Methodology of numerical coupling for transient conjugate heat transfer

• We present a conservative method for coupling unsteady fluid and solid solvers.
• Both general constraints and application to the Finite Volume Method are addressed.
• Coupling schemes are defined to compute thermal boundary conditions at interfaces.
• A robust corrective process is designed to ensure conservativity.
• The corrective process and the proper coupling scheme notably improve accuracy.

This paper deals with the construction of a conservative method for coupling a fluid mechanics solver and a heat diffusion code. This method has been designed for unsteady applications.Fluid and solid computational domains are simultaneously integrated by dedicated solvers. A coupling procedure is periodically called to compute and update the boundary conditions at the solid/fluid interface. First, the issue of general constraints for coupling methods is addressed. The concept of interpolation scheme is introduced to define the way to compute the interface conditions. Then, the case of the Finite Volume Method is thoroughly studied. The properties of stability and accuracy have been optimized to define the best coupling boundary conditions: the most robust method consists in assigning a Dirichlet condition on the fluid side of the interface and a Robin condition on the solid side. The accuracy is very dependent on the interpolation scheme. Moreover, conservativity has been specifically addressed in our methodology. This numerical property is made possible by the use of both the Finite Volume Method and the corrective method proposed in the current paper. The corrective method allows the cancellation of the possible difference between heat fluxes on the two sides of the interface.This method significantly improves accuracy in transient phases. The corrective process has also been designed to be as robust as possible. The verification of our coupling method is extensively discussed in this article: the numerical results are compared with the analytical solution of an infinite thick plate in a suddenly accelerated flow (and with the results of other coupling approaches).