Since we have finished all the important components of numerical simulation, we can now address a typical gas dynamic problem, one-dimensional shock-tube problem, and see how to produce a practical numerical simulation. An important reason for us to choose this problem as an example is that, we have an analytical solution for it. Thus it is very easy to compare simulation result with analytical solution and to judge the accuracy of the simulation result. To avoid unnecessary complexity, we do not include in this problem the electric field and magnetic field, which are extremely important in MHD simulations. We will go step by step to see how a complete numerical simulation can be achieved.

- Definition of problem
- Boundary condition
- Initial condition
- Time and space discretization and variable arrangement
- Computation scheme