Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

Using Habitat Equivalency Analysis to Assess the Cost Effectiveness of Restoration Outcomes in Four Institutional Contexts

At the national level, with a fixed amount of resources available for public investment in the restoration of biodiversity, it is difficult to prioritize alternative restoration projects. One way to do this is to assess the level of ecosystem services delivered by these projects and to compare them with their costs. The challenge is to derive a common unit of measurement for ecosystem services in order to compare projects which are carried out in different institutional contexts having different goals (application of environmental laws, management of natural reserves, etc.). This paper assesses the use of habitat equivalency analysis (HEA) as a tool to evaluate ecosystem services provided by restoration projects developed in different institutional contexts. This tool was initially developed to quantify the level of ecosystem services required to compensate for non-market impacts coming from accidental pollution in the US. In this paper, HEA is used to assess the cost effectiveness of several restoration projects in relation to different environmental policies, using case studies based in France. Four case studies were used: the creation of a market for wetlands, public acceptance of a port development project, the rehabilitation of marshes to mitigate nitrate loading to the sea, and the restoration of streams in a protected area. Our main conclusion is that HEA can provide a simple tool to clarify the objectives of restoration projects, to compare the cost and effectiveness of these projects, and to carry out trade-offs, without requiring significant amounts of human or technical resources.