3. Conclusion

The methods described here are a good starting point, but rarely the end of the story. Even without talking about adding terms to the equations to model other phenomena, there are competing techniques for all numerical points: first-order schemes, high-order extensions, taking viscosity into account, and so on. Their effectiveness depends on the configuration, but often also on the programming style and the particular skills of the user. There are sometimes bad choices, but no uniformly optimal ones.

Readers are therefore encouraged to try them out for themselves, to see for themselves the difficulties or the effect of a particular choice. For this, a dedicated modular code is a good investment of time.