Comprehensive Mathematical Modeling and Dynamic Simulation of Fixed Bed Reactor with Finite Element Method

2011 ◽  
Author(s):  
Davood Dehestani ◽  
Hung Nguyen ◽  
Fahimeh Eftekhari ◽  
Jafar Madadnia ◽  
Steven Su ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Simulation ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Element Method

scholarly journals Algorithms for Numerical Solution to the Problem of Diffusion in Nanoporous Media

2020 ◽  
pp. 44-52
Author(s):  
N.A. Vareniuk ◽  
N.I. Tukalevska
Keyword(s):  
Mathematical Modeling ◽  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Solution ◽  
Heterogeneous Media ◽  
Mutual Influence ◽  
Single Substance ◽  
Nonstationary Diffusion ◽  
Element Method

Introduction. Mathematical modeling of mass transfer in heterogeneous media of microporous structure and construction of solutions to the corresponding problems of mass transfer was considered by many authors [1–9, etc.]. In [6, 7] authors proposed a methodology for modeling mass transfer systems and parameter identification in nanoporous particle media (diffusion, adsorption, competitive diffusion of gases, filtration consolidation), which are described by non-classical boundary and initial-boundary value problems taking into account the mutual influence of micro- and macro-transfer flows, heteroporosity, the structure of microporous particles, multicomponent and other factors. In [8, 9] for a mathematical model of nonstationary diffusion of a single substance in a nanoporous medium described in [2] in the form of a multi-scale differential mathematical problem, the classical problems in the weak formulation were obtained. In this paper, algorithms for solving the above mathematical problems are constructed by using the finite element method. The results of the numerical solution of the test problem are presented. The results confirm the efficiency of the developed algorithms. The purpose is to solve a problem of nonstationary diffusion of single substance in nanoporous medium by constructing discretization algorithms using FEM quadratic basis functions. Results. Algorithms for the numerical solution of the problem of nonstationary diffusion of single substance in a nanoporous medium are proposed. Peculiarities of discretization of the region and construction of the matrix of masses, stiffness, and vector of right-hand sides when solving the problem by using FEM are described. The efficiency of the developed algorithms is confirmed by the results of solving a model example. Keywords: mathematical modeling, numerical methods, nonstationary diffusion, nanoporous medium, finite element method.

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