Flux limiters fourth and sixth order high resolution method for hyperbolic conservation laws

References

• Abarbanel , S. , Gottlieb , D. and Turkel , E. 1975 . Difference Schemes with Fourth Order Accuracy for Hyperbolic Equations . SIAM J. Appl. Math. , 29 : 329 – 351 .
   Google Scholar
• Berkenbosch , A. C. , Kaasschieter , E. F. and Ten Thije Boonkkamp , J. H. M. 1994 . Finite-Difference Methods for One-Dimensional Hyperbolic Conservation Law . An International Journal , 10 : 225 – 269 .
   Google Scholar
• Boris , J. P. and Book , D. L. 1973 . Flux Corrected Transport, I, SHASTA, A fluid transports algorithm that works . J. Comp. Phys. , 11 : 38 – 69 .
   Web of Science ®Google Scholar
• Chakravarthy , S. and Osher , S. 1983 . AIAA paper presented at 6th CFD conference . High Resolution applications of the Osher upwind scheme for the Euler equations . 1983 .
   Google Scholar
• Harten , A. 1977 . The Artificial Compression Method for Computing Shocks and Discontinuities. I. Single Conservation Laws . Comm. Pure Appl. Math. , 30 611 – 638 .
   Web of Science ®Google Scholar
• Harten , A. 1983 . High Resolution Schemes for Hyperbolic Conservation Laws . J. Comput. Phys. , 49 357 – 357 .
   Web of Science ®Google Scholar
• Harten , A. 1984 . On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes . SIAM J. Numer. Anal. , 21 ( 1 )
   Web of Science ®Google Scholar
• Harten , A. and Zwas , G. 1972 . Self-Adjusting Hybrid Schemes for Shock Computations . J. Comput. Phys. , 9 ( 1 ) 568 – 568 .
   Google Scholar
• Le Veque , R. J. 1992 . Numerical Methods for Conservation Laws , Boston, , Berlin : Birkhauser Verlag . Besel
   Google Scholar
• Roe , P. L. 1983 . Proc ANS/SIAM Seminar . Some Contributions to the Modeling of Discontinuous Flows . 1983 , San Diego. to appear
   Google Scholar
• Sweby , P. K. 1984 . High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws . SIAM J. Numer. Anal. , 21 : 995 – 1011 .
   Web of Science ®Google Scholar
• Tadmor , E. 1987 . The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws 1 . Math. Comput. , 49 : 91 – 91 .
   Web of Science ®Google Scholar
• Van Leer , B. 1974 . Towards the Ultimate Conservation Difference Scheme II Monotonicity and Conservation Combined in a Second Order Scheme . J. Comput. Phys. , 14 : 361 – 370 .
   Web of Science ®Google Scholar
• Zalesak , S. T. 1979 . Fully Multidimensional Flux Correct Transport Algorithms for Fluid . J. Comp. Phys. , 31 : 335 – 362 .
   Web of Science ®Google Scholar