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 addit...

[1]  José María Montanero,et al.  Nonlinear Couette flow in a dilute gas: Comparison between theory and molecular-dynamics simulation , 1998 .

[2]  D. Risso,et al.  Erratum: Dilute gas Couette flow: Theory and molecular-dynamics simulation [Phys. Rev. E 56 , 489 (1997)] , 1998 .

[3]  D. Risso,et al.  DILUTE GAS COUETTE FLOW : THEORY AND MOLECULAR DYNAMICS SIMULATION , 1997 .

[4]  Andrés Santos,et al.  Simulation of the Enskog equation à la Bird , 1997 .

[5]  J. Montanero,et al.  Stability of uniform shear flow , 1997, cond-mat/9705168.

[6]  M. López de Haro,et al.  Nonlinear transport for a dilute gas in steady Couette flow , 1997 .

[7]  Santos,et al.  Monte Carlo simulation method for the Enskog equation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Andrés Santos,et al.  Combined heat and momentum transport in a dilute gas , 1995 .

[9]  M. L. Haro,et al.  KINETIC MODEL FOR HEAT AND MOMENTUM TRANSPORT , 1994 .

[10]  G. Bird.  Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[11]  Dean C. Wadsworth,et al.  Slip effects in a confined rarefied gas. I: Temperature slip , 1993 .

[12]  Santos,et al.  Analysis of nonlinear transport in Couette flow. , 1989, Physical review. A, General physics.

[13]  Santos,et al.  Heat and momentum transport far from equilibrium. , 1987, Physical review. A, General physics.

[14]  N. K. Makashev,et al.  Steady-state Couette flow /with heat transfer/ of a gas of Maxwellian molecules , 1980 .

[15]  Carlo Cercignani,et al.  Mathematical Methods in Kinetic Theory , 1970 .

[16]  J. Banavar,et al.  Thermal walls in computer simulations , 1998 .

[17]  Santos,et al.  Monte Carlo simulation of the Boltzmann equation for steady Fourier flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  J. McLennan.  Introduction to nonequilibrium statistical mechanics , 1989 .

[19]  M. Kogan.  Rarefied Gas Dynamics , 1969 .

[20]  ARTHUR SCHUSTER,et al.  The Kinetic Theory of Gases , 1895, Nature.