High accuracy compact schemes and Gibbs' phenomenon

Journal of Scientific Computing

Volumn 21, Issue 3, 2004, Pages 253-268

  Sengupta, T K ^a   Ganerwal, G ^a   Dipankar, Anurag ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Burgers' equation; Compact difference scheme; Gibbs' phenomenon; Spectral analysis

Indexed keywords

AEROSPACE ENGINEERING; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; FINITE VOLUME METHOD; NATURAL SCIENCES COMPUTING; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SPECTRUM ANALYSIS;

BURGERS' EQUATION; COMPACT DIFFERENCE SCHEMES; GIBBS' PHENOMENON; TRANSITIONAL FLOWS;

GIBBS FREE ENERGY;

EID: 9144270606     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-1317-2     Document Type: Article

References (18)

1. Lele S. K. (1992). Compact finite difference schemes with spectral like resolution. J. Comp. Phys. 103, 16-42.
2. Haras Z., and Ta'asan S. (1994). Finite difference schemes for long-time integration. J. Comput. Phys. 114, 265-279.
3. Adams N. A., and Shariff K. (1996). A high resolution hybrid compact -ENO scheme for shock-turbulence interaction problems. J. Comp. Phys. 127, 27-51.
4. Zhong X. (1998). High order finite difference schemes for numerical simulation of hypersonic boundary layer transition. J. Comp. Phys. 144, 622-709.
5. Sengupta T. K., Ganerwal G., and De S. (2003). Analysis of central and compact schemes. J. Comp. Phys. 192(2), 677-694.
6. Tam C. K. W., and Webb J. C. (1993). Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comp. Phys. 107, 262-281.
7. Lighthill M. J. (1978). Waves in Fluids, Cambridge University Press, U.K.
8. Sengupta T. K., Sridar D., Sarkar S., and De S. (2001). Spectral analysis of flux vector splitting finite volume methods. Int. J. Numer. Meth. Fluids. 37, 149-174.
9. Jiang G. S and Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comp. Phys. 126, 202.
10. Pirozzoli S. (2002). Conservative hybrid compact-WENO scheme for shock- turbulence interaction. J. Comp. Phys. 178, 81-117.
11. van Leer B. (1974). Towards the ultimate conservative difference scheme. II.Monotonicity and conservation combined in a second-order scheme. J. Comp. Phys. 14, 361-370.
12. Roe P. L., and Baines M. J. (1982). Algorithms for advection and shock problems. In the Proc. of 4th GAMM Conf. on Numerical Methods in Fluid Mechanics. Vieweg, Braunschweig.
13. Roe P. L. (1985). Some contribution to the modelling of discontinuous flows. Lectures in Applied Mathematics, 22, 163-193.
14. van Leer B. (1979). Towards the ultimate conservative difference scheme.V. A second order sequel to Godunov's method. J. Comp. Phys. 32, 101-136.
15. Koren B. (1993). A robust upwind discretization method for advection, diffusion and source term. In Numerical Methods for Advection-Diffusion Problems (C. B. Vreugdenhil and B. Koren, eds.), Vieweg. braunschweig, pp. 117-137.
16. Sengupta T. K., Anuradha G., and De S. (2003). Incompressible Navier- Stokes solution by new compact schemes. In Proc. of 2nd MIT Conf. on Comp. Fluid and Solid Mech. (K. J. Bathe, ed.,).
17. Lax P. D., and Wendroff B. (1960). Systems of conservation laws. Comm. Pure Appl. Math. 13, 217-237.
18. Harten A., Engquist B., Osher S., und Chakravarthy S. (1987). Uniformly high order essentially non oscillatory schemes III. J. Comp. Phys. 71, 213.