Two-dimensional simulation of debris flows over mobile bed: Enhancing the TRENT2D model by using a well-balanced Generalized Roe-type solver

The mathematical description of debris flows over mobile-bed is performed by using a two-phase shallow-water approach. The system of partial differential equations that follows by using the mass and momentum conservation principles is hyperbolic and characterized by a nonconservative nature. This feature, as well as the highly nonlinear relationship between the conserved and the primitive variables, is particularly challenging in the framework of finite-volume, explicit Godunov-type numerical approaches. This paper presents our effort to enhance the capabilities of the TRENT2D model (acronym for Transport in Rapidly Evolutive, Natural Torrent, see Armanini et al., Computers and Geosciences, 2009). Firstly, from a mathematical point of view, the eigenstructure of the original system has been analysed in detail in order to obtain useful information for improving the numerical scheme. Moreover, some previously neglected physical mechanisms, leading to a diffusive behavior, have been investigated and a new term has been added in order to account for them. On the other hand, from a numerical point of view, the original Riemann solver (LHLL), which satisfies only the CC-property, has been substituted with a more accurate well-balanced Generalized Roe solver and the discretization of the diffusive terms has been introduced in the numerical scheme. The application of the two versions of TRENT2D to a set of test cases, both theoretical and real, allows to appreciate the improvement of the new version of the model.

► The TRENT2D shallow debris-flow model has been improved.
► A complete eigenstructure analysis of the model has been performed.
► Diffusive-like mechanisms have been implemented.
► A new well-balanced Generalized Roe approach has been introduced in the numerics.
► Several tests show the capabilities and the limits of the new model.