Optimal solutions of numerical interface conditions in fluid–structure thermal analysis

This paper presents major and new results in the numerical treatment of conjugate heat transfer problems.The stability analysis of a 1D implicit model problem for heat transfer between a fluid and a solid is performed in the traditional finite-volume (fluid)/finite-element (solid) configuration. The interface stability study is carried out according to the Godunov–Ryabenkii theory normal-mode analysis. Two interface boundary conditions are studied.First, the commonly used Dirichlet–Robin algorithm is described in detail and, to the best of our knowledge, the exact expression of an optimal coupling coefficient is formulated for the first time. It is shown that this optimal coefficient is the best choice in terms of stability and convergence rate. The effect and impact on stability of various solid data are also discussed.In the last section of this paper the same stability analysis is carried out for a general Robin–Robin interface condition and an optimal relationship between the two coupling parameters is also provided. No stability restrictions are introduced by these optimal interface treatments and some noteworthy expressions are provided.