Zdas,
I really like and adhere to your approach.
This also remind a course I have attended long time ago on numerical methods. The Teacher was a master of computational methods.
But because he was a real engineer instead of a mathematician, although mastering the subject of numerical methods, he always told us to avoid using numerical methods when possible. What to use instead ? try to use basic equations, to define order of magnitude first.
Have a physical understanding of what is going there by defining the amplitude of the variables (velocities, pressures, concentrations etc.) by use of simple (analytical) methods. When you build that physical screening then "maybe" move ahead with numerical methods but with great care (avoid if possible to deal fluid dynamics problems). He also used to tell us that validation of numerical results is not via comparison with experiments, but it has to be mathematical, indeed by bounding the results with upper/lower limits for instance using the order of magnitude philosophy mentioned before.
I really liked this teacher and the caution and the serious in dealing with problems of mother nature.
That is why I say back to the liquid carry over topic, it was good to know about how things deviate from theoretical models.
It is also good to know which application requires accuracy and good confidence and on which one it suffices to have some sort of estimates.