Steady-state shear flows via nonequilibrium molecular dynamics and smooth-particle applied mechanics

Abstract

We simulate both microscopic and macroscopic shear flows in two space dimensions using nonequiIi brium molecular dynamics and smooth-particle applied mechanics. The time-reversible microscopic equations of motion are isomorphic to the smooth-particle description of inviscid macroscopic continu um mechanics. The corresponding microscopic particle interactions are relatively weak and long ranged. Though conventional Green-Kubo theory suggests instability or divergence in two-dimensional flows, we successfully define and measure a finite shear viscosity coefficient by simulating stationary plane Couette flow. The special nature of the weak long-ranged smooth-particle functions corresponds to an unusual kind of microscopic transport. This microscopic analog is mainly kinetic, even at high density. For the soft Lucy potential which we use in the present work, nearly all the system energy is po tential, but the reSUlting shear viscosity is nearly all kinetic. We show that the measured shear viscosi ties can be understood, in terms of a simple weak-scattering model, and that this understanding is useful in assessing the usefulness of continuum simulations using the smooth-particle method. We apply that method to the Rayleigh-Benard problem of thermally driven convection in a gravitational field.

An improvement for tensile instability in smoothed particle hydrodynamics

“…Because of the advantages of being Lagrangian, meshfree, and simple, it is currently receiving a great deal of attention for applications in the areas of computational mechanics, such as impact and shock damage Petschek and Libersky 1993;Stellingwerf and Wingate 1993;Randles et al 1995;Randles and Libersky 1996;Johson and Beissel 1996;Chen et al 1997;Bashurov et al 1997aBashurov et al , 1997bHayhurst and Clegg 1997;Plimpton et al 1998;Swift et al 1998),¯uid dynamics (Takeda et al 1994;Kum et al 1995;Posch et al 1995;Morris et al 1997;Welton and Pope 1997;Welton 1998), multi-phase¯ow (Monaghan 1997),¯uid-structure interaction , magneto-hydrodynamics (Dalpino and Ceroqueira 1996), and pack ice Savage 1997, 1998). In and Attaway et al (1998), SPH was coupled into the transient dynamics ®nite element code, PRONTO (Taylor and Flanagan 1987).…”

Microscopic Computer Simulation of Fluids

“…On the other hand, recent high-precision simulations as in , Posch, Hoover, Kum (1995), Hansen, Evans (1995), for short range steep repulsive potential (hard disks in ) produced size-independent, though rate dependent transport coefficients fairly close to the predictions of Gass (1971) from the 2D Enskog theory, namely, no divergence is detected. The reproducible finite nature of viscosity in and thermal conductivity in Hansen, Evans (1995), could be made understandable if the coefficients only diverge in some unobtainable zerorange large system limit.…”

Flow Pattern and Heat Transfer Rate in Three-Dimensional Rayleigh-Benard Convection

“…The chaotic motion of atoms in the transition between heat conduction and convection was studied using the MD method by Watanabe and Kaburaki [10]. Posch et al studied the RB system using the smooth-particle applied mechanics (SPAM), which is a grid-free particle method for solving the partial differential equations of fluid or solid mechanics [11,12]. The good agreement between the smooth-particle and the NavierStokes results was obtained, and SPAM was shown to be an interesting bridge be-tween continuum mechanics and molecular dynamics [13].…”