Research Article

Year 2020,
Volume: 17 Issue: 2, 108 - 117, 01.11.2020
### Abstract

### Keywords

### Supporting Institution

### References

An in-depth comparative performance evaluation of the HLLC (Harten-Lax-van Leer-Contact) and the latest version of the AUSM (Advection Upstream Splitting Method), the AUSM+-up, numerical schemes is carried out with the help of the one-dimensional shock tube problem. The efficiency of schemes is assessed on the basis of the accuracy in capturing of the shock, contact discontinuity, and the expansion fan in the solution. Numerical schemes viz., the upwind difference, the Godunov, the MacCormack, and the basic AUSM scheme are also investigated for their performance while solving the same problem to do a wider comparison. Numerical results from each method are compared against the exact solution to the problem. The HLLC numerical scheme is found to be the most efficient followed by AUSM+-up, which is marginally inferior with respect to the shock capturing accuracy.

Indian Institute of Space Science and Technology, Thiruvananthapuram.

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- [15] M. Hajzman, J. Vimmr, O. Bublk, “On the modelling of compressible inviscid flow problems using AUSM schemes,” Applied and Computational Mechanics, 1(2), pp. 469-478, 2007.
- [16] M. S. Liou, “The evolution of AUSM schemes,” Defence Science Journal, 60(6), pp. 606-613, 2010.
- [17] C. H. Chang, M. S. Liou, “A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme,” Journal of Computational Physics, 225(1), pp. 840-873, 2007.
- [18] X. Y. Hua, N. A. Adams, G. Iaccarino, “On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow,” Journal of Computational Physics, 228(17), pp. 6572-6589, 2009.
- [19] S. D. Kima, B. J. Lee, H. J. Lee, I. S. Jeung, “Robust HLLC Riemann solver with weighted average flux scheme for strong shock,” Journal of Computational Physics, 228(20), pp. 7634-7642, 2009.
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- [21] F. Asakura, “Entropy conditions for solutions to a system of conservation laws,” Otemon Economic Studies, 21, pp. 1-8, 1988.

Year 2020,
Volume: 17 Issue: 2, 108 - 117, 01.11.2020
### Abstract

### References

- [1] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 3rd ed., Springer Science & Business Media, Verlag, 2009.
- [2] C. H. Chang and M. S. Liou, “A conservative compressible multi-fluid model for multiphase flow: Shock-interface interaction problems,” in 17th AIAA Computational Fluid Dynamics Conference, Toronto, Ontario, Canada, 2005, Paper No. AIAA (5344), pp.1-16.
- [3] G. A. Sod, “A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws,” Journal of Computational Physics, 27(1), pp.1-31, 1978.
- [4] P. L. Roe, “The use of the Riemann problem in finite difference schemes,” in Seventh International Conference on Numerical Methods in Fluid Dynamics: Proceedings of the Conference, W. C. Reynolds and R. W. MacCormack, Eds. Stanford University, Stanford, California and NASA/Ames (USA), Springer-Verlag, 26, 1980, pp. 354-359.
- [5] P. Colella and H. Glaz, “Efficient solution algorithms for the Riemann problem for real gases,” Journal of Computational Physics, 59(2), pp. 264-289, 1985.
- [6] T. Chang and L. Hsiao, The Riemann problem and interaction of waves in gas dynamics, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman, 1989.
- [7] R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.
- [8] J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed., Siam, 2004.
- [9] I. Danaila, P. Joly, S. M. Kaber, and M. Postel, An Introduction to Scientific Computing: Twelve Computational Projects Solved with MATLAB, Springer Science & Business Media, 2007.
- [10] J. E. John and T. G. Keith, Gas Dynamics, 3rd ed., Pearson Education India, 2006.
- [11] M. S. Liou, C. J. Stefen, “A new flux splitting scheme,” Journal of Computational Physics, 107(1), pp. 23-39, 1993.
- [12] M. S. Liou, “A sequel to AUSM, Part II: AUSM+-up for all speeds,” Journal of Computational Physics, 214(1), pp. 137-170, 2006.
- [13] M. S. Liou, “A sequel to Ausm: Ausm+,” Journal of Computational Physics,129(2), pp. 364-382, 1996.
- [14] Y. Wada, M. S. Liou, “An accurate and robust flux splitting scheme for shock and contact discontinuities,” SIAM Journal on Scientic Computing, 18(3), pp. 633-657, 1997.
- [15] M. Hajzman, J. Vimmr, O. Bublk, “On the modelling of compressible inviscid flow problems using AUSM schemes,” Applied and Computational Mechanics, 1(2), pp. 469-478, 2007.
- [16] M. S. Liou, “The evolution of AUSM schemes,” Defence Science Journal, 60(6), pp. 606-613, 2010.
- [17] C. H. Chang, M. S. Liou, “A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme,” Journal of Computational Physics, 225(1), pp. 840-873, 2007.
- [18] X. Y. Hua, N. A. Adams, G. Iaccarino, “On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow,” Journal of Computational Physics, 228(17), pp. 6572-6589, 2009.
- [19] S. D. Kima, B. J. Lee, H. J. Lee, I. S. Jeung, “Robust HLLC Riemann solver with weighted average flux scheme for strong shock,” Journal of Computational Physics, 228(20), pp. 7634-7642, 2009.
- [20] C. M. Dafermos, “Structure of solutions of the Riemann problem for hyperbolic systems of conservation laws,” Archive for Rational Mechanics and Analysis, 53(3), pp. 203-217, 1974.
- [21] F. Asakura, “Entropy conditions for solutions to a system of conservation laws,” Otemon Economic Studies, 21, pp. 1-8, 1988.

There are 21 citations in total.

Primary Language | English |
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Subjects | Engineering |

Journal Section | Articles |

Authors | |

Publication Date | November 1, 2020 |

Published in Issue | Year 2020 Volume: 17 Issue: 2 |