Analytical solution for testing debris avalanche numerical models

We present here the analytical solution of a one-dimensional dam-break prob lem over inclined planes. This solution is used to test a numerical model d eveloped for debris avalanches. We consider a dam with infinite length in o ne direction where material is released from rest at the initial instant. W e solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system. The numerical and analyt ical solutions provide for a Coulomb-type friction law at the base of the h ow. The analytical solution is obtained by using the method of characterist ics and describes the flow over a constant slope, provided that the angle i s higher than the friction angle. The numerical model utilizes a finite-dif ference method based on a Godunov-type scheme. Comparison between analytica l and numerical results illustrates the remarkable stability and precision of the numerical method as well as its ability to deal with strong disconti nuities.