Publications (10) View all
-
Dataset: article
-
Dataset: article
-
Article: Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes
[show abstract] [hide abstract]
ABSTRACT: a b s t r a c t Transport problems occurring in porous media and including convection, diffusion and chemical reac-tions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical pro-cedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The transport problem is solved applying a prediction/correction procedure. The prediction step analytically solves the convec-tive/reactive components in the context of a MAST Finite Volume scheme. The correction step computes the anisotropic diffusive components in the context of a recently proposed Finite Elements scheme. Massa balance is locally and globally satisfied in all the solution steps. Convergence order and computa-tional costs are investigated and model results are compared with literature ones.Advances in Water Resources 10/2012; · 2.45 Impact Factor -
Article: The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media.
J. Comput. Physics. 01/2012; 231:1387-1425. -
Article: Author's personal copy MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
[show abstract] [hide abstract]
ABSTRACT: a b s t r a c t A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstruc-tured 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 con-forming 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 sug-gested, 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 compu-tational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discret-ized 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 com-pared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented.Advances in Water Resources 10/2011; · 2.45 Impact Factor
