A high resolution total variation diminishing scheme for hyperbolic conservation law and related problems

Applied Mathematics and Computation

Volumn 175, Issue 2, 2006, Pages 1556-1573

  Kadalbajoo, M K ^a   Kumar, Ritesh ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Conservation law; Convection; Finite difference schemes; High resolution schemes; Total variation diminishing schemes

Indexed keywords

FINITE DIFFERENCE METHOD; MATHEMATICAL TECHNIQUES; NUMERICAL ANALYSIS;

CONSERVATION LAW; CONVECTION; HIGH RESOLUTION SCHEMES; TOTAL VARIATION DIMINISHING (TVD) DIFFERENCE SCHEME;

PROBLEM SOLVING;

EID: 33645864676     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.09.006     Document Type: Article

References (16)

1. Leonard B.P. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19 (1979) 59-98
2. Leonard B.P. Order of accuracy of QUICK and related convection-diffusion schemes. Appl. Math. Modell. 19 11 (1995) 640-653
3. Wang Y., and Hutter K. Comparisons of numerical methods with respect to convectively dominated problems. Int. J. Numer. Meth. Fluids 37 (2001) 721-745
4. Ewing R.E., and Wang H. A summary of numerical methods for time-dependent advection-dominated partial differential equations. J. Comput. Appl. Math. 128 (2001) 423-445
5. Hou T.Y., and Lefloch P.G. Why non conservative schemes converge to wrong solutions: error analysis?. Math. Comput. 62 206 (1994) 497-530
6. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 5 (1984)
7. Boris J.P., and Book D.L. Flux corrected transport, I, SHASTA, A fluid transport algorithm that works. J. Comput. Phys. 11 (1973) 38-69
8. P.L. Roe, Numerical algorithms for the linear wave equation, Royal Aircraft Establishment Technical Report 81047, 1981.
9. Vanleer B. Towards the ultimate conservative scheme. II. Monotonicity and conservation combined in a second order scheme. J. Comput. Phys. 14 (1974) 361-370
10. Harten A. High resolution schemes for conservation law. J. Comput. Phys. 49 (1983) 357-393
11. Thomas J.W. Numerical partial differential equations, conservation laws and elliptic equations. Text in Applied Mathematics 33 (1999), Springer
12. Levaque R.J. Numerical methods for conservation laws. Lectures in Mathematics (1999), ETH Zurich, Birkhauser
13. Toro E.F. Riemann Solvers and Numerical methods for Fluid Dynamics, A Practical Introduction. second ed. (1999), Springer
14. C.A.J. Fletcher, Computational Techniques for Fluid Dynamics, Part I, Springer Series in Computational Physics, 1988.
15. Jonathan B., and Levaque R.J. A geometric approach to high resolution schemes. SIAM J. Numer. Anal. 25 2 (1998) 268-284
16. Shu C.W. An overview on high order numerical methods for convection dominated PDEs. In: Hou T.Y., and Tadmor E. (Eds). Hyperbolic Problems: Theory, Numerics, Applications (2003), Springer-Verlag, Berlin 79-88