Finite element analysis of diffusion problem during cheese salting: combined influence of space and time discretization

Abstract

Numerical simulation of solute (sodium chloride) transfer process during salting through a three-dimensional matrix (cheese) was studied applying the finite element method. It was verified that both mesh refinement level and time step length were relevant to control oscillatory behaviors even when unconditional stability schemes as Crank-Nicolson and modified Euler were used. A discussion of the combined influence of time and space adaptation in the context of diffusion problem is also presented, taking in consideration a lumped capacity matrix to overcome the difficulties and determine the minimum length of the time step. Differential mathematical modeling had as theoretical basis the Fick’s second law. The proposed model brought good estimation of salt gain in the soft cheese studied. Choosing the appropriate mesh and a convenient time step length we suggest Crank-Nicolson scheme for the simulation of diffusion during cheese brining.