Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems
In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented. The analog equation method is utilized to transform the linear and nonlin...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-04-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.807445/full |
| _version_ | 1818355008880508928 |
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| author | L Zhang L Zhang FZ Wang FZ Wang J Zhang J Zhang YY Wang S Nadeem TA Nofal |
| author_facet | L Zhang L Zhang FZ Wang FZ Wang J Zhang J Zhang YY Wang S Nadeem TA Nofal |
| author_sort | L Zhang |
| collection | DOAJ |
| description | In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented. The analog equation method is utilized to transform the linear and nonlinear convection-diffusion equation into an equivalent one. The expressions of the homogeneous solution and particular solution are derived by utilizing the radial basis function approximation and the method of fundamental solutions, respectively. By enforcing the desired solution to satisfy the original convection-diffusion equation with boundary conditions at boundary and internal collocation points yield a nonlinear system of equations, which can be solved by using the Newton-Raphson iteration or the Picard method of iteration. The error convergence curves of the proposed meshless method have been investigated by using different globally supported radial basis functions. Numerical experiments show that the proposed CMFS method is promising for anisotropic convection-diffusion problems with accurate and stable results. |
| first_indexed | 2024-12-13T19:34:30Z |
| format | Article |
| id | doaj.art-8fdb0de78e854307938a20533c79f8ea |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-13T19:34:30Z |
| publishDate | 2022-04-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-8fdb0de78e854307938a20533c79f8ea2022-12-21T23:33:51ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-04-011010.3389/fphy.2022.807445807445Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion ProblemsL Zhang0L Zhang1FZ Wang2FZ Wang3J Zhang4J Zhang5YY Wang6S Nadeem7TA Nofal8Yellow River Institute of Hydraulic Research, YRCC, Zhengzhou, ChinaHenan Engineering Research Center of Hydropower Engineering Abrasion Test and Protection, Zhengzhou, ChinaGuangdong ATV Academy for Performing Arts, Dongguan, ChinaNanchang Institute of Technology, Nanchang, ChinaGuangdong ATV Academy for Performing Arts, Dongguan, ChinaSchool of Computer Science and Technology, Huaibei Normal University, Huaibei, ChinaSchool of Economics and Management, Nantong University, Nantong, ChinaDepartment of Mathematics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Mathematic, College of Science, Taif University, Taif, Saudi ArabiaIn this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented. The analog equation method is utilized to transform the linear and nonlinear convection-diffusion equation into an equivalent one. The expressions of the homogeneous solution and particular solution are derived by utilizing the radial basis function approximation and the method of fundamental solutions, respectively. By enforcing the desired solution to satisfy the original convection-diffusion equation with boundary conditions at boundary and internal collocation points yield a nonlinear system of equations, which can be solved by using the Newton-Raphson iteration or the Picard method of iteration. The error convergence curves of the proposed meshless method have been investigated by using different globally supported radial basis functions. Numerical experiments show that the proposed CMFS method is promising for anisotropic convection-diffusion problems with accurate and stable results.https://www.frontiersin.org/articles/10.3389/fphy.2022.807445/fullradial basis functionmeshless methodconvection-diffusion problemsnonlinear partial difference equationboundary value problem |
| spellingShingle | L Zhang L Zhang FZ Wang FZ Wang J Zhang J Zhang YY Wang S Nadeem TA Nofal Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems Frontiers in Physics radial basis function meshless method convection-diffusion problems nonlinear partial difference equation boundary value problem |
| title | Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems |
| title_full | Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems |
| title_fullStr | Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems |
| title_full_unstemmed | Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems |
| title_short | Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems |
| title_sort | novel numerical method based on the analog equation method for a class of anisotropic convection diffusion problems |
| topic | radial basis function meshless method convection-diffusion problems nonlinear partial difference equation boundary value problem |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.807445/full |
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