A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media
Modeling pollutant transport in heterogeneous media is an important task of hydrology. Pollutant transport in a non-homogeneous environment typically exhibits non-local transport dynamics, whose efficient characterization requires a parsimonious model with the non-local feature. This study encapsula...
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MDPI AG
2022-08-01
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| Online Access: | https://www.mdpi.com/2073-4441/14/16/2455 |
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| author | Tianyi Li Xin Gu Qing Zhang |
| author_facet | Tianyi Li Xin Gu Qing Zhang |
| author_sort | Tianyi Li |
| collection | DOAJ |
| description | Modeling pollutant transport in heterogeneous media is an important task of hydrology. Pollutant transport in a non-homogeneous environment typically exhibits non-local transport dynamics, whose efficient characterization requires a parsimonious model with the non-local feature. This study encapsulates the non-local transport characteristic of pollutants into the peridynamic differential operator (PDDO) and develops a PDDO-based model for quantifying the observed pollutant non-local transport behavior. The simulation results show that the proposed model can describe pollutant non-local transport behavior in various heterogeneous media. The non-local nature of pollutant transport can be adjusted by pre-defined weight function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mo>(</mo><mo>|</mo><mi>ξ</mi><mo>|</mo><mo>)</mo></mrow></semantics></math></inline-formula> and horizon <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mi>x</mi></msub></semantics></math></inline-formula>. Applications show that the PDDO-based model can better capture pollutant non-local transport behavior than the classical advection–diffusion equation (ADE) model, especially for quantifying the tail of the experimental data late. Analyses further reveal that the PDDO-based model can characterize both normal (Fickian) and anomalous (Lévy) diffusion regimes. |
| first_indexed | 2024-03-09T03:41:37Z |
| format | Article |
| id | doaj.art-96beb8daa6804681950d220c885495bd |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-09T03:41:37Z |
| publishDate | 2022-08-01 |
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| spelling | doaj.art-96beb8daa6804681950d220c885495bd2023-12-03T14:40:01ZengMDPI AGWater2073-44412022-08-011416245510.3390/w14162455A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous MediaTianyi Li0Xin Gu1Qing Zhang2College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCollege of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCollege of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaModeling pollutant transport in heterogeneous media is an important task of hydrology. Pollutant transport in a non-homogeneous environment typically exhibits non-local transport dynamics, whose efficient characterization requires a parsimonious model with the non-local feature. This study encapsulates the non-local transport characteristic of pollutants into the peridynamic differential operator (PDDO) and develops a PDDO-based model for quantifying the observed pollutant non-local transport behavior. The simulation results show that the proposed model can describe pollutant non-local transport behavior in various heterogeneous media. The non-local nature of pollutant transport can be adjusted by pre-defined weight function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>w</mi><mo>(</mo><mo>|</mo><mi>ξ</mi><mo>|</mo><mo>)</mo></mrow></semantics></math></inline-formula> and horizon <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mi>x</mi></msub></semantics></math></inline-formula>. Applications show that the PDDO-based model can better capture pollutant non-local transport behavior than the classical advection–diffusion equation (ADE) model, especially for quantifying the tail of the experimental data late. Analyses further reveal that the PDDO-based model can characterize both normal (Fickian) and anomalous (Lévy) diffusion regimes.https://www.mdpi.com/2073-4441/14/16/2455pollutant transportnon-local modelheterogeneous mediaperidynamic differential operatorweight function |
| spellingShingle | Tianyi Li Xin Gu Qing Zhang A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media Water pollutant transport non-local model heterogeneous media peridynamic differential operator weight function |
| title | A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media |
| title_full | A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media |
| title_fullStr | A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media |
| title_full_unstemmed | A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media |
| title_short | A Peridynamic Differential Operator-Based Model for Quantifying Spatial Non-Local Transport Behavior of Pollutants in Heterogeneous Media |
| title_sort | peridynamic differential operator based model for quantifying spatial non local transport behavior of pollutants in heterogeneous media |
| topic | pollutant transport non-local model heterogeneous media peridynamic differential operator weight function |
| url | https://www.mdpi.com/2073-4441/14/16/2455 |
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