The multigrid method: Fast relaxation

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g. 4 x 2 mesh cells) to fine (e.g. 64 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with optimal iterations on the finest grid. To date the method was applied quite successfully to the solution of the transonic small-disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is the example studied, with meshes of both constant and variable step size

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size

Conservative versus nonconservative differencing: Transonic streamline shape effects

Streamline patterns calculated from transonic flow solutions which were generated using a nonconservative finite difference scheme showed a net streamtube area increase far downstream of the disturbance indicating that the global mass balance was destroyed. Similar calculations using a conservative finite difference scheme did not show this defect. Comparative calculations were made at several free-stream Mach numbers for nonlifting flow over a 10% parabolic arc airfoil. In a transonic internal flow, this nonconservation of mass may be of greater concern than in an unconfined external flow

Health promotion education in changing and challenging times: reflections from the UK

Health education has changed in numerous ways since the inception of this journal, with many developments moving the discipline forward in ways that perhaps were not envisaged 75 years ago. Whilst there have been reported concerns about the decline of the discipline of health promotion and therefore associated worries about education, the contemporary evidence base has grown (Woodall et al 2017 in press), which we argue supports the delivery of quality education and the development of capable, skilled practitioners. Pedagogy has further developed too, and technology now enables health education to have a broader global reach through online teaching, social media and open-access publications. Many global challenges remain, and the UK context is one in which both health education and indeed practice faces major trials despite the traditions and approaches to health education developed by those educated and trained in this setting over a period of many years. We argue that the broader UK policy environment remains a challenge to current health promotion education, research and practice