Experimental validation of high-order time integration for non-linear heat transfer problems

An accurate prediction of the temperature distribution in space and time plays an important role in many industrial applications, in particular when phase transformations are involved. In this article the thermo-physical properties of steel 51CrV4 (SAE 6150) are determined and used in numerical simulations. For the simulation of the temperature field a semi-discrete approach is used, consisting of a finite element approximation in space and a high order Runge– Kutta integration in time. Several adaptive high-order time integration method (stiffly accurate diagonally implicit Runge–Kutta methods) are applied and their computational efficiency is investigated. The theoretical rates of convergence are achieved for all problems, including the non-linear case. Whereas the second order accurate method of Ellsiepen with time adaptive step-size control proves to be most efficient. Further, the influence of the material model on the simulation results is studied and the numerical results are verified by experiments. The best correlation of the simulation and experimental data is achieved using temperature-dependent parameters.