THE ADAPTATION OF STRUCTURED GRIDS TO NUMERICAL-SOLUTIONS FOR TRANSONIC FLOW

Methods are described for adapting a structured grid in response to a numerical solution, so that grid nodes become clustered where 'solution activity' is high, the aim being to reduce solution truncation errors without increasing the number of grid nodes employed, or modifying their connectivity. After introducing the concept of 'equidistribution', and discussing options for the measurement of solution activity, the paper concentrates mainly on two alternative techniques for producing smooth, regular grids which apply constraints on this equidistribution. The first technique described is based on a spring analogy, and is demonstrated here with examples of two- and three-dimensional inviscid flows, and with two-dimensional viscous flows. The second technique employs a Poisson grid generator with adaptive terms included in the control functions, and is demonstrated with a two-dimensional inviscid flow. A third method is then introduced, termed the LPE method, which allows a compromise to be chosen between grids generated by solving Laplace equations, Poisson equations and equidistribution equations. Since this method is still being developed, results are currently limited and tentative.