Stability analysis of partitioned methods for predicting conjugate heat transfer

摘要

The prediction of the heat transfer between a fluid and a solid object, known as conjugate heat transfer, is a very common problem in engineering sciences. This work investigates coupling methods which allow to solve such problems numerically by using separate solvers for both domains. The methods converge to the conjugate solution by exchanging boundary conditions at their interface. We review three known methods while postulating a forth novel method with improved stability properties. Even though this coupling methods use standard solvers for each domain with known stability properties, many reports in the literature are found on instabilities occurring during the coupling procedure. While it is known that the origin of this problem lies at the exchange of boundary conditions, to date no closing stability criterion could be found. The present work aims to provide a quantitative answer as to why these instabilities occur and to provide guidelines with respect to the use of the different methods. A new stability criterion is derived based on several simplifications. It shows that each method has its own stability limit and can be used within a specific range of applications, mainly dominated by the Biot number. Although the criterion is derived by making strong assumptions, it is validated through series of numerical experiments on a flat plate test case. It shows that we have correctly identified the mechanism leading to instabilities. Finally, we compare the novel coupling strategy with the established methods. Considering the stability the new approach is advantageous especially for high Biot numbers, concluding that it can improve efficiency and accuracy of conjugate heat transfer computations.