On efficient approaches for solving a cake filtration model under parameter variation

In this work, we are considering a mathematical model for an industrial cake filtration process. The model is of moving boundary type and involves a set of parameters, which vary in a given range. We are interested in the case when the model has to be solved for thousands of different parameter values, and therefore model order reduction (MOR) is desirable, so that from full order solutions with one or several sets of parameters we derive a reduced model, which is used further to perform the simulations with new parameters. We study and compare the performance of several MOR techniques known from the literature. We start with standard MOR based on proper orthogonal decomposition (POD) and consider also several more advanced techniques based on combination of MOR and reduced basis techniques, including approaches relying on computation of sensitivities. The transformation from a moving to a fixed domain introduces time varying coefficients into the equations, which makes it reasonable to use an offline/online decomposition. Several test cases involving different simulation time horizons and short time training are considered. Numerical tests show that the discussed methods can approximate the full model solution accurately and work efficiently for new parameters belonging to a given parameter range.