High-order multistep coupling: convergence, stability and PDE application
Résumé
Designing coupling schemes for specialized advanced mono-physics solvers in order to conduct accurate and efficient multiphysics simulations is a key issue that has recently received a lot of attention. A novel high-order adaptive multistep coupling strategy has shown potential to improve the efficiency and accuracy of such simulations, but requires further analysis. The purpose of the present contribution is to conduct the numerical analysis of convergence of the explicit and implicit variants of the method and to provide a first analysis of its absolute stability. A simplified coupled problem is constructed to assess the stability of the method along the lines of the Dahlquist’s test equation for ODEs. We propose a connection with the stability analysis of other methods such as splitting and ImEx schemes. A stability analysis on a representative conjugate heat transfer case is also presented. This work constitutes a first building block to an a priori analysis of the stability of coupled PDEs.