Fluid simulation are usually done in the periodic boundary conditions. I believe that if there is no flow in the cell, it is necessary to measure the thermodynamic properties, the moment will be conserved.

There is no angular momentum (quantum number) for non-spherically symmetric system.

For example in a simulation box with periodic boundary conditions I is shown that angular momentum is not conserved(Allen and Tildesley ) and as Mr. Eugene says only preserved in a spherical symmetry.

If the angular momentum is not conserved in a box with periodic boundary conditions the situation would not have physical meaning . However , periodic boundary conditions are used because the thermodynamic quantities not depend explicitly of angular momentum . It is the latter right?

A possible answer is that the conservation of momentum constraint adds little to the final results and can be ignored.  This needs to be confirmed.  For example in nuclear reactor neutronic calculations the force of gravity is ignored because the change is very small.  A neutron falling a fraction of a mm has little change.

Under room temperature and pressure if the molecules exhibit Brownian Motion then it can be shown (cf. my paper of Political Environment on my RG page) that angular momentum can be conserved (closed Entropy function) by Lorentz type micro transformations of the closed space around every molecule and hence by using a D-Branes -String coupling developed by me the system can be spacially and over time systems integrated by using Lagrangian closure of spacextime algorithmically within a genetic 4 dimensional utility field which preserves continnuity and chiral symmetry to give rise to equivalent orthogonal resolutions so as to convert the enrire system into a information-energy general relativistic-geometric-D-Branes-String Duality M(Econophysics) system which can be a vectorial Hilbert Algebra characterised by Boolean field. SKM QC FEPS.

Angular momentum is not conserved: www.baur-research.com/Physics