Numerical study of two optimized coupling interface treatments for steady conjugate heat transfer problems

Abstract

This paper presents two transmission interface treatments, Dirichlet-Robin and Neumann-Robin procedures, that may be employed for conjugate heat transfer problems. These conditions are analyzed on the basis of a 1D simplified model problem. In the first part of the paper, the Dirichlet-Robin procedure is presented. This interface treatment is the most widely employed in the literature. The same analysis is then performed with a Neumann-Robin procedure. On the basis of the model problem, the general expression of the amplification factor, the stability bounds and the optimal coefficients are provided. It is shown that the two interface treatments are opposite and complementary. Moreover, the so-called optimal coefficient provides the best results in terms of stability and convergence in the Dirichlet-Robin procedure. A criterion is expressed to choose the most appropriate transmission procedure and its importance is underlined by a test case.