Monte Carlo simulation of nonlinear Couette flow in a dilute gas
  The Direct Simulation Monte Carlo method is applied to solve the Boltzmann equation in the steady planar Couette flow for Maxwell molecules and hard spheres. Nonequilibrium boundary conditions based on the solution of the Bhatnagar-Gross-Krook (BGK) model for the Couette flow are employed to diminish the influence of finite-size effects. Non-Newtonian properties are characterized by five independent generalized transport coefficients: a viscosity function, a thermal conductivity function, two viscometric functions, and a cross coefficient measuring the heat flux orthogonal to the thermal gradient. These coefficients depend nonlinearly on the shear rate. The simulation results are compared with theoretical predictions given by the Grad method and the BGK and the ellipsoidal statistical (ES) models. It is found that the kinetic models present a good agreement with the simulation, especially in the case of the ES model, while the Grad method is only qualitatively reliable for the momentum transport. In addition, the velocity distribution function is also measured and compared with the BGK and ES distributions. 
J. M. Montanero, A. Santos, V. Garz\'o