Improvement of the WENO scheme smoothness estimator

38th AIAA Fluid Dynamics Conference and Exhibit

Volumn , Issue , 2008, Pages

  Shen, Yiqing ^a   Zha, Gecheng ^a  

^a University of Miami College of Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL TESTS; WENO SCHEMES; WENO(WEIGHTED ESSENTIALLY NONOSCILLATORY) SCHEME;

EID: 78049522579     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2008-3993     Document Type: Conference Paper

References (17)

1. G.S. Jiang, and C.W. Shu, "Efficient implementation of weighted ENO schemes," J.Comput.Phys., vol. 126, pp. 202-228, 1996.
2. S. Pirozzoli, "Conservative hybrid compact-WENO schemes for shock-turbulence interaction," J.Comput.Phys., vol. 178, pp. 81-117, 2002.
3. B. Sjogreen and H.C. Yee, "Grid convergence of high order methods for multiscale complex unsteady viscous compressible flows," Journal of Computational Physics, vol. 185, pp. 1-26, 2003.
4. M. Latini, O. Schilling, W.S. Don, "Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability," Journal of Computational Physics, vol. 221, pp. 805-836, 2007.
5. Y.Q. Shen and G.W. Yang, "Hybrid finite compact-WENO schemes for shock calculation," Interational Journal for Numerical Methods in Fluids, vol. 53, pp. 531-560, 2007.
6. Y.Q. Shen, G.C. Zha, and B.Y. Wang, "Improvement of the stability and accuracy of implicit WENO scheme for transonic flows." Submitted to AIAA J., 2007.
7. X.D. Liu, S. Osher, and T. Chan, "Weighted essentially non-oscillatory schemes," J.Comput.Phys., vol. 126, pp. 200-212, 1994.
8. A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, "Uniformly High Order Essentially Non- Oscillatory Schemes, III," Journal of Computational Physics, vol. 71, pp. 231-303, 1987.
9. C.-W. Shu and O. Osher, "Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes, II," Journal of Computational Physics, vol. 83, pp. 32-78, 1989.
10. A.K. Henrick, T.D. Aslam, J.M. Powers, "Mapped weighted essentially non-oscillatory schemes:Achiving optimal order near critical points," J.Comput.Phys., vol. 208, pp. 206-227, 2005.
11. R. Borges, M. Carmona, B. Costa and W.S. Don, "An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws," Journal of Computational Physics, vol. 227, pp. 3191-3211, 2008.
12. Y.Q. Shen, G.C. Zha, and B.Y. Wang, "Improvement of the stability and accuracy of implicit WENO scheme for transonic flows." AIAA-paper 2007-4431, Submitted to AIAA J., 2008.
13. C.-W. Shu and O. Osher, "Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes," Journal of Computational Physics, vol. 77, pp. 439-471, 1988.
14. B. Cockburn, C.W. Shu, "Nonlinearly stable compact schemes for shock calculations," SIAM Journal on Numerical Analysis, vol. 31, pp. 607-627, 1994.
15. Y.Q. Shen, G.W. Yang, Z. Gao, "High-resolution finite compact difference schemes for hyperbolic conservation laws," J.Comput.Phys., vol. 216, pp. 114-137, 2006.
16. J. Steger and R. Warming, "Flux Vvector Splitting of the Inviscid Gasdynamic Equations with Application to Finite-Difference Methods," Journal of Computational Physics, vol. 40, pp. 263-293, 1981.
17. Z.J. Wang and R.F. Chen, "Optimized weighted essentially non-oscillatory schemes for linear waves with discontinuity," J.Comput.Phys., vol. 174, pp. 381-404, 2001.