An Efficient Space-Time Two-Grid Compact Difference Scheme for the Two-Dimensional Viscous Burgers' Equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915559335002112 |
|---|---|
| author | Peng, Xiangyi Ding, Lisen Qiu, Wenlin |
| author_facet | Peng, Xiangyi Ding, Lisen Qiu, Wenlin |
| contents | This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a compact finite difference discretization with a two-grid strategy to achieve high computational efficiency without sacrificing accuracy. In the coarse-grid stage, a fixed-point iteration is employed to handle the nonlinear system, while in the fine-grid stage, linear temporal and cubic spatial Lagrange interpolations are used to construct initial approximations. The final fine-grid solution is refined through a carefully designed linearized correction scheme. Rigorous analysis establishes unconditional convergence of the method, demonstrating second-order accuracy in time and fourth-order accuracy in space. Numerical experiments verify the theoretical results and show that the ST-TGCD scheme reduces CPU time by more than 70\% compared with the traditional nonlinear compact difference (NCD) method, while maintaining comparable accuracy. These findings confirm the proposed scheme as a highly efficient alternative to conventional nonlinear approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Efficient Space-Time Two-Grid Compact Difference Scheme for the Two-Dimensional Viscous Burgers' Equation Peng, Xiangyi Ding, Lisen Qiu, Wenlin Numerical Analysis 65M06, 65M15, 65M55 This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a compact finite difference discretization with a two-grid strategy to achieve high computational efficiency without sacrificing accuracy. In the coarse-grid stage, a fixed-point iteration is employed to handle the nonlinear system, while in the fine-grid stage, linear temporal and cubic spatial Lagrange interpolations are used to construct initial approximations. The final fine-grid solution is refined through a carefully designed linearized correction scheme. Rigorous analysis establishes unconditional convergence of the method, demonstrating second-order accuracy in time and fourth-order accuracy in space. Numerical experiments verify the theoretical results and show that the ST-TGCD scheme reduces CPU time by more than 70\% compared with the traditional nonlinear compact difference (NCD) method, while maintaining comparable accuracy. These findings confirm the proposed scheme as a highly efficient alternative to conventional nonlinear approaches. |
| title | An Efficient Space-Time Two-Grid Compact Difference Scheme for the Two-Dimensional Viscous Burgers' Equation |
| topic | Numerical Analysis 65M06, 65M15, 65M55 |
| url | https://arxiv.org/abs/2510.15274 |