A Comparison of the Roe’s FDS, HLLC, AUFS, and AUSMDV+ Schemes on Triangular Grids
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Published:
Aug 22, 2019
Keywords:
AUFS AUSMDV HLLC Roe’s FDS Triangular Grids
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Abstract
The upwind schemes had proved to be effective for solving a wide variety of high-speed compressible flow problems due to their accuracy and robustness concerning other schemes. The unstructured grids had been commonly used to discretize the complex geometry then it is necessary to evaluate the performance of the upwind schemes on unstructured grids. This paper presents a comparison study of the accuracy and numerical stability of the Roe’s FDS (RoeVLPA), HLLC, AUFS, and AUSMDV+ schemes on two-dimensional triangular grids. It is found that the AUSMDV+ scheme provides the most accurate solution and the AUFS scheme is the most dissipative scheme.
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Phongthanapanich, S., & Takayama, K. (2019). A Comparison of the Roe’s FDS, HLLC, AUFS, and AUSMDV+ Schemes on Triangular Grids. Applied Science and Engineering Progress, 12(3), 150–157. Retrieved from https://ph02.tci-thaijo.org/index.php/ijast/article/view/210868
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References
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[3] M. Pandolfi and D. D'Ambrosio, “Numerical instabilities in upwind methods: Analysis and cures for the “Carbuncle” phenomenon,” Journal of Computational Physics, vol. 166, pp. 271–301, 2001.
[4] M. Dumbser, J. M. Moschetta, and J. Gressier, “A matrix stability analysis of the carbuncle phenomenon,” Journal of Computational Physics, vol. 197, pp. 647–670, 2004.
[5] S. Phongthanapanich and P. Dechaumphai, “Healing of shock instability for Roe's fluxdifference splitting scheme on triangular meshes,” International Journal for Numerical Methods in Fluids, vol. 59, pp. 559–575, 2009.
[6] M. V. C. Ramalho, J. H. A. Azevedo, and J. L. F. Azevedo, “Further investigation into the origin of the carbuncle phenomenon in aerodynamic simulations,” presented at the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Florida, US, Jan. 4–7, 2011.
[7] S. Phongthanapanich, “Healing of the carbuncle phenomenon for AUSMDV scheme on triangular grids,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 17, pp. 15–28, 2016.
[8] P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,” Journal of Computational Physics, vol. 43, pp. 357–372, 1981.
[9] A. Harten, P. D. Lax, and B. Van Leer, “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws,” SIAM Review, vol. 25, pp. 35–61, 1983.
[10] E. F. Toro, M. Spruce, and W. Speares, “Restoration of the contact surface in the HLL-Riemann solver,” Shock Waves, vol. 4, pp. 25–34, 1994.
[11] P. Batten, N. Clarke, C. Lambert, and D. M. Causon, “On the choice of waves speeds for the HLLC Riemann solver,” SIAM Journal on Scientific Computing (SISC), vol. 18, pp. 1553–1570, 1997.
[12] M. Sun and K. Takayama, “An artificial upstream flux vector splitting scheme for the Euler equations,” Journal of Computational Physics, vol. 189, pp. 305–329, 2003.
[13] M. S. Liou and C. J. Steffen, “A new flux splitting scheme,” Journal of Computational Physics, vol. 107, pp. 23–39, 1993.
[14] M. S. Liou, “A sequel to AUSM: AUSM+,” Journal of Computational Physics, vol. 129, pp. 364–382, 1996.
[15] Y. Wada and M. S. Liou, “An accurate and robust flux splitting scheme for shock and contact discontinuities,” SIAM Journal on Scientific Computing (SISC), vol. 18, pp. 633–657, 1997.
[16] K. H. Kim, C. Kim, and O. H. Rho, “Methods for the accurate computations of hypersonic flows I. AUSMPW+ scheme,” Journal of Computational Physics, vol. 174, pp. 38–80, 2001.
[17] K. Kitamura and E. Shima, “Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes,” Journal of Computational Physics, vol. 245, pp. 62–83, 2013.
[18] S. Phongthanapanich, “An accurate and robust AUSM-family scheme on two-dimensional triangular grids,” Shock Waves, vol. 29, no. 5, pp. 755–768, 2019.
[19] S. Phongthanapanich, “A parameter-free AUSM-based scheme for healing carbuncle phenomenon,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 38, pp. 691–701, 2016.
[20] G. A. Sod, “A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws,” Journal of Computational Physics, vol. 27, pp. 1–31, 1978.
[21] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Berlin, Germany: Springer, 1999.