On adaptive time stepping for large-scale parabolic problems: Computer simulation of heat and mass transfer in vacuum freeze-drying

The work is motivated by the problem of freeze-drying, which is a process of dehydrating frozen materials by sublimation under high vacuum. In particular, it concerns the mathematical modelling and computer simulation of the heat and mass transfer with the core in solving the time-dependent nonlinear partial differential equation of parabolic type.Instead of a uniform discretization of the considered time interval, an adaptive time-stepping procedure is applied in an effort to optimize the whole simulation. The procedure is based on the local comparison of the Crank–Nicolson and backward Euler approximations. The results of numerical experiments performed on a selected real-life problem are included.