Higher order time integration schemes for thermal coupling of flows and structures

The application of higher order implicit time integration schemes to conjugate heat transfer problems is analyzed with Dirichlet-Neumann as the decomposition method. In the literature, only up to second order implicit time integration schemes have been reported while there is a potential for gaining computational efficiency using higher orders. For loose coupling of the domains, the IMEX scheme consisting of the ESDIRK scheme for integrating the governing equations within the subdomains and an ERK scheme for explicit integration of the explicit coupling terms is utilized. The IMEX scheme is analyzed for two cases. In one, the material properties of the coupled domains are the same and in the other they are different. While for both cases, the IMEX scheme preserves the design order of the time integration scheme, different stability and accuracy properties are observed for the two. Finally, the computational efficiency of the higher order IMEX schemes relative to the second order scheme is demonstrated using a test case in 2-D involving coupled conduction problem of three domains