| 147 | As with all methods of linearizing the Euler equations, discontinuities are resolved, but continuous fan-like structures are not. Thus the Roe solver has trouble solving the RP inside of a sonic (aka transonic) rarefaction wave (see below figure), but less of a problem with contacts and shocks. This problem is refered to as the 'entropy problem', because the method treats the rarefaction wave as a 'rarefaction shock', which is entropy violating. Recall that the entropy condition that must be satisfied for a discontinuous wave jump is that the characteristics ''run into'' each other. That is, Sb>S>Sa, where Sb is the speed BEHIND the wave, S is the speed of the wave, and Sa is the speed ahead of the wave. There was a later 'entropy fix' developed for the Roe solver that corrected this issue. |