High-resolution finite volume methods for the shallow water equations with bathymetry and dry states
by Randall J. LeVeque and David L. George
In Advanced Numerical Models for Simulationg Tsunami Waves and Runup, P. L-F. Liu, H. Yeh, C. Synolakis, eds., Advances in Coastal and Ocean Engineering, Vol 10, pp. 43-73, World Scientific, 2007.

These are the proceedings of the Third International Workshop on Long-Wave Runup Models, Catalina, 2004.

Abstract. We give a brief review of the wave-propagation algorithm, a high-resolution finite volume method for solving hyperbolic systems of conservation laws. These methods require a Riemann solver to resolve the jump in variables at each cell interface into waves. We present a Riemann solver for the shallow water equations that works robustly with bathymetry and dry states. This method is implemented in clawpack and applied to benchmark problems from the Third International Workshop on Long-Wave Runup Models, including a two-dimensional simulation of runup during the 1993 tsunami event on Okushiri Island. Comparison is made with wave tank experimental data provided for the workshop. Some preliminary results using adaptive mesh refinement on the 26 December 2004 Sumatra event are also presented.

Preprint (revised January 11, 2006): catalina.pdf

Simulations to accompany this paper:

• Benchmark problems
• Results on the 26 December 2004 Sumatra event.

Other work on tsunami modeling

bibtex entry:

@InProceedings{rjl-george:catalina04,
  author =       "R. J. LeVeque and D. L. George",
  title =        "High-resolution finite volume methods for the shallow
                 water equations with bathymetry and dry states",
  booktitle =    "Advanced Numerical Models for Simulationg Tsunami Waves
and Runup",
  editor =       "P. L-F. Liu, H. Yeh, C.  Synolakis",
  year =         "2007",
  pages =        "43-73",
  note = "http://faculty.washington.edu/rjl/pubs/catalina04/"
}