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In this work, we showed a calculation method of local stress tensorapplicable to non-equilibrium MD systems based on the Method of Plane (MoP).From the relation between the macroscopic velocity distribution function andthe microscopic molecular passage across a fixed control plane, we derived amethod to calculate the basic properties of the macroscopic momentumconservation law including the density, the velocity, the momentum flux, theinteraction and kinetic terms of the stress tensor defined on a surface with afinite area. Any component of the streaming velocity can be obtained on acontrol surface, which enables the separation of the kinetic momentum flux intothe advection and stress terms in the framework of MoP. We verified the presentmethod through the extraction of the density, velocity and stress distributionsin a quasi-1D steady-state Couette flow system and in a quasi-2D steady-statesystem with a moving contact line. In our method, as opposed to volume averagemethod, the density, mass and momentum fluxes are defined on a surface, whichis essential to be consistent with the mass and momentum conservation laws indynamic systems.

Local stress tensor calculation by the Method-of-Plane in microscopic  systems with macroscopic flow: a formulation based on the velocity  distribution function