A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil
Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/7104852 |
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| author | Elias Mwakilama Vusi Magagula Duncan Gathungu |
| author_facet | Elias Mwakilama Vusi Magagula Duncan Gathungu |
| author_sort | Elias Mwakilama |
| collection | DOAJ |
| description | Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications. |
| format | Article |
| id | doaj-art-636ba2064cd14b49810192111e5014b8 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-636ba2064cd14b49810192111e5014b82025-02-03T06:42:50ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/7104852A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in SoilElias Mwakilama0Vusi Magagula1Duncan Gathungu2Department of MathematicsDepartment of MathematicsDepartment of Pure & Applied MathematicsConventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.http://dx.doi.org/10.1155/2023/7104852 |
| spellingShingle | Elias Mwakilama Vusi Magagula Duncan Gathungu A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil Journal of Applied Mathematics |
| title | A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil |
| title_full | A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil |
| title_fullStr | A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil |
| title_full_unstemmed | A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil |
| title_short | A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil |
| title_sort | novel multivariate spectral local quasilinearization method mv slqlm for modelling flow moisture heat and solute transport in soil |
| url | http://dx.doi.org/10.1155/2023/7104852 |
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