Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows?

Current smoothed particle dynamics discretizations for macroscopic and mesoscopic viscous flows usually do not conserve angular momentum. Angular-momentum conservation, however, potentially stabilizes the solution for long-time simulations. We show that a simple angular-momentum conservative formulation of the viscous force, which was proposed previously based on empirical findings, can be derived theoretically under the condition of incompressible flow. The properties of this formulation are asserted by numerical simulations of two-dimensional Taylor-Green flow.