Abstract
—We present here the analytical solution of a one-dimensional dam-break problem over inclined planes. This solution is used to test a numerical model developed for debris avalanches. We consider a dam with infinite length in one direction where material is released from rest at the initial instant. We solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system. The numerical and analytical solutions provide for a Coulomb-type friction law at the base of the flow. The analytical solution is obtained by using the method of characteristics and describes the flow over a constant slope, provided that the angle is higher than the friction angle. The numerical model utilizes a finite-difference method based on a Godunov-type scheme. Comparison between analytical and numerical results illustrates the remarkable stability and precision of the numerical method as well as its ability to deal with strong discontinuities.
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Received April 28, 1998, revised October 10, 1998, accepted October 30, 1998
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Mangeney, A., Heinrich, P. & Roche, R. Analytical Solution for Testing Debris Avalanche Numerical Models . Pure appl. geophys. 157, 1081–1096 (2000). https://doi.org/10.1007/s000240050018
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DOI: https://doi.org/10.1007/s000240050018