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The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

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Objective: To assess the clinical and cost-effectiveness of cognitive rehabilitation for attention and memory problems in people with multiple sclerosis. Design: Multicentre, pragmatic, randomized controlled trial. Setting: Community Participants: People with multiple sclerosis aged 18–69 years, who reported cognitive problems in daily life and had cognitive problems on standardized assessment. Interventions: A group cognitive rehabilitation programme delivered in 10 weekly sessions in comparison with usual care. Main measures: The primary outcome was the Multiple Sclerosis Impact Scale Psychological subscale at 12 months after randomization. Secondary outcomes included measures of everyday memory problems, mood, fatigue, cognitive abilities and employment at 6 and 12 months after randomization. Results: In all, 245 participants were allocated to cognitive rehabilitation and 204 to usual care. Mean Multiple Sclerosis Impact Scale Psychological at 12 months was 22.2 (SD = 6.1) for cognitive rehabilitation and 23.4 (SD = 6.0) for usual care group; adjusted difference −0.6, 95% confidence interval (CI) = −1.5 to 0.3, P = 0.20. No differences were observed in cognitive abilities, fatigue or employment. There were small differences in favour of cognitive rehabilitation for the Multiple Sclerosis Impact Scale Psychological at 6 months and everyday memory and mood at 6 and 12 months. There was no evidence of an effect on costs (−£808; 95% CI = −£2248 to £632) or on quality-adjusted life year gain (0.00; 95% CI = −0.01 to 0.02). Conclusion: This rehabilitation programme had no long-term benefits on the impact of multiple sclerosis on quality of life, but there was some evidence of an effect on everyday memory problems and mood.