The design of characterizing-integral schemes and the application to the shallow water wave problems

in this paper a new approach for designing upwind type schemes-the characterizingintegral method and its applied skills are introduced. The method is simple, convenient and eff ective. And the method isn't only limited to conservation laws unlike other methods and may be easily extended to multi-dimension problems. Furthermore, the numerical dissipation of the method can be flexibly regulated, so that it is especially suitable for solving various discontinuity problems. The paper shows us now to use this approach to simulate deformation and breaking of a nonlinear shallow water wave on a gentle slope, and to compute two-dimensional dam failure problem.