Fermionic gradient flow in combination with the short-flow-time expansion provides a computational method where the renormalisation of hadronic matrix elements on the lattice can be simplified to address e.g.~the issue that operators with different mass dimension can mix.

We demonstrate our gradient flow renormalisation procedure by determining matrix elements of four-quark operators describing neutral meson mixing or meson lifetimes.
While meson mixing calculations are well-established on the lattice and serve to validate our procedure, a lattice calculation of matrix elements for heavy meson lifetimes is still outstanding.
Preliminary results for mesons formed of a charm and strange quark are presented.