Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Estimation of the Redistribution Behavior in the Biflux Anomalous Diffusion Problem
Submission Author:
Douglas Corrêa , RJ
Co-Authors:
Douglas Corrêa, Jefferson Gomes, David Pelta, Claudio Toledo, Antônio Silva Neto
Presenter: Douglas Corrêa
doi://10.26678/ABCM.COBEM2023.COB2023-1099
Abstract
The phenomenon of diffusion, which refers to the scattering of particles in a medium, is widely observed in nature and everyday life. It is utilized to model various phenomena such as disease transmission, population dynamics, fluid and particle transport, heat transfer, financial markets, and others. Recently, a fourth-order partial differential equation was proposed to model more complex anomalous diffusion processes that involve temporary retention, allowing a more complex class of phenomena to be analyzed. In a particle spreading process with retention, a portion (α) of the particles is retained and the non-retained portion (β) is redistributed into neighboring cells. This implies that in order to predict the spreading process we must have knowledge about the redistribution behavior, i.e, β. In real-case scenarios it is possible that no knowledge about β is available. To overcome this problem we estimate β by using an inverse problem approach, given the registered particle spreading pattern at an arbitrary time t, i.e, the collected experimental data, here syntethic experimental data. We begin with the assumption that β is a a polynomial of degree N and our objective is to estimate both N and its coefficients that best generates the behavior of the spreading process according to the experimental data following the biflux anomalous diffusion equation. Finally, the polynomial degree and its coefficients are searched with the help of Metaheuristics, since more than one polynomial can accurately approximate the same function in a limited given interval. Our approach of an inverse problem of the redistribution estimation with the aid Metaheuristics has proved itself worthy of effort as the final result was a really close prediction with error of magnitude of order 10^(-2) with respect to that predicted by the model with the exact parameters which indicates that this approach can be a solution for those who wants to try out the biflux anomalous diffusion model but has no available priori knowledge about β.
Keywords
Biflux Diffusion Equation, Fourth Order Diffusion, Optimization metaheuristics, Inverse problem
