18 | | 3. Using p* and u*, the solution is sampled at every point on the grid. The position is determined by comparing speeds in the grid. First it is determined whether point is on left or right side of the contact discontinuity. (The speed of the contact disc. is given by u*) |

| 18 | 3. Using p* and u*, the solution is sampled at every point on the grid. The position is determined by comparing speeds in the grid. First it is determined whether point is on left or right side of the contact discontinuity. (The speed of the contact disc. is given by u*). If s<u*, point is on left of the contact. If s>u*, it is on right. |

| 19 | |

| 20 | 4. Next, given the initial L- and R- pressure compared to P*, the type of wave is determined. If p_L < p* - left wave is shock else it is a rarefaction. If p_R < p*, wave is shock else it is a rarefaction. Note, this assumes waves always travel away from the contact. |

| 21 | |

| 22 | 5. Once waves present are known, then the different speeds in the grid are compared to the speeds of the different left and right waves. The appropriate analytic expression is then chosen, based on relative position to wave. |