A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws

SIAM Journal on Numerical Analysis

Volumn 48, Issue 2, 2010, Pages 772-795

  Zhang, Xiangxiong ^a   Shu, Chi Wang ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Conservative form; Finite volume scheme; High order accuracy; Hyperbolic conservation laws; Total variation bounded; Total variation diminishing

Indexed keywords

FINITE VOLUME SCHEMES; HIGH-ORDER ACCURACY; HYPERBOLIC CONSERVATION LAWS; TOTAL VARIATION BOUNDED; TOTAL VARIATION DIMINISHING;

NUMERICAL ANALYSIS;

SANDERS;

EID: 77954196127     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/090764384     Document Type: Article

References (16)

1. A. HARTEN, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49 (1983), pp. 357-393.
2. A. HARTEN, B. ENGQUIST, S. OSHER, AND S. R. CHAKRAVARTHY, Uniformly high-order essentially nonoscillatory schemes, III, J. Comput. Phys., 71 (1987), pp. 231-303.
3. D. HELBING, A. HENNECKE, V. SHVETSOV, AND M. TREIBER, MASTER: Macroscopic tra.c simulation based on a gas-kinetic, non-local tra.c model, Transportation Res. Part B, 35 (2001), pp. 183-211.
4. G.-S. JIANG AND C.-W. SHU, E.cient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
5. X.-D. LIU AND S. OSHER, Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes, SIAM J. Numer. Anal., 33 (1996), pp. 760-779.
6. X.-D. LIU, S. OSHER, AND T. CHAN, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), pp. 200-212.
7. Y. LU, S. C. WONG, M. ZHANG, C.-W. SHU, AND W. CHEN, Explicit construction of entropy solutions for the Lighthill-Whitham-Richards tra.c.ow model with a piecewise quadratic.ow-density relationship, Transportation Res. Part B, 42 (2008), pp. 355-372.
8. S. OSHER AND S. CHAKRAVARTHY, High resolution schemes and the entropy condition, SIAM J. Numer. Anal., 21 (1984), pp. 955-984.
9. B. PERTHAME AND C.-W. SHU, On positivity preserving.nite volume schemes for Euler equations, Numer. Math., 73 (1996), pp. 119-130.
10. J.-M. QIU AND C.-W. SHU, Convergence of Godunov-type schemes for scalar conservation laws under large time steps, SIAM J. Numer. Anal., 46 (2008), pp. 2211-2237.
11. J.-M. QIU AND C.-W. SHU, Convergence of high order.nite volume weighted essentially nonoscillatory scheme and discontinuous Galerkin method for nonconvex conservation laws, SIAM J. Sci. Comput., 31 (2008), pp. 584-607.
12. R. SANDERS, A third-order accurate variation nonexpansive di.erence scheme for single nonlinear conservation law, Math. Comp., 51 (1988), pp. 535-558.
13. R. SANDERS AND A. WEISER, High resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws, J. Comput. Phys., 101 (1992), pp. 314-329.
14. C.-W. SHU, TVB uniformly high-order schemes for conservation laws, Math. Comp., 49 (1987), pp. 105-121.
15. C.-W. SHU AND S. OSHER, E.cient implementation of essentially nonoscillatory shockcapturing schemes, J. Comput. Phys., 77 (1988), pp. 439-471.
16. X. ZHANG AND C.-W. SHU, On maximum-principle-satisfying high order schemes for scalar conservation laws, J. Comput. Phys., 229 (2010), pp. 3091-3120.