A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations

Asmouh, Ilham; El-Amrani, Mofdi; Seaid, Mohammed; Yebari, Naji

Abstract

A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.

Citation

Asmouh, I., El-Amrani, M., Seaid, M., & Yebari, N. (2022). A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations. Computational and mathematical methods, 2022, Article 8192192. https://doi.org/10.1155/2022/8192192

• Journal Article Type: Article
• Acceptance Date: Jan 21, 2022
• Online Publication Date: Feb 13, 2022
• Publication Date: 2022
• Deposit Date: Jun 24, 2022
• Publicly Available Date: Jun 24, 2022
• Journal: Computational and Mathematical Methods
• Electronic ISSN: 2577-7408
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Article Number: 8192192
• DOI: https://doi.org/10.1155/2022/8192192
• Public URL: https://durham-repository.worktribe.com/output/1203148