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Development and Implementation of a High-Order Compact Finite Difference Method in Numerical Analysis of Fluid Flows
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Mohamad Hamed Hekmat *   |
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Abstract: (10 Views) |
In this research, the performance and efficiency of a higher compact finite difference scheme in the generation of a structured grid were investigated. Elliptic partial differential equations have been used to generate a grid system and clustering the grid points in the vicinity of a line or near a point or a combination of them, and also orthogonality of the grid lines on an arbitrary surface was implemented. The main focus of this research was on the extraction of the grid generation equation using a higher compact finite difference. After that, the grid generation equation was discretized using the higher compact finite difference scheme and then was solved numerically by the Gauss-Seidel iterative method. An algebraic grid system was used as the initial distribution of grid points required by the elliptic grid generation. The numerical results for the various test cases, such as grid generation for internal and external flows, were obtained and investigated qualitatively and quantitatively. Moreover, these results were compared with the results of the standard finite difference method. The numerical results showed that using this scheme in comparison with the standard finite difference method increases the efficiency of the grid generation and decreases computational efforts. Based on this, the use of this method results in a reduction of computational time by 70 to 90 percent in grid generation, depending on the grid size and problem conditions. The results showed that the higher compact finite difference scheme can be used as an efficient and high-performance discretization scheme in complex grid generation problems. |
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| Keywords: elliptic grid generation, higher order compact finite difference method, standard finite difference method, computational cost |
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Full-Text [PDF 1414 kb]
(7 Downloads)
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Type of Study: Research |
Subject:
Special
Received: 2025/08/3 | Accepted: 2025/11/17 | Published: 2025/12/1
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