2D and 3D Dense-Fluid Shear Flows via Nonequilibrium Molecular Dynamics.   Comparison of Time-and-Space-Averaged Tensor Temperature and Normal Stresses   from Doll's, Sllod, and Boundary-Driven Shear Algorithms
  Homogeneous shear flows (with constant strainrate du/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. The nonlinear stress differences are small, but significant, in both two and three space dimensions. In homogeneous systems the sign and magnitude of the shearplane stress difference, P(xx) - P(yy), depend on both the thermostat type and the chosen shearflow algorithm. The Doll's and Sllod algorithms predict opposite signs for this stress difference, with the Sllod approach definitely wrong, but somewhat closer to the (boundary-driven) truth. Neither of the homogeneous shear algorithms predicts the correct ordering of the kinetic temperatures, T(xx) > T(zz) > T(yy). 
Wm. G. Hoover, Carol G. Hoover, Janka Petravic