Advection-diffusion-reaction equations are widely used in applied science, since they are able to describe real-life phenomena in which transport phenomena and chemical reactions take place. Here, they are used to predict the amount of extracted substances during the percolation of espresso coffee. The corresponding initial-boundary value problem is solved by the Crank-Nicolson scheme and a nested fixed-point iteration. The reliability of the model and the solving strategy is assessed experimentally, by comparing the amount of chemical substances in real and simulated extractions performed under different extractive conditions.
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