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

Abstract

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. 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.

A robust coupled model for solute transport driven by severe flow conditions

“…Among them, the diffusion-wave models have gained particular popularity due to the use of substantially simplified governing equations and hence the possibility of increased computational efficiency (e.g. Bates and De Roo, 2000;Bates et al, 2010;Aric o et al, 2011;. Aric o et al (2011) and several references therein provided a more detailed discussion.…”

A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

“…Both local and global mass balances are attained (see in Aricò et al (2011Aricò et al ( , 2013a ) the proof for the hydrostatic model). The solution of the non-hydrostatic problem relies on the local mass balance, where the surface horizontal fluxes balance the vertical ones (see Eqs.…”

“…(42,b), as well as the M -property and the positive definite condition for the matrix of system ( 35 ). Additional comments concerning the formulation of the flux coefficients can be found in Aricò et al (2011Aricò et al ( , 2013aAricò et al ( , 2013b. A preconditioned Conjugate Gradient method is adopted for the solution of the system, with incomplete Cholesky preconditioning.…”

“…We adopt unstructured triangular Generalized Delaunay (GD) meshes ( Aricò et al, 2011 ) for spatial discretization of the domain. We briefly describe the main mesh properties for reader's comprehension.…”

Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver

“…To facilitate the reader, we briefly remind some basic concepts and nomenclatures of the unstructured triangular Generalized Delaunay (GD) meshes [29] adopted in the present study to discretize the domain. Ω is a 2D bounded domain and T h an unstructured triangulation of Ω .…”