Search results for "numerical method"
showing 10 items of 82 documents
Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes
2013
Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure 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…
Global sensitivity analysis for urban water quality modelling: Terminology, convergence and comparison of different methods
2015
Abstract Sensitivity analysis represents an important step in improving the understanding and use of environmental models. Indeed, by means of global sensitivity analysis (GSA), modellers may identify both important ( factor prioritisation ) and non-influential ( factor fixing ) model factors. No general rule has yet been defined for verifying the convergence of the GSA methods. In order to fill this gap this paper presents a convergence analysis of three widely used GSA methods (SRC, Extended FAST and Morris screening) for an urban drainage stormwater quality–quantity model. After the convergence was achieved the results of each method were compared. In particular, a discussion on peculiar…
Global sensitivity analysis in wastewater treatment modelling
2019
Global sensitivity analysis (GSA) is a valuable tool to support the use of mathematical models. GSA allows the identifcation of the effect of model and input factor uncertainty on the model response, also considering the effect due to the interactions among factors. During recent years, the wastewater modelling feld has embraced the use of GSA. Wastewater modellers have tried to transfer the knowledge and experience from other disciplines and other water modelling felds.
Rockfall hazard assessment of the Monte Gallo Oriented Nature Reserve area (Southern Italy)
2021
Abstract The Monte Gallo area is a carbonate relief that develops a significant nature reserve and highly attracts tourism to the urbanized area of the City of Palermo (Southern Italy). The slopes are affected by several rockfall events, which have also caused death, injuries, material damage, and a strong social and economic impact. Here, a detailed geological and geotechnical study to assess the rockfall hazard relating to two sectors of the mount has been carried out. The hazard assessment at the slope scale was performed based on geological, geomorphological, geomechanical, and seismic analysis. Using both analytical and empirical methods and by means of different software, the reconstr…
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
2011
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 t…
Mathematical and numerical analysis of initial boundary valueproblem for a linear nonlocal equation
2019
We propose and study a numerical scheme for bounded distributional solutions of the initial boundary value problem for the anomalous diffusion equation ∂t u +Lμu = 0 in a bounded domain supplemented with inhomogeneous boundary conditions. Here Lμ is a class of nonlocal operators including fractional Laplacian. ⃝c 2019 InternationalAssociation forMathematics andComputers in Simulation (IMACS). Published by ElsevierB.V.All rights reserved.
A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model
2007
Abstract A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are…
A numerical meshless particle method in solving the magnetoencephalography forward problem
2012
In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…
A multi-technique simultaneous approach for the design of a sailing yacht
2015
In this paper, most significant steps involved during the whole process of designing a sailing yacht are outlined. In particular, a novel simultaneous approach has been proposed to optimize the design process of a sailing yacht. Analytical resistance prediction models are simultaneously used with CAD systems and computational fluid dynamics tools to find, in the more effective way, the best solution for the chosen design conditions. As a general rule, in fact, once the target point has been decided, task of the designer is the definition of those systems of aerodynamic and hydrodynamic forces that are in equilibrium when the boat sails at its target. Unfortunately, a multi-purpose yacht doe…
Anisotropic potential of velocity fields in real fluids: Application to the MAST solution of shallow water equations
2013
In the present paper it is first shown that, due to their structure, the general governing equations of uncompressible real fluids can be regarded as an "anisotropic" potential flow problem and closed streamlines cannot occur at any time. For a discretized velocity field, a fast iterative procedure is proposed to order the computational elements at the beginning of each time level, allowing a sequential solution element by element of the advection problem. Some closed circuits could appear due to the discretization error and the elements involved in these circuits could not be ordered. We prove in the paper that the total flux of these not ordered elements goes to zero by refining the compu…