  Open quantum systems provide an essential theoretical basis for the
development of novel quantum technologies, since any real quantum system
inevitably interacts with its environment. Lindblad master equations capture
the effect of Markovian environments. Closed quantum systems can be treated
using flow equations with the particle conserving generator. We generalize this
generator to non-Hermitian matrices and open quantum systems governed by
Lindbladians, comparing our results with recently proposed generators by Rosso
et al. (arXiv:2007.12044). In comparison, we find that our advocated generator
provides an efficient flow with good accuracy in spite of truncations.
