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pure and applied geophysics

, Volume 157, Issue 6–8, pp 1081–1096 | Cite as

Analytical Solution for Testing Debris Avalanche Numerical Models

  • A. Mangeney
  • P. Heinrich
  • R. Roche

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.

Key Words: Analytical solution, shallow-water model, dam-break, debris avalanche. 

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Copyright information

© Birkhäuser Verlag Basel, 1999

Authors and Affiliations

  • A. Mangeney
    • 1
  • P. Heinrich
    • 1
  • R. Roche
    • 1
  1. 1.Laboratoire de Détection et de Géophysique, CEA, Bruyères-le-Châtel, France. E-mail: anne.mangeney@ccr.jussieu.frFR

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