An optimized algorithm for numerical solution of coupled Burgers equations
Investigation of the solutions of the coupled viscous Burgers system is crucial for realizing and understanding some physical phenomena in applied sciences. Particularly, Burgers equations are used in the modeling of fluid mechanics and nonlinear acoustics. In the present study, a modified meshless...
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| Published in: | Applied numerical mathematics Vol. 204; pp. 352 - 361 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.10.2024
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| ISSN: | 0168-9274 |
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| Abstract | Investigation of the solutions of the coupled viscous Burgers system is crucial for realizing and understanding some physical phenomena in applied sciences. Particularly, Burgers equations are used in the modeling of fluid mechanics and nonlinear acoustics. In the present study, a modified meshless quadrature method based on radial basis functions is used to discretize the partial derivatives in the spatial variable. A technique to find the best value of the shape parameter is introduced. A high-resolution optimized hybrid block method is then used to solve the problem in the temporal variable. To validate the proposed method, several test problems are considered and the simulated results are compared with exact solutions and previous works. Moreover, a sensitivity analysis for parameter c is conducted, and the unconditional stability of the proposed algorithm has been validated. |
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| AbstractList | Investigation of the solutions of the coupled viscous Burgers system is crucial for realizing and understanding some physical phenomena in applied sciences. Particularly, Burgers equations are used in the modeling of fluid mechanics and nonlinear acoustics. In the present study, a modified meshless quadrature method based on radial basis functions is used to discretize the partial derivatives in the spatial variable. A technique to find the best value of the shape parameter is introduced. A high-resolution optimized hybrid block method is then used to solve the problem in the temporal variable. To validate the proposed method, several test problems are considered and the simulated results are compared with exact solutions and previous works. Moreover, a sensitivity analysis for parameter c is conducted, and the unconditional stability of the proposed algorithm has been validated. |
| Author | Kanwar, V. Ramos, Higinio Kaur, Anurag |
| Author_xml | – sequence: 1 givenname: Anurag orcidid: 0000-0001-8751-2372 surname: Kaur fullname: Kaur, Anurag email: ahsikh@gmail.com organization: Department of Mathematics, Panjab University, Chandigarh, India – sequence: 2 givenname: V. surname: Kanwar fullname: Kanwar, V. organization: University Institute of Engineering and Technology, Panjab University, Chandigarh, India – sequence: 3 givenname: Higinio orcidid: 0000-0003-2791-6230 surname: Ramos fullname: Ramos, Higinio organization: Departamento de Matemática Aplicada, University of Salamanca, Spain |
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| Keywords | 35F50 Radial basis functions 65N35 Hybrid block method Coupled Burgers' equation Local meshless differential quadrature |
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