depends on the conserved quantities via
An overshoot in velocity may lead to
(or an attempt to access values beyond the limits of a tabulated equation of state).
- This restriction is so severe that in some cases the
conservation of total energy
might be given up in favor of a (non-conservative) formulation
where the positivity of the internal energy is guaranteed.
- The total variation of e.g. density, pressure,...of the true solution can increase
stability arguments no longer hold.