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Motivations

Currently, the unphysically high velocity and energy can be obtained by the fluid solver without being caught and corrected.

For example, when the density is $+\varepsilon$ to machine precision while the momentum density is finite after the update, we can get huge kinetic energy, which is not physical. And this high energy can have a tremendous dynamical effect in the simulations later. With the check, we can avoid keeping running with an unrealistic explosion.

In non-relativistic simulations, we expect the speed of the fluid to be much less than the speed of light and the energy much less than the rest-mass energy. When these cases happen, it usually hints that there is an unphysical update numerically, and we should invoke the correction for it. The relativistic limit here is just a bottom-line check. We hope that when the numerical issue happens, the speed/energy will be much larger than this limit. Otherwise, it will be hard to catch it, as there is no general upper limit for the speed and energy.

Changes

  • Add a speed check against the speed of light
  • Add a total energy check against the rest-mass energy

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