A Hermite upwind WENO scheme for solving hyperbolic conservation laws

Journal of Computational Physics

Volumn 227, Issue 4, 2008, Pages 2430-2454

  Capdeville, G ^a  

^a LABORATOIRE DE MÉCANIQUE DES FLUIDES   (France)

Author keywords

Central WENO interpolation; Hermite polynomial; Hyperbolic systems; Non uniform meshes; Upwind discretization

Indexed keywords

ACOUSTIC FIELDS; FINITE VOLUME METHOD; INTERPOLATION; RUNGE KUTTA METHODS;

CENTRAL WENO INTERPOLATION; HERMITE; HERMITE INTERPOLATION; HERMITE'S POLYNOMIALS; HYPERBOLIC CONSERVATION LAWS; HYPERBOLIC SYSTEM; NON-UNIFORM MESH; SYMMETRICS; UPWIND DISCRETIZATIONS; WENO SCHEMES;

POLYNOMIALS;

EID: 38049064464     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.10.017     Document Type: Article

References (24)

1. Harten A., Engquist B., Osher S., and Chakravarthy S. Uniformly high-order essentially non-oscillatory schemes, III. J. Comput. Phys. 71 (1987) 231-303
2. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report 97-65.
3. Lele S.K. Compact finite-difference schemes with spectra-like resolution. J. Comput. Phys. 103 (1992) 16
4. Van-Leer B. Towards the ultimate conservative difference scheme: III. A new approach to numerical convection. J. Comput. Phys. 23 (1977) 276-299
5. Pirozzoli S. Conservative hybrid compact WENO schemes for shock-turbulence interaction. J. Comput. Phys. 178 (2002) 81-117
6. Ren Y.-X., Liu M., and Zhang H. A characteristic-wise hybrid compact WENO scheme for solving hyperbolic conservation laws. J. Comput. Phys. 192 (2003) 365-386
7. Bouchut F., Bourdarias C., and Perthame B. A MUSCL method satisfying all the numerical entropy inequalities. Math. Comput. 65 (1996) 1439-1461
8. Dougherty R.L., Edelman A.S., and Hyman J.M. Nonnegativity-, monoticity-, or convexity preserving cubic quintic Hermite interpolation. Math. Comput. 52 (1989) 471-494
9. Nakamura T., Tanaka R., Yabe T., and Takizawa K. Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique. J. Comput. Phys. 174 (2001) 171-207
10. Qiu J., and Shu C.-W. Hermite WENO schemes and their applications as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case. J. Comput. Phys. 193 (2004) 115-135
11. Qiu J., and Shu C.-W. Hermite WENO schemes and their applications as limiters for Runge-Kutta discontinuous Galerkin method: two-dimensional case. Comput. Fluids 34 (2005) 642-663
12. Levy D., Pupo G., and Russo G. Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656-672
13. Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439-471
14. R.G. Hindman, On shock-capturing methods and why they work, AIAA-paper-88-0622.
15. Leveque R.J. Numerical Methods for Conservation Laws (1990), Birkhaüser Verlag 115-121
16. Henrick A.K., Aslam T.D., and Powers J.M. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207 (2005) 542-567
17. Harten A., Lax P.D., and Van-Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35
18. Hirsch C. Numerical Computation of Internal and External Flows vol. I (1987), Ed. Wiley & Sons pp. 371-401
19. J. Casper, M.H. Carpenter, Computational considerations for the simulation of shock-induced sound, NASA-TM 110222, 1995.
20. Mc Kenzie J., and Westphal K. Interaction of linear waves with oblique shock waves. Phys. Fluids 11 (1968) 2350-2362
21. Zang T.A., Hussaini M.Y., and Bushnell D.M. Numerical computations of turbulence amplification in shock wave interactions. AIAA J. 22 (1984) 13-21
22. Third computational aeroacoustics workshop on benchmark problems, NASA/CP-2000-209790.
23. Qiu J., and Shu C.-W. On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. J. Comput. Phys. 183 (2002) 187-209
24. Woodward P., and Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115-173