155 | | Here is an example of the Roe solver poorly computing the flow inside of a left rarefaction. As you can see, it computes the solution as if there was a discontinuity inside of the wave, not a continuous fan. |

| 155 | The waves are as follows: (a) left supersonic shock, (b) right supersonic shock, (c) left supersonic rarefaction, (d) right supersonic rarefaction, (e) transonic or sonic rarefaction. |

| 156 | |

| 157 | Here is an example of the Roe solver poorly computing the flow inside of a left sonic rarefaction. As you can see, it computes the solution as if there was a discontinuity inside of the wave, not a continuous fan. Note the sonic point inside of the wave is where the eigenvalue for the left wave, Lambda1 = u-a = 0. Throughout the wave, the eigenvalue should change sign through this sonic point. |