Choosing norms in adaptive FSI calculations

The thermal coupling of a fluid and a structure is of great significance for many industrial processes. As a model for cooling processes in heat treatment of steel we consider the coupling of the compressible Navier‐Stokes equations along a surface with the heat equation. A partitioned approach is considered, where different codes for the sub‐problems are employed. We use a finite volume method (FVM) for the fluid and a finite element method (FEM) for the heat equation. The semi‐discrete coupled system is solved using stiffly stable SDIRK methods, where on each stage an FSI problem is solved. This has a black box character, since a stage calculation corresponds to a specific Backward‐Euler integration step. For the resulting method it was shown by numerical experiments in [1] that second order convergence rate is obtained. This property is used for a simple time‐step control, which saves considerable computational time and guarantees a specified maximum error of time integration. Here, we will consider different norms for measuring the error. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)