Accuracy of Cell-Centre Derivation of Unstructured-Mesh Finite Volume Solver

Accuracy of Cell-Centre Derivation of Unstructured-Mesh Finite Volume Solver

© 2022 by IJETT Journal
Volume-70 Issue-8
Year of Publication : 2022
Authors : Adek Tasri
DOI : 10.14445/22315381/IJETT-V70I8P217

How to Cite?

Adek Tasri, "Accuracy of Cell-Centre Derivation of Unstructured-Mesh Finite Volume Solver," International Journal of Engineering Trends and Technology, vol. 70, no. 8, pp. 166-171, 2022. Crossref,

This study compared the accuracy of existing and a proposed second-order least square based cell centre derivation of velocity within an unstructured mesh finite volume solver. We tested the algorithms in isolation on ideal data to determine their basic numerical accuracy on good quality and artificially distorted meshes. The study found that the least-square-based cell centre derivations were more accurate than Gauss divergence-based derivations. The preliminary interpolation stage in cell centre derivation increased L1 error and reduced the order of accuracy in the distorted mesh. The second-order least square-based cell centre derivations were the most accurate among the methods tested in this study. The Frink's cell centre derivation was the least accurate.

Finite volume, Cell centre derivation, Unstructured mesh.

[1] J. A. White, H. Nishikawa and R. Baurle, “Weighted Least-squares Cell-Average Gradient Construction Methods for the VULCANCFD Second-Order Accurate Unstructured Grid Cell-Centered Finite-Volume Solver,” in AIAA Scitech Forum, San Diego, 2019.
[2] A. Tasri, A. Susilawati, “Accuracy of Compact-Stencil Interpolation Algorithms for Unstructured Mesh Finite Volume Solver,” Heliyon, vol. 7, pp. e06875, 2021.
[3] A. Tasri, “Accuracy of Cell Centres to Vertices Interpolation for Unstructured Mesh Finite Volume Solver,” Journal of the Institution of Engineers (India): Series C, vol. 102, pp. 577-584, 2021.
[4] T. J. Barth and D. C. Jespersen, "The Design and Application of Upwind Schemes on Unstructured Meshes," in AIAA 27th Aerospace Sciences Meeting, Reno,1989.
[5] W. K. Anderson and D. L. Bonhaus, “An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids,” Computers and Fluids, vol. 23, pp. 1-21, 1994.
[6] J. A. White, H. Nishikawa, R. A. Baurle, “Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured Grid Cell-Centred Finite-Volume Solver,” in AIAA Scitech Forum, (2019).
[7] H. Nishikawa, “Efficient Gradient Stencils for Robust Implicit Finite-Volume Solver Convergence on Distorted Grids,” Journal of Computational Physics, vol. 386, pp. 486-501, 2019.
[8] S. S. Athkuri, V. Eswaran, “A New Auxiliary Volume-Based Gradient Algorithm for Triangular and Tetrahedral Meshes,” Journal of Computational Physics, vol. 422, pp. 109780, 2020.
[9] S. S. Athkuri, M. R. Nived, V. Eswaran, “The Mid Point Green‐Gauss Gradient Method and Its Efficient Implementation in A 3D Unstructured Finite Volume Solver,” International Journal for Numerical Methods in Fluids, 2021.
[10] M. Aftosmis, D. Gaitonde and T. Tavares, “Behavior of Linear Reconstruction Techniques on Unstructured Meshes,” AIAA Journal, vol. 11, pp. 2038-2049, 1995.
[11] D. Mavriplis, “Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes,” in The 16th AIAA Computational Fluid Dynamics Conference, Florida, (2003).
[12] C. D. Correa, R. Hero and K. L. Ma, “A Comparison of Gradient Estimation Methods for Volume Rendering on Unstructured Meshes,” IEEE Transactions on Visualisation and Computer Graphics, vol. 18, pp. 305-319, 2001.
[13] A. Syrakos, S. Varchanis, Y. Dimakopoulos, A. Goulas, J. Tsamopoulos, “A Critical Analysis of Some Popular Methods for the Discretisation of the Gradient Operator in Finite volume Methods, Physics of Fluids, vol. 29, pp. 12703, 2017.
[14] B. Diskin, J.L Thomas, “Comparison of Node-Centred and Cell-Centred Unstructured Finite-Volume Discretisations: Inviscid Fluxes,” AIAA Journal, vol. 49, pp. 836-854, 2011.
[15] N. T. Frink, “Upwind Scheme for Solving the Euler Equations on Unstructured Tetrahedral Meshes,” AIAA Journal, vol. 30, pp. 70-77, 1992.
[16] S. R. Mathur and J. T. Murthy, “A Pressure-Based Method for Unstructured Meshes,” Numer. Heat Transfer, Part B, vol. 31, pp. 195- 215, 9197.
[17] G. H. Golub and C. V. van Loan, “Matrix Computations,” 3rd edition, London, The Johns Hopkins University Press, 1996.
[18] A. Tasri, “Accuracy of Nominally 2nd Order, Unstructured Grid, CFD Codes,” PhD Thesis, University of Newcastle Upon Tyne, Newcastle, UK, 2005.
[19] F.M. White, “Fluid Mechanics,” 8th Edition, New York, McGraw-Hill, 2015.
[20] N. Wang, M. Li, R. Ma, L. Zhang, “Accuracy Analysis of Gradient Reconstruction on Isotropic Unstructured Meshes and its Effects on Inviscid Flow Simulation,” Adv. Aerodyn., vol. 1, no. 1-31, 2019.
[21] B. Diskin, J. L. Thomasy, E. J. Nielsenz, H. Nishikawa, J. A. White, “Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretisations, Part I: Viscous Fluxes,” AIAA Paper, pp. 579, 2009.