Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

Adaptive re®nement and shock capture in Euler problems 187
Analysis domain
Fig. 6.11 Interaction of an impinging and bow shockwave. 17 Adapted mesh and pressure contours.
1. A detached shock forms in front of the body.
2. A very coarse mesh su ces in front of such a shock where simple free stream ¯ow
continues and the mesh is made `®nite' by a maximum element size prescription.
3. For the same minimum element size a reduction of degrees of freedom is achieved
by re®nement which shows much improved accuracy.
For such hypersonic problems, it is often claimed that special methodologies of
solution need to be used. References 62±64 present quite sophisticated methods for
dealing with such high-speed ¯ows.
In Figs 6.9 and 6.10, we show the results of supersonic Mach 3 ¯ow past a full
cylinder. 56 The mesh (Fig. 6.9(b)) is adapted along the shock front to get a good
resolution of the shock. The mesh behind the cylinder is very ®ne to capture the
recirculatory motion. In Figs 6.9(c) and 6.9(d), the Mach contours are obtained
using the CBS algorithm using the second derivative based shock capture and