MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes

Abstract

A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains the Delaunay condition for all the triangle sides without changing the original nodes location and also maintains the internal boundaries. The original governing system is solved applying a fractional time step procedure, that solves consecutively a convective prediction system and a diffusive correction system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system of the order of the number of computational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discretized formulation of the governing equations allows to handle also wetting and drying processes without any additional specific treatment. Local energy dissipations, mainly the effect of vertical walls and hydraulic jumps, can be easily included in the model. Several numerical experiments have been carried out in order to test (1) the stability of the proposed model with regard to the size of the Courant number and to the mesh irregularity, (2) its computational performance, (3) the convergence order by means of mesh refinement. The model results are also compared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented.