The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

International audienceRandom walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied for two test cases with discontinuous diffusivity, highlighting the advantages of this method

Endovascular Repair of Inflammatory Abdominal Aortic Aneurysms with Special Reference to Concomitant Ureteric Obstruction

AbstractObjectives: to study the technical feasibility and results of endovascular treatment of inflammatory abdominal aortic aneurysms (AAA).Design: prospective study.Material and methods: seven patients underwent endovascular repair of an inflammatory AAA. Five patients (8 ureters) were treated with ureteric stents CT scans were obtained one year.Results: the early technical success rate was 100%. Four ureters remained entrapped at one year. Partial regression of periaortic fibrosis was documented in three patients, while four patients showed no regression.Conclusion: endovascular reconstruction of inflammatory abdominal aneurysms is technically feasible. Further study is warranted with regard to the evolution of the periaortic fibrosis and the possible benefits for patients with concomitant hydronephrosis

Finite element modelling of the Scheldt estuary and the adjacent Belgian/Dutch coastal zone with application to the transport of fecal bacteria

A fundamental problem in coastal modelling is the need to simultaneously consider large- and small-scale processes, especially when local dynamics or local environmental issues are of interest. The approach widely resorted to is based on a nesting strategy by which coarse grid large scale model provide boundary conditions to force fine resolution local models. This is probably the best solution for finite difference methods, needing structured grids. However, the use of structured grids leads to a marked lack of flexibility in the spatial resolution. Another solution is to take advantage of the potential of the more modern finite element methods, which allow the use of unstructured grids in which the mesh size may vary over a wide spectrum. With these methods only one model is required to describe both the larger and the smaller scales.Such a model is use herein, namely the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, http://www.climate.be/SLIM). For one of its first realistic applications, the Scheldt Estuary area is studied. The hydrodynamics is primarily forced by the tide and the neatest way to take it into account is to fix it at the shelf break. This results in a multi-scale problem since the domain boundary lies at the shelf break, and covers about 1000km of the North Sea and 60km of the actual estuary, and ends with a 100km long section of the Scheldt River until Ghent where the river is not more than 50 m wide.Two-dimensional elements are used to simulate the hydrodynamics from the shelf break to Antwerp (80km upstream of the mouth) and one-dimensional elements for the riverine part between Antwerp and Ghent.For first application we consider the transport of faecal bacteria (Escherichia coli) which is an important water quality indicator.The model will be described in detail and the simulation results will be discussed. This modelling exercise actually falls within the framework of the interdisciplinary project TIMOTHY (http://www.climate.be/TIMOTHY) dedicated to the modelling of ecological indicators in the Scheldt area

Lagrangian ocean analysis: fundamentals and practices

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing

Numerical simulation of the three-dimensional tidal circulation in an island's wake

The formation of shallow-water tidal eddies in the lee of an island is studied by means of a three-dimensional marine model. The mathematical and numerical models are detailed. The role of the advection terms, the upwelling velocity and the stresses due to subgrid-scale phenomenons is briefly investigated. Comparison of the numerical results with the available data field is outlined

Simulation mathématique des nappes d'hydrocarbures et comparaison avec les observations par télédétection = Mathematical simulation of oil spill at sea and comparison with observations by remote sensing

A mathematical model of oil spill's transport and spreading is presented. The model differs from previous ones by its capability of taking simultaneously gravity, friction and surface tension into account - allowing the simulation of small experimental spills as well as large accidental spills - and by a new parameterization of surface tension and interface stresses, better adapted to real field conditions. The model is tested by the simulation of in situ experiments where the position and the thickness of the spill are measured by remote sensing. An excellent agreement is found between the model's predictions and the observations