This will be useful for many galaxy cluster applications.

There is

• HLLC-LM: https://ui.adsabs.harvard.edu/abs/2020JCoPh.42309762F/abstract
• low-dissipation HLLD: https://ui.adsabs.harvard.edu/abs/2021arXiv210804991M/abstract

HLLC-LM is not stable for very low-amplitude linear waves, but it works well otherwise. I'm not sure which is best. Both have ad-hoc modifications to recover the $\mathcal{M} \rightarrow 0$ limit, and both suppress carbuncles.