Table of Contents
Journal of Computational Methods in Physics
Volume 2014, Article ID 827034, 13 pages
http://dx.doi.org/10.1155/2014/827034
Research Article

A New Flux Splitting Scheme Based on Toro-Vazquez and HLL Schemes for the Euler Equations

1Department of Physics, Laboratory of Mechanics and Modelling of Physical Systems (L2MPS), Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2Faculté des Sciences et de Technologie, Université des Montagnes, P.O. Box 208, Bangangté, Cameroon
3Laboratory of Industrial and Systems Engineering Environment (LISIE), IUT/FV Bandjoun, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

Received 24 July 2014; Revised 28 October 2014; Accepted 11 November 2014; Published 2 December 2014

Academic Editor: Xavier Ferrieres

Copyright © 2014 Pascalin Tiam Kapen and Tchuen Ghislain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. L. Roe, “A survey of upwind differencing techniques,” in 11th International Conference on Numerical Methods in Fluid Dynamics, vol. 323 of Lecture Notes in Physics, pp. 69–78, Springer, New York, NY, USA, 1989. View at Publisher · View at Google Scholar
  2. S. K. Godunov, “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics,” Matematicheskii Sbornik, vol. 47 (89), pp. 271–306, 1959. View at Google Scholar · View at MathSciNet
  3. A. Harten, P. D. Lax, and B. van Leer, “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws,” SIAM Review, vol. 25, no. 1, pp. 35–61, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  4. B. Einfeldt, “On Godunov-type methods for gas dynamics,” SIAM Journal on Numerical Analysis, vol. 25, no. 2, pp. 294–318, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  5. P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,” Journal of Computational Physics, vol. 43, no. 2, pp. 357–372, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. J. J. Quirk, ICASE Report 92-64, 1992.
  7. J. J. Quirk, “A contribution to the great Riemann solver debate,” International Journal for Numerical Methods in Fluids, vol. 18, no. 6, pp. 555–574, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,” Journal of Computational Physics, vol. 40, no. 2, pp. 263–293, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. W. K. Anderson, J. L. Thomas, and B. Van Leer, “Comparison of finite volume flux vector splittings for the Euler equations,” AIAA Journal, vol. 24, no. 9, pp. 1453–1460, 1986. View at Publisher · View at Google Scholar · View at Scopus
  10. M.-S. Liou and J. Steffen, “A new flux splitting scheme,” Journal of Computational Physics, vol. 107, no. 1, pp. 23–39, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. S. Liou and Y. Wada, “A flux splitting scheme with high-resolution and robustness for discontinuities,” AIAA Paper 94-0083, 1994. View at Google Scholar
  12. M.-S. Liou, “A sequel to AUSM: AUSM+,” Journal of Computational Physics, vol. 129, no. 2, pp. 364–382, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. K. H. Kim, J. H. Lee, and O. H. Rho, “An improvement of AUSM schemes by introducing the pressure-based weight functions,” Computers & Fluids, vol. 27, no. 3, pp. 311–346, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. 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, no. 1, pp. 38–80, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M.-S. Liou, “A sequel to AUSM, part II: AUSM+-up for all speeds,” Journal of Computational Physics, vol. 214, no. 1, pp. 137–170, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. R. Edwards, “A low-diffusion flux-splitting scheme for Navier-Stokes calculations,” Computers & Fluids, vol. 26, no. 6, pp. 635–659, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. J. R. Edwards, R. K. Franklin, and M.-S. Liou, “Low-diffusion flux-splitting methods for real fluid flows with phase transitions,” AIAA Journal, vol. 38, no. 9, pp. 1624–1633, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. S.-W. Ihm and C. Kim, “Computations of homogeneous-equilibrium two-phase flows with accurate and efficient shock-stable schemes,” AIAA Journal, vol. 46, no. 12, pp. 3012–3037, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. E. F. Toro and M. E. Vázquez-Cendón, “Flux splitting schemes for the Euler equations,” Computers & Fluids, vol. 70, pp. 1–12, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. S. F. Davis, “Simplified second-order Godunov-type methods,” SIAM Journal on Scientific and Statistical Computing, vol. 9, no. 3, pp. 445–473, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  21. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin, Germany, 2nd edition, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  22. R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, “A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method),” Journal of Computational Physics, vol. 152, no. 2, pp. 457–492, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. X. Y. Hu and B. C. Khoo, “An interface interaction method for compressible multifluids,” Journal of Computational Physics, vol. 198, no. 1, pp. 35–64, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. X. Y. Hu, B. C. Khoo, N. A. Adams, and F. L. Huang, “A conservative interface method for compressible flows,” Journal of Computational Physics, vol. 219, no. 2, pp. 553–578, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. R. Abgrall and S. Karni, “Computations of compressible multifluids,” Journal of Computational Physics, vol. 169, no. 2, pp. 594–623, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus