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ARTICLE
Performance of Geometric Multigrid Method for Two-Dimensional Burgers’ Equations with Non-Orthogonal, Structured Curvilinear Grids
Daiane Cristina Zanatta1,*, Luciano Kiyoshi Araki2, Marcio Augusto Villela Pinto2, Diego Fernando Moro3
1 State University of Centro-Oeste, Irati, Brazil
2 Federal University of Parana, Department of Mechanical Engineering, Curitiba, Brazil
3 Positivo University, Curitiba, Brazil
* Corresponding Author: Daiane Cristina Zanatta. Email:
Computer Modeling in Engineering & Sciences 2020, 125(3), 1061-1081. https://doi.org/10.32604/cmes.2020.012634
Received 07 July 2020; Accepted 02 September 2020; Issue published 15 December 2020
Abstract
This paper seeks to develop an efficient multigrid algorithm for
solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were
discretized by Finite Volume Method (FVM) with second-order approximation scheme and deferred correction. Moreover, the algebraic method and
the differential method were used to generate the non-orthogonal structured
curvilinear grids. Furthermore, the influence of some parameters of geometric
multigrid method, as well as lexicographical Gauss–Seidel (Lex-GS), η-line
Gauss–Seidel (η-line-GS), Modified Strongly Implicit (MSI) and modified
incomplete LU decomposition (MILU) solvers on the Central Processing
Unit (CPU) time was investigated. Therefore, several parameters of multigrid method and solvers were tested for the problem, with the use of nonorthogonal structured curvilinear grids and multigrid method, resulting in an
algorithm with the combination that achieved the best results and CPU time.
The geometric multigrid method with Full Approximation Scheme (FAS),
V-cycle and standard coarsening ratio for this problem were utilized. This
article shows how to calculate the coordinates transformation metrics in the
coarser grids. Results show that the MSI and MILU solvers are the most
efficient. Moreover, the MSI solver is faster than MILU for both grids generators; and the solutions are more accurate for the Burgers problem with grids
generated using elliptic equations.
Keywords
Cite This Article
Zanatta, D. C., Araki, L. K., Augusto, M., Moro, D. F. (2020). Performance of Geometric Multigrid Method for Two-Dimensional Burgers’ Equations with Non-Orthogonal, Structured Curvilinear Grids.
CMES-Computer Modeling in Engineering & Sciences, 125(3), 1061–1081. https://doi.org/10.32604/cmes.2020.012634