CENTRAL-DIFFERENCE AND UPWIND-BIASED SCHEMES FOR STEADY AND UNSTEADY EULER AEROFOIL COMPUTATIONS

Two numerical methods are presented for the computation of steady and unsteady Euler flows. These are applied to steady and unsteady flows a bout the NACA 0012 aerofoil, using structured grids generated by the t ransfinite interpolation technique. An explicit central-difference sch eme is produced based on the cell-vertex method of Ni modified by Hall . The method is second-order accurate in time and space, and with flow quantities stored at boundaries the boundary conditions are simple to apply. This is a definite advantage over the cell-centred approach of Jameson, where extrapolation of the flow quantities is required at th e boundaries, making unsteady boundary conditions difficult to apply. An explicit upwind-biased scheme is also produced, based on the flux-v ector splitting of van Leer. The method adopts a three stage Runge-Kut ta time-stepping scheme and a high-order spatial discretisation which is formally third-order accurate for one-dimensional calculations. The upwind scheme is shown to be slightly more accurate than the central- difference scheme for steady aerofoil flows, but it is not clear which is the more accurate for unsteady aerofoil hows. However, the central -difference scheme requires less than half the CPU time of the upwind- difference scheme, and hence is attractive, especially when considerin g three-dimensional flows. The transfinite interpolation technique is ideal for generating moving structured grids due to its simplicity, an d grid speeds are available algebraically by the same interpolation as grid points. The method is also ideal for use in a multiblock approac h.