Evaluation and reduction of numerical diffusion effects in viscous aerofoil flow calculations
The Reynolds-averaged Navier-Stokes (RANS) equations form the most accurate model of viscous flow which can currently be solved computationally on a routine basis for practical engineering problems, given the size and cost of present-day computers. Before RANS solution methods can be used with confidence for the design of aircraft components, a number of areas related to solution accuracy must be investigated, one of which is numerical diffusion. Numerical diffusion, arising from the discrete solution method employed, is necessary to ensure numerical stability, but if too much is included the ability to predict physical phenomena (particularly diffusive ones) accurately can be seriously impaired, with obvious implications for the rational assessmenot f turbulence models. The amount of numerical diffusion in solutions of the RANS equations is evaluated in the present work using two currently popular algorithms, for aerofoil flow test cases. The effect of the numerical diffusion on the prediction of physical processes is investigated, as is the behaviour of the numerical diffusion and corresponding solution when grid quality and algorithm smoothing parameters are varied. Results are presented in two ways, line diagrams giving detailed information along individual grid lines, and contour plots (showing a quantity called the Numerical Diffusion Ratio, NDR) giving overall information on accuracy of the solution throughout the field. The level of numerical diffusion in certain parts of the solution is shown to be unacceptably high in a number of cases. Methods for modifying the NDR are investigated, with the aim of making it suitable for use as a "weighting function" for guiding automatic grid adaptation, to improve solution accuracy. It is shown that some of the modified forms of NDR can be used successfully in this manner. The advantages and disadvantages of using such a solution-accuracy measure (as opposed to the usual solution-activity measures) are discussed and some conclusions and recommendations are made.