A specific reduction method for the branch modal formulation: Application to a highly non-linear configuration

In the domain of the linear thermal problem reduction, this paper develops a reduction method specific to the modal formulation using branch modes. This method is applied to a solidification problem in which all the physical parameters (thermal capacity and conductivity, boundary conditions) are highly non-linear. 2D and 3D configurations are studied. Comparison with other reduction methods enables to show the interest of these methods. The reduced model leads to a CPU time which is from 10 to 40 times smaller than the complete model, for an acceptable precision in the whole simulated domain.