I am currently using the HLLC solver to solve a 1-D system of Euler equations with very satisfactory results.
However, there are cases where my solution produces low-density, high velocity states, which lead to strange heating at the origin. The heating is strange, as I am running with a $\gamma_{adiabatic}$ close to 1, hence the simulation is quais-isothermal.
I've double and triple-checked my boundary conditions, and am fairly certain its not that. My other idea is that this situation is resembling the anomalous shock tube test-2 heating, as seen in HLLC solvers in general (circled in red in the image below).
Hence my question:
As the HLLC solver is otherwise a nearly perfect solver, I was curious whether there is a fix for this near-vacuum overheating. I am mainly asking for a reference.
Toro's references in the HLLC chapter turned out interesting papers, but not a fix for this specific issue. I am also aware of the keyword 'drying and wetting' for near-vacuum problems with the shallow water equations, but searching for this in conjunction with the Euler system and fixing the overheating amounted to nothing. Therefore I am turning to the community.
