26 | | Numerical results are presented at the end of chapter 9. These results show that the 2 methods tested, 1) TSRS everywhere, and 2) a non-iterative hybrid scheme using PVRS in smooth flow, and TSRS in sharp gradient flow, both produce results that exactly match up to the Godunov method that uses the ERS. This shows that 1) you can get the same order of accuracy of the Godunov method, using computationally cheaper methods, and 2) using a non-iterative TSRS method can further reduce the computational cost without reducing accuracy of the solution. It is interesting to note that according to Toro, most problems use are able to use a simple PVRS over 90% of grid, and a more sophisticated scheme over the remaining domain. |

| 26 | Numerical results are presented at the end of chapter 9. These results show that the 2 methods tested, 1) TSRS everywhere, and 2) a non-iterative hybrid scheme using PVRS in smooth flow, and TSRS in sharp gradient flow, both produce results that exactly match up to the Godunov method that uses the ERS. This shows that 1) you can get the same order of accuracy of the Godunov method, using computationally cheaper methods, and 2) using a non-iterative hybrid TSRS method can further reduce the computational cost without reducing accuracy of the solution. It is interesting to note that according to Toro, most problems use are able to use a simple PVRS over 90% of grid, and a more sophisticated scheme over the remaining domain. |