Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

HIV treatment as prevention: optimising the impact of expanded HIV treatment programmes.

Until now, decisions about how to allocate ART have largely been based on maximising the therapeutic benefit of ART for patients. Since the results of the HPTN 052 study showed efficacy of antiretroviral therapy (ART) in preventing HIV transmission, there has been increased interest in the benefits of ART not only as treatment, but also in prevention. Resources for expanding ART in the short term may be limited, so the question is how to generate the most prevention benefit from realistic potential increases in the availability of ART. Although not a formal systematic review, here we review different ways in which access to ART could be expanded by prioritising access to particular groups based on clinical or behavioural factors. For each group we consider (i) the clinical and epidemiological benefits, (ii) the potential feasibility, acceptability, and equity, and (iii) the affordability and cost-effectiveness of prioritising ART access for that group. In re-evaluating the allocation of ART in light of the new data about ART preventing transmission, the goal should be to create policies that maximise epidemiological and clinical benefit while still being feasible, affordable, acceptable, and equitable