ut + f(u)x= 0
A Beginner's Reading to Numerical Solution for Hyperbolic Conservation Laws:
Books
E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer, 2009, (Read the reviews of this book on Amazon.com)
C. B. Laney, Computational Gasdynamics. Cambridge University Press, 1998. (Read the reviews of this book on Amazon.com)
Articles
H. Nessyahu and E. Tadmor [pdf]
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics 87 (1990), 408-463.
C.-W. Shu [pdf]
Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998, pp.325-432.
D. Levy, G. Puppo and G. Russo [pdf]
Central WENO schemes for hyperbolic systems of conservation laws
Mathematical Modelling and Numerical Analysis 33 (1999), 547-571.
A. Kurganov and E. Tadmor [pdf]
New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
Journal of Computational Physics 160 (2000), 214-282.
Lectures from Nonlinear Conservation Laws and Applications
Institute for Mathematics and its Applications (IMA), Minneapolis MN, July 13-31, 2009
E. Tadmor, Selected topics in approximate solutions of nonlinear conservation laws
C.-W. Shu, Numerical methods for multi-dimensional systems of conservation laws
Useful Links
Central Station - A collection of references on High-Resolution Non-Oscillatory Central Schemes (CSCAMM, University of Maryland)
Conservation Laws - Preprint server (NTNU, Trondheim, Norway)
NA Digest - A collection of articles on topics related to numerical analysis