A new analytical solution for testing debris avalanche numerical models

Abstract

An analytical solution to a debris avalanche problem in the one dimensional topography-linked coordinate system was found by Man- geney, Heinrich, and Roche [Pure Appl. Geophys., 157:1081-1096, 2000]. We derive an analytical solution to a debris avalanche problem in the standard Cartesian coordinate system. Characteristics and a transformation technique obtain the analytical solution. This analyti-cal solution is used to test finite volume methods with reconstruction of the conserved quantities based on: either stage, height, and veloc- ity; or stage, height, and momentum. Numerical tests show that the finite volume method with reconstruction based on stage, height, and momentum is slightly more accurate in solving the debris avalanche problem. © Austral. Mathematical Soc. 2011.