Two numerical methods are presented for the computation
of steady and unsteady Euler flows. These are
applied to steady and unsteady flows about the NACA
0012 aerofoil, using structured grids generated by
the transfinite interpolation technique. An explicit
central-difference scheme 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 the boundaries, making unsteady
boundary conditions difficult to apply. An explicit
upwind-biased scheme is also produced, based on the
flux-vector splitting of van Leer. The method adopts
a three stage Runge-Kutta 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 flows. However, the central-difference
scheme requires less than half the CPU time of the
upwind-difference scheme, and hence is attractive,
especially when considering three-dimensional flows.
The transfinite interpolation technique is ideal for
generating moving structured grids due to its
simplicity, and grid speeds are available
algebraically by the same interpolation as grid
points. The method is also ideal for use in a
multi-block approach.