Comparative study of coupling coefficients in Dirichlet–Robin procedure for fluid–structure aerothermal simulations

This paper tests the performance of coupling coefficients of a Dirichlet–Robin transmission procedure in the context of steady conjugate heat transfer (CHT). Particular emphasis is put on the optimal coefficients highlighted recently in a theoretical study based on a normal mode stability analysis. This work can be seen as the logical continuation of that study in order to assess the relevance of the coefficients provided by the model problem in a realistic aerothermal computation. First, the numerical and physical CHT modeling methodologies are presented. Then, the optimal procedure applied to a Dirichlet–Robin algorithm (one-coefficient method) is briefly described. In order to gauge the ability of this model to predict the stability and convergence properties of a realistic case, it is compared on a heated cylinder in a flowfield test case. A series of five coupling coefficients and three Fourier numbers are considered. These parameters are introduced into the model problem as data to compute the amplification factor and the stability limits. The stability and convergence properties predicted by the model problem are then compared to those obtained in the CHT computation. This comparison shows an excellent overall agreement. Moreover, for all the Fourier numbers considered, the numerical solution is stable and oscillation-free when the optimal coefficient of the model problem is used. This would suggest that the one-dimensional normal mode analysis can provide relevant coefficients directly applicable to real CHT problems.