A time-adaptive fluid-structure interaction method for thermal coupling

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 surface coupling of the compressible Navier-Stokes equations bordering at one part of the surface with the heat equation in a solid region. The semi-discrete coupled system is solved using stiffly stable SDIRK methods of higher order, where on each stage a fluid-structure-coupling problem is solved. For the resulting method it is shown by numerical experiments that a second order convergence rate is obtained. This property is further used to implement a simple time-step control, which saves considerable computational time and, at the same time, guarantees a specified maximum error of time integration.