Search results for "numerical methods"

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…

Detection of the Lowest-Lying Odd-Parity Atomic Levels in Actinium

2020

Two lowest-energy odd-parity atomic levels of actinium, 7s27pP21/2o, 7s27pP23/2o, were observed via two-step resonant laser-ionization spectroscopy and their respective energies were measured to be 7477.36(4) and 12 276.59(2) cm-1. The lifetimes of these states were determined as 668(11) and 255(7) ns, respectively. In addition, we observed the effect of the hyperfine structure on the line for the transition to P23/2o. These properties were calculated using a hybrid approach that combines configuration interaction and coupled-cluster methods, in good agreement with the experiment. The data are of relevance for understanding the complex atomic spectra of actinides and for developing efficien…

Numerical methods in the design process of a sailing yacht

2014

Minimally implicit Runge-Kutta methods for Resistive Relativistic MHD

2016

The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative …

Global sensitivity analysis in environmental water quality modelling: Where do we stand?

2014

Global sensitivity analysis (GSA) is a valuable tool to support the use of mathematical models for environmental systems. During the last years the water quality modelling field has embraced the use of GSA. Environmental water quality modellers have tried to transfer the knowledge and experience acquired in other disciplines. The main objective of this paper is to provide an informed problem statement of the issues surrounding GSA applications in the environmental water quality modelling field. Specifically, this paper aims at identifying, for each GSA method, the potential use, the critical issues to be solved and the limits identified in a comprehensive literature review. The paper shows …

New Indicators of Approximation Errors for Problems in Continuum Mechanics

2010

In this paper we present a new error indicator for approximate solutions of elliptic problems. We discuss error indication with the paradigm of the diffusion problem, however the techniques are easily adaptable to more complicated elliptic problems, for example to linear elasticity, viscous flow models and electromagnetic models. The proposed indicator does not contain mesh dependent constants and it admits parallelization. nonPeerReviewed

Etude numérique d'équations aux dérivées partielles non linéaires et dispersives

2011

Numerical analysis becomes a powerful resource in the study of partial differential equations (PDEs), allowing to illustrate existing theorems and find conjectures. By using sophisticated methods, questions which seem inaccessible before, like rapid oscillations or blow-up of solutions can be addressed in an approached way. Rapid oscillations in solutions are observed in dispersive PDEs without dissipation where solutions of the corresponding PDEs without dispersion present shocks. To solve numerically these oscillations, the use of efficient methods without using artificial numerical dissipation is necessary, in particular in the study of PDEs in some dimensions, done in this work. As stud…

Increasing understanding and confidence in THM simulations of engineered barrier systems

2020

Previous studies on the modelling of coupled thermo-hydro-mechanical (THM) processes in bentonite-based engineered barrier systems (EBSs) showed the sensitivity of the output quantities to changes in the input parameters. To investigate the effects of uncertainties on the modelling results, to improve the understanding of the coupled processes active in the repository near field and to gain in-depth understanding of model uncertainties of different codes, a sensitivity analysis and code comparison of EBS simulations was performed within the Task Force on Engineered Barrier Systems. The analysis included variations in material parameter values, boundary and initial conditions, considered phy…

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…

Fast simulation of muons produced at the SHiP experiment using Generative Adversarial Networks

2019

This paper presents a fast approach to simulating muons produced in interactions of the SPS proton beams with the target of the SHiP experiment. The SHiP experiment will be able to search for new long-lived particles produced in a 400~GeV$/c$ SPS proton beam dump and which travel distances between fifty metres and tens of kilometers. The SHiP detector needs to operate under ultra-low background conditions and requires large simulated samples of muon induced background processes. Through the use of Generative Adversarial Networks it is possible to emulate the simulation of the interaction of 400~GeV$/c$ proton beams with the SHiP target, an otherwise computationally intensive process. For th…