Simple finite volumes and finite elements procedures for food quality and safety simulations

Modelagem e simulação da desidratação osmótica em pedaços de abacaxi utilizando o método de elementos finitos

“…14 O método de elementos finitos (MEF) é capaz de simular fenô-menos, como a transferência de calor e/ou de massa, dinâmica de fluidos, elasticidade, assim como processos químicos e biológicos responsáveis pela perda de qualidade dos alimentos. 15 De acordo com Puri e Anantheswaran, 16 as principais vantagens do MEF são: a variação espacial das propriedades materiais pode ser tratada com relativa facilidade; regiões irregulares podem ser modeladas com grande precisão; o método é o mais indicado para problemas não lineares; as dimensões dos elementos podem ser facilmente alteradas; a interpolação espacial é muito realista e, os problemas com as mais diversas condições de contorno podem ser facilmente trabalhados.…”

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

“…Several authors have studied diffusion in food using the Fick's laws for binary and ternary systems, including diffusion during the salting of Prato cheese (BONA et al, 2007) and Pategras cheese (GERLA; RUBIOLO, 2003); salting (ZORRILLA; RUBIOLO, 1994a) The Finite Element Method (FEM) is a set of powerful numerical techniques for solving differential equations frequently used in food science, which allows the simulation of systems under realistic conditions (WANG; SUN, 2003). The FEM can provide solutions for differential equations that simulate phenomena such as heat and/or mass transfer, radiation, fluid dynamics, and elasticity, as well as chemical and biological processes responsible for the loss of food quality (MARTINS, 2006). According to Puri and Anantheswaran (1993), the primary advantages of FEM include: (i) easier handling of spatial variation of material properties, (ii) more accurate modeling of irregular regions, (iii) ready indication for non-linear problems, (iv) easy variation of element size, (v) more meaningful spatial interpolation, and (vi) easier handling of mixed-boundary-value problems.…”

Computational Shelf-Life Dating: Complex Systems Approaches to Food Quality and Safety

“…FE methods discretize physical, chemical, biochemical, and PM differential equations, which can be used to simulate most of the phenomenon that occur during food production, storage, and distribution. Fundamental levels can also use the fusion of FEs method discretizations with cellular automata (CA) (Martins 2006) and individual-based modeling for describing noncontinuous phenomena in the FE space (Martins and Lopes 2007). FE can hold many object-oriented paradigms and, by making the FE discretization independent of the PDE to be descretized on it, gives the necessary flexibility to describe physical, biochemical, and microbiological phenomena inside the elementary space.…”

“…Each increase in temperature accelerates the degradation process, which is calculated by an ordinary differential equation discretization of chemical reactions inside the FE space (Martins 2006). Furthermore, kinetics are highly influenced by biological variability, which can be implemented by using the stochastic FE methodologies, being possible to propagate uncertainties on physical and chemical laws across the physical domain to obtain a statistically representative solution (Martins 2006).…”