Discretization coarsening for the accurate meshless solution of Poisson problems

Meshless methods are nowadays emerging, alternative or subsidiary techniques to classical Finite Element (FE) and Finite Difference (FD) methods, for the numerical solution of Partial Differential Equations (PDE). Among the huge number of proposed meshless methods, the Meshless Petrov–Galerkin (MLPG) class of methods is one of the most promising. Recently, the Direct MLPG (DMLPG) methods were added to the MLPG class. MLPG is a Generalized FE method, while DMLPG is a Generalized FD method. Notwithstanding elegant theoretical anal- ysis of meshless methods have been performed, effective, practical ap- plications rely upon numerical experiments. That is why our paper is focused on performing neat numerical experiments on simple test prob- lems. Adaptive methods are the most efficient for solving many prob- lems, and MLPG techniques are well apt for adaptivity. The adaptive methods for MLPG techniques that one can find in the literature are based upon intricate norm estimations. This paper aims at proposing a simple yet effective technique for coarsening a discretization cloud, by deleting only “useless” nodes, hence allowing for reducing the computa- tional cost without loosing accuracy. We analyze the effectiveness and efficiency of MLPG and DMLPG methods when coupled with our coarsening procedure. We point out some differences in the performances of these two methods

Hydrogeological effects of dredging navigable canals through lagoon shallows. A case study in Venice

For the first time a comprehensive investigation has been carried out to quantify the possible effects of dredging a navigable canal on the hydrogeological system underlying a coastal lagoon. The study is focused on the Venice Lagoon, Italy, where the port authority is planning to open a new 10m deep and 3km long canal to connect the city passenger terminal to the central lagoon inlet, thus avoiding the passage of large cruise ships through the historic center of Venice. A modeling study has been developed to evaluate the short (minutes), medium (months), and long (decades) term processes of water and pollutant exchange between the shallow aquifer system and the lagoon, possibly enhanced by the canal excavation, and ship wakes. An in-depth characterization of the lagoon subsurface along the channel has supported the numerical modeling. Piezometer and sea level records, geophysical acquisitions, laboratory analyses of groundwater and sediment samples (chemical analyses and ecotoxicity testing), and the outcome of 3-D hydrodynamic and computational fluid dynamic (CFD) models have been used to set up and calibrate the subsurface multi-model approach. The numerical outcomes allow us to quantify the groundwater volume and estimate the mass of anthropogenic contaminants (As, Cd, Cu, Cr, Hg, Pb, Se) likely leaked from the nearby industrial area over the past decades, and released into the lagoon from the canal bed by the action of depression waves generated by ships. Moreover, the model outcomes help to understand the effect of the hydrogeological layering on the propagation of the tidal fluctuation and salt concentration into the shallow brackish aquifers underlying the lagoon bottom.Facultad de Ciencias Naturales y MuseoCentro de Investigaciones Geológica

Hydrogeological effects of dredging navigable canals through lagoon shallows. A case study in Venice

For the first time a comprehensive investigation has been carried out to quantify the possible effects of dredging a navigable canal on the hydrogeological system underlying a coastal lagoon. The study is focused on the Venice Lagoon, Italy, where the port authority is planning to open a new 10m deep and 3km long canal to connect the city passenger terminal to the central lagoon inlet, thus avoiding the passage of large cruise ships through the historic center of Venice. A modeling study has been developed to evaluate the short (minutes), medium (months), and long (decades) term processes of water and pollutant exchange between the shallow aquifer system and the lagoon, possibly enhanced by the canal excavation, and ship wakes. An in-depth characterization of the lagoon subsurface along the channel has supported the numerical modeling. Piezometer and sea level records, geophysical acquisitions, laboratory analyses of groundwater and sediment samples (chemical analyses and ecotoxicity testing), and the outcome of 3-D hydrodynamic and computational fluid dynamic (CFD) models have been used to set up and calibrate the subsurface multi-model approach. The numerical outcomes allow us to quantify the groundwater volume and estimate the mass of anthropogenic contaminants (As, Cd, Cu, Cr, Hg, Pb, Se) likely leaked from the nearby industrial area over the past decades, and released into the lagoon from the canal bed by the action of depression waves generated by ships. Moreover, the model outcomes help to understand the effect of the hydrogeological layering on the propagation of the tidal fluctuation and salt concentration into the shallow brackish aquifers underlying the lagoon bottom.Facultad de Ciencias Naturales y MuseoCentro de Investigaciones Geológica

Numerical Methods for the solution of Hyperbolic Conservation Laws

In this paper we consider numerical approximations of hyperbolic conservation laws in the one-dimensional scalar case, by studying Godunov and van Leer's methods. Before to present the numerical treatment of hyperbolic conservation laws, a theoretical introduction is given together with the definition of the Riemann problem. Next the numerical schemes are discussed. We also present numerical experiments for the linear advection equation and Burgers' equation. The first equation is used for modeling discontinuities in fluid dynamics; the second one is used for modeling shocks and rarefaction waves. In this way we can compare the different behavior of both schemes

High-order transverse schemes for the numerical solution of PDEs

Many existing numerical schemes for the solution of initial-boundary value problems for partial differential equations can be derived by the method of lines. The PDEs are converted into a system of ordinary differential equations either with initial conditions (longitudinal scheme) or with boundary conditions (transverse scheme). In particular, this paper studies the performance of the transverse scheme in combination with boundary value methods. Moreover, we do not restrict the semi-discretization by the usual first- or second-order finite-difference approximations to replace the derivative with respect to time, but we use high-order formulae

Laboratorio di calcolo numerico. Apllicazioni con Matlab e Octave

supporto didattico per gli studenti di Ingegneri

Mixed finite elements and finite volumes for solutions to flow and transport problem of heavy radioactive contaminants in porous media

In questo lavoro \`e stato sviluppato un metodo numerico accurato ed efficiente per risolvere problemi accoppiati di flusso e trasporto di contaminanti radioattivi in acque sotterranee. Lo studio \`e finalizzato, soprattutto, allo studio del sito pi\`u contaminato del mondo, il lago Karachai, negli Urali del Sud (Russia)

Programmare in Matlab. Guida passo dopo passo

Programmare vuol dire saper tradurre un algoritmo in un linguaggio specializzato in modo che il computer possa risolvere per noi problemi molto complicati e, in molti casi, difficilmente risolvibili con carta e penna. Questo libro insegna come risolvere problemi di matematica e di ingegneria lavorando in MATLAB e applicando metodi numerici di base (quali, ad esempio, metodi per risolvere zeri di funzione, per interpolare e approssimare dati, per integrare funzioni o risolvere semplici equazioni differenziali o affrontare problemi di algebra lineare). Numerosi esercizi completano ogni capitolo

Elementi Finiti Misti e Volumi Finiti per la soluzione del problema di flusso e trasporto di contaminanti radioattivi pesanti in mezzi porosi

In questo lavoro \`e stato sviluppato un metodo numerico accurato ed efficiente per risolvere problemi accoppiati di flusso e trasporto di contaminanti radioattivi in acque sotterranee. Lo studio \`e finalizzato, soprattutto, allo studio del sito pi\`u contaminato del mondo, il lago Karachai, negli Urali del Sud (Russia). Questo lago fu utilizzato, fin dagli anni cinquanta, per immagazzinarvi residui radioattivi provenienti da esperimenti nucleari e, successivamente, come discarica dei rifiuti liquidi radioattivi della centrale nucleare di Mayak