Sharp Error Estimates on a Stochastic Structure-Preserving Scheme in Computing Effective Diffusivity of 3D Chaotic Flows

Symmetric Error Structure in Stochastic DEA

The effective diffusivity of cellular flows

In the previous chapter we dealt with unidirectional flows. Now we turn to the slightly more complicated case of incompressible two-dimensional cellular flows. The velocity field can be obtained from a streamfunction ψ(x, y) according to our usual convention u = (u, v) = (−ψy, ψx). The domain is a periodic array of square cells, each with side , so that the streamfunction has the periodicity ψ(...

symmetric error structure in stochastic dea

Robustness of an Effective Diffusivity Diagnostic in Oceanic Flows

The robustness of Nakamura’s effective diffusivity diagnostic for quantifying eddy diffusivities of tracers within a streamwise-average framework is carefully examined in an oceanographic context, and the limits of its applicability are detailed. The near-surface Southern Ocean geostrophic flow, obtained from altimetric observations, is chosen for particular examination since it exhibits strong...

A Posteriori Error Estimates Based on the Polynomial Preserving Recovery

Superconvergence of order O(h), for some ρ > 0, is established for the gradient recovered with the Polynomial Preserving Recovery (PPR) when the mesh is mildly structured. Consequently, the PPR-recovered gradient can be used in building an asymptotically exact a posteriori error estimator.