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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Veröffentlicht in:Applied numerical mathematics Jg. 204; S. 352 - 361
Hauptverfasser: Kaur, Anurag, Kanwar, V., Ramos, Higinio
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.10.2024
Schlagworte:
Coupled Burgers' equation
Hybrid block method
Local meshless differential quadrature
Radial basis functions
35F50
Radial basis functions
65N35
Hybrid block method
Coupled Burgers' equation
Local meshless differential quadrature
ISSN:0168-9274
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Zusammenfassung: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.
ISSN:0168-9274
DOI:10.1016/j.apnum.2024.06.019