In principle, when a fluid element is shock-heated from Region I to Region III, it should cross the shock too fast to cool radiatively as it passes thru Region II. The numerical shock has a finite thickness which is unphysically large, however, so the shock transit time, t_shock, can artificially exceed the physical cooling time in Region II, t_cool, causing spurious radiative cooling. Since t_shock scales like the shock thickness divided by the preshock velocity, it depends on resolution, as the number of particles across the shock tends to be constant. If the cooling rate is so large or the resolution so poor that t_shock > t_cool, particles will be unable to cross Region II, as cooling forces them back to Region I, and the shock will not form. We call this the False Cooling Problem.
The false cooling problem only affects particles that are going through a shock transition. If the algorithm could track the location of shocks, then false cooling could be eliminated, simply by not allowing particles undergoing shock transitions to cool. There is already a shock-tracking algorithm in ASPH, which is used to restrict viscous heating. The algorithm identifies particles located in shock transitions and turns viscous heating on for them. We can attempt to solve the false cooling problem by turning cooling off for the same particles. Preminary results show that this approach can effectively eliminate the false cooling problem, and allow shocks to form even in presence of strong cooling.
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