Cargando…
Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos
Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properti...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7435789/ https://www.ncbi.nlm.nih.gov/pubmed/32722278 http://dx.doi.org/10.3390/molecules25153370 |
_version_ | 1783572404094631936 |
---|---|
author | AbdelFattah, Hesham Al-Johani, Amnah El-Beltagy, Mohamed |
author_facet | AbdelFattah, Hesham Al-Johani, Amnah El-Beltagy, Mohamed |
author_sort | AbdelFattah, Hesham |
collection | PubMed |
description | Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem. |
format | Online Article Text |
id | pubmed-7435789 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-74357892020-08-25 Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos AbdelFattah, Hesham Al-Johani, Amnah El-Beltagy, Mohamed Molecules Article Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem. MDPI 2020-07-24 /pmc/articles/PMC7435789/ /pubmed/32722278 http://dx.doi.org/10.3390/molecules25153370 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article AbdelFattah, Hesham Al-Johani, Amnah El-Beltagy, Mohamed Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title | Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title_full | Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title_fullStr | Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title_full_unstemmed | Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title_short | Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos |
title_sort | analysis of the stochastic quarter-five spot problem using polynomial chaos |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7435789/ https://www.ncbi.nlm.nih.gov/pubmed/32722278 http://dx.doi.org/10.3390/molecules25153370 |
work_keys_str_mv | AT abdelfattahhesham analysisofthestochasticquarterfivespotproblemusingpolynomialchaos AT aljohaniamnah analysisofthestochasticquarterfivespotproblemusingpolynomialchaos AT elbeltagymohamed analysisofthestochasticquarterfivespotproblemusingpolynomialchaos |