This paper proposes a two-dimensional (2D) model for the analysis
of the propagation of fast landslides involving a ﬂuidized material
such as debris and mud ﬂows, ﬂowslides and avalanching ﬂows.
The model is based on the Navier–Stokes depth-integrated equations.
To incorporate the effect of steep slopes and centrifugal forces
due to the high velocities characterizing the ﬂowslides and the
bed curvature, a curvilinear system of reference is used. The corresponding
equations of motion are complemented by depth-averaged constitutive
equations and bed friction laws. The resulting set of differential
equations are solved using the two-step Taylor–Galerkin algorithm.
This algorithm has been used by the authors to solve hydraulic and
dam-break problems using the ﬁnite element method. Owing to the
importance of the source term compared to the advection component,
the proposed algorithm follows a splitting scheme using a fourth-order
Runge–Kutta method for integrating the friction and slope components.
The performance of the overall approach has been checked in a number
of examples. The analysis of the results provides insights into the
key elements of the model and shows the adequacy of the method to
solve real problems where merging and splitting of the ﬂow occur.
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