Uncoupling Techniques for Multispecies Diffusion–Reaction Model
We consider the multispecies model described by a coupled system of diffusion–reaction equations, where the coupling and nonlinearity are given in the reaction part. We construct a semi-discrete form using a finite volume approximation by space. The fully implicit scheme is used for approximation by...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/8/153 |
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| author | Maria Vasilyeva Sergei Stepanov Alexey Sadovski Stephen Henry |
| author_facet | Maria Vasilyeva Sergei Stepanov Alexey Sadovski Stephen Henry |
| author_sort | Maria Vasilyeva |
| collection | DOAJ |
| description | We consider the multispecies model described by a coupled system of diffusion–reaction equations, where the coupling and nonlinearity are given in the reaction part. We construct a semi-discrete form using a finite volume approximation by space. The fully implicit scheme is used for approximation by time, which leads to solving the coupled nonlinear system of equations at each time step. This paper presents two uncoupling techniques based on the explicit–implicit scheme and the operator-splitting method. In the explicit–implicit scheme, we take the concentration of one species in coupling term from the previous time layer to obtain a linear uncoupled system of equations. The second approach is based on the operator-splitting technique, where we first solve uncoupled equations with the diffusion operator and then solve the equations with the local reaction operator. The stability estimates are derived for both proposed uncoupling schemes. We present a numerical investigation for the uncoupling techniques with varying time step sizes and different scales of the diffusion coefficient. |
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| format | Article |
| id | doaj.art-6b26722bfd454b87ba95eae7bfc29812 |
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| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-11T00:01:19Z |
| publishDate | 2023-08-01 |
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| spelling | doaj.art-6b26722bfd454b87ba95eae7bfc298122023-11-19T00:42:58ZengMDPI AGComputation2079-31972023-08-0111815310.3390/computation11080153Uncoupling Techniques for Multispecies Diffusion–Reaction ModelMaria Vasilyeva0Sergei Stepanov1Alexey Sadovski2Stephen Henry3Department of Mathematics and Statistics, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USALaboratory of Computational Technologies for Modeling Multiphysical and Multiscale Permafrost Processes, North-Eastern Federal University, Yakutsk 677980, RussiaDepartment of Mathematics and Statistics, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USADepartment of Mathematics and Statistics, Texas A&M University—Corpus Christi, Corpus Christi, TX 78412, USAWe consider the multispecies model described by a coupled system of diffusion–reaction equations, where the coupling and nonlinearity are given in the reaction part. We construct a semi-discrete form using a finite volume approximation by space. The fully implicit scheme is used for approximation by time, which leads to solving the coupled nonlinear system of equations at each time step. This paper presents two uncoupling techniques based on the explicit–implicit scheme and the operator-splitting method. In the explicit–implicit scheme, we take the concentration of one species in coupling term from the previous time layer to obtain a linear uncoupled system of equations. The second approach is based on the operator-splitting technique, where we first solve uncoupled equations with the diffusion operator and then solve the equations with the local reaction operator. The stability estimates are derived for both proposed uncoupling schemes. We present a numerical investigation for the uncoupling techniques with varying time step sizes and different scales of the diffusion coefficient.https://www.mdpi.com/2079-3197/11/8/153multispecies diffusion–reaction modelspatial–temporal modelsexplicit–implicit schemeoperator-splitting methoduncoupling techniques |
| spellingShingle | Maria Vasilyeva Sergei Stepanov Alexey Sadovski Stephen Henry Uncoupling Techniques for Multispecies Diffusion–Reaction Model Computation multispecies diffusion–reaction model spatial–temporal models explicit–implicit scheme operator-splitting method uncoupling techniques |
| title | Uncoupling Techniques for Multispecies Diffusion–Reaction Model |
| title_full | Uncoupling Techniques for Multispecies Diffusion–Reaction Model |
| title_fullStr | Uncoupling Techniques for Multispecies Diffusion–Reaction Model |
| title_full_unstemmed | Uncoupling Techniques for Multispecies Diffusion–Reaction Model |
| title_short | Uncoupling Techniques for Multispecies Diffusion–Reaction Model |
| title_sort | uncoupling techniques for multispecies diffusion reaction model |
| topic | multispecies diffusion–reaction model spatial–temporal models explicit–implicit scheme operator-splitting method uncoupling techniques |
| url | https://www.mdpi.com/2079-3197/11/8/153 |
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