A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples
Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds als...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/3/396 |
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| author | Roman Cherniha Joanna Stachowska-Pietka Jacek Waniewski |
| author_facet | Roman Cherniha Joanna Stachowska-Pietka Jacek Waniewski |
| author_sort | Roman Cherniha |
| collection | DOAJ |
| description | Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail. |
| first_indexed | 2024-04-12T19:41:46Z |
| format | Article |
| id | doaj.art-21af6b0f74b54d9a921026b5e707ada2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:41:46Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-21af6b0f74b54d9a921026b5e707ada22022-12-22T03:19:03ZengMDPI AGSymmetry2073-89942020-03-0112339610.3390/sym12030396sym12030396A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and ExamplesRoman Cherniha0Joanna Stachowska-Pietka1Jacek Waniewski2Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs’ka Street, 01004 Kyiv, UkraineInstitute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 796 Warsaw, PolandInstitute of Biocybernetics and Biomedical Engineering, PAS, Ks. Trojdena 4, 02 796 Warsaw, PolandFluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail.https://www.mdpi.com/2073-8994/12/3/396poroelastic materialcontinuity equationsnonlinear pdelie symmetryexact solutionsteady-state solution |
| spellingShingle | Roman Cherniha Joanna Stachowska-Pietka Jacek Waniewski A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples Symmetry poroelastic material continuity equations nonlinear pde lie symmetry exact solution steady-state solution |
| title | A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples |
| title_full | A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples |
| title_fullStr | A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples |
| title_full_unstemmed | A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples |
| title_short | A Mathematical Model for Transport in Poroelastic Materials with Variable Volume:Derivation, Lie Symmetry Analysis, and Examples |
| title_sort | mathematical model for transport in poroelastic materials with variable volume derivation lie symmetry analysis and examples |
| topic | poroelastic material continuity equations nonlinear pde lie symmetry exact solution steady-state solution |
| url | https://www.mdpi.com/2073-8994/12/3/396 |
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