Finding force/drag coefficient on amolecule in constant flow

Just an idea, not sure if this gives you what you want.

Restrain the molecules com with fix recenter and impose the flow on the solvent. You'll probably need two time integrations, one for the molecule, one for the solvent with a biased temp. The compute group/group then should give you the forces.
Anyways you'll need some time to get to an "equilibrated" flow and fluctuations are to be expected (like in one of your cases). In viscosity simulations a running average over time can be used to overcome this.

Regards
Wolfgang

Just an idea, not sure if this gives you what you want.

Restrain the molecules com with fix recenter and impose the flow on the solvent.

​fix recenter doesn’t apply a restraint, it simply translates all other coordinates so that the recenter COM remains stationary. i don’t think that is a good idea when also imposing a flow.
you probably were thinking about fix spring. this can be used to tether a group of atoms to an arbitrary point in space with a harmonic spring.
the fix itself makes the restraining force available as a thermo property, this is the force of the spring (as total force or individual components).
the force constant then should be chosen to have the group remain close, but not too stiff as then the accuracy suffers.​

You’ll probably need two time integrations, one for the molecule, one for the solvent with a biased temp. The compute group/group then should give you the forces.

​it probably doesn’t make much of a difference, but i agree, using fix nve separately for the tethered group should be used separately from time integrating the rest.​

axel.