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This paper presents the stability, convergence and optimization characteristics of interface treatments for steady conjugate heat transfer problems. The Dirichlet-Robin and Neumann-Robin procedures are presented in detail and compared on the basis of the Godunov-Ryabenkii normal mode analysis theory applied to a canonical aero-thermal coupling prototype. Two fundamental parameters are introduced, a "numerical" Biot number that controls the stability process and an optimal coupling coefficient that ensures unconditional stability. This coefficient is derived from a transition of the amplification factor. A comparative study of these two treatments is made in order to implement numerical schemes based on adaptive and local coupling coefficients, with no arbitrary relaxation parameters, and with no assumptions on the temporal advancement of the fluid domain. The coupled numerical test case illustrates that the optimal Dirichlet-Robin interface conditions provide effective and oscillation-free solutions for low and moderate fluidstructure interactions. Moreover, the computation time is slightly shorter than the time required for a CFD computation only. However, for higher fluid-structure interactions, a Neumann interface condition on the fluid side presents good numerical properties so that no relaxation coefficients are required.

SUMMARYThis paper outlines the development and adaptation of a coupling strategy for transient temperature analysis in a solid via a conjugate heat transfer method. This study proposes a quasi‐dynamic coupling procedure to bridge the temporal disparities between the fluid and the solid. In this approach, dynamic thermal modeling in the solid is coupled with a sequence of steady states in the fluid. This quasi‐dynamic algorithm has been applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate using the severe thermal conditions of a solid propellant rocket. Two different coupled thermal computations have been performed. In the first one—referred to as the reference computation—the coupling period is equal to the smallest solid time constant. In the second one, a very large coupling period is used. The results show that the procedure can predict accurate transient temperature fields at a reasonable computational cost. The simulation CPU time is approximately reduced by up to 90%, while maintaining a very good accuracy. All the details of the numerical test case are given in the paper. This application illustrates the capabilities and the overall efficiency of this coupled approach in a solid transient problem using long term simulations of time dependent flows. Copyright © 2013 John Wiley & Sons, Ltd.

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A B S T R A C TThe goal of this paper is to propose a single interface treatment, based on the Dirichlet-Robin interface condition to deal with all steady CHT scenarios. These scenarios depend on the so-called numerical Biot number that controls the stability process and the optimal coefficient that ensures, in theory, unconditional stability. It is shown that this coefficient is closely related to fundamental thermal quantities. For very large thermal fluid-solid interactions, the Dirichlet-Robin condition may result in profound stability issues. A thorough examination of the stability behavior has highlighted a narrow and slow-varying stable zone located around the optimal coefficient. This allows us to determine coupling coefficients valid in any case and the reasonable value of these coefficients avoids significantly impairing the accuracy of CHT solutions. A flat plate, partially protected by a thermal barrier coating, is presented as a test case. Stability analysisThe Godunov-Ryabenkii (G-R) stability analysis [27] is very similar to the standard Fourier stability method, although unlike the Fourier method, the G-R method takes into account the boundary conditions. A normal mode solution is thus applied to the case defined by the discrete model problem [17][18], and after elementary transformations, we obtain the following temporal amplification factor