal diiusion in a solid and uid with continuity of temperature and heat ux at the interface. A simple one-dimensional model is employed with uniform material properties and grid density in each domain. A number of diierent 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 uid and Neumann boundary conditions are imposed on the solid; in each case, the imposed values are obtained from the other domain.