Non-equilibrium behaviour of equilibrium reservoirs in molecular simulations

Tysanner, Martin W.; Garcia, Alejandro L.

doi:10.1002/fld.983

Cited by 33 publications

(19 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore the simulation domain is kept in contact with an infinite reservoir of the gas at the specified equilibrium conditions. Care must be taken, in this case, to sample accurately the statistics of the incoming particles [62].…”

Section: Simulation Of Spontaneuos Fluctuations In a Dilute Gasmentioning

confidence: 99%

Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

View full text Add to dashboard Cite

We investigate the relaxation of internal temperature and the concept of volume viscosity in nonequilibrium gas models derived from the kinetic theory. We first investigate a nonequilibrium gas model with two temperatures-translational and internal-where the volume viscosity is absent. We establish that, in a relaxation regime, the temperature difference becomes proportional to the divergence of the velocity fields and define a nonequilibrium, multitemperature, volume viscosity coefficient. We next analyze the convergence of the two temperature model towards the one temperature model when the relaxation is fast. We then investigate a nonequilibrium two temperature gas model with a fast and a slow internal energy mode. We establish that, in a relaxation regime, there are four contributions to the volume viscosity, namely the fast internal mode volume viscosity, the slow internal mode volume viscosity, the relaxation pressure and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. We finally perform Monte Carlo simulations of spontaneous fluctuations near thermodynamic equilibrium. The numerical results obtained from the Boltzmann equation are compared to the predictions of the one and two temperature fluid models and the agreement between theory and calculations is complete.

show abstract

Section: Simulation Of Spontaneuos Fluctuations In a Dilute Gasmentioning

confidence: 99%

Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…It is not clear why this occurs since the correlation in a related AR hybrid of the "train" model is diminished [5]. One possible explanation is the induction of spurious correlations, even at equilibrium, when a reservoir does not generate the correct fluctuations spectrum [34].…”

Section: Rarefaction Steady Statementioning

confidence: 90%

Algorithm refinement for the stochastic Burgers’ equation

Bell

Foo

Garcia

2007

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations in the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency.

show abstract

“…The number of particles to be injected is derived from the density information, while the molecular velocity distribution of the injected particles must correspond to the mean flow macroscopic variables characteristic to the external flow as have been outlined in works such as that by Bird [7], Lilley and Macrossan [8] and Tysanner and Garcia [9]. For hybrid continuum-atomistic methods that couple the continuum solutions to the DSMC region, reservoir regions upstream and downstream of the inflow/outflow boundaries are incorporated to impose the boundary conditions.…”

Section: Considerations For Imposing Boundary Conditionsmentioning

confidence: 99%

Computation of head–disk interface gap micro flowfields using DSMC and continuum–atomistic hybrid methods

John¹,

Damodaran²

2009

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThis paper discusses computational modeling of micro flow in the head-disk interface (HDI) gap using the direct simulation Monte Carlo (DSMC) method. Modeling considerations are discussed in detail both for a stand-alone DSMC computation and for the case of a hybrid continuum-atomistic simulation that couples the Navier-Stokes (NS) equation to a DSMC solver. The impact of the number of particles and number of cells on the accuracy of a DSMC simulation of the HDI gap is investigated both for twoand three-dimensional configurations. An appropriate implicit boundary treatment method for modeling inflow and outflow boundaries is used in this work for a three-dimensional DSMC micro flow simulation. As the flow outside the slider is in the continuum regime, a hybrid continuum-atomistic method based on the Schwarz alternating method is used to couple the DSMC model in the slider bearing region to the flow outside the slider modeled by NS equation. Schwarz coupling is done in two dimensions by taking overlap regions along two directions and the Chapman-Enskog distribution is employed for imposing the boundary condition from the continuum region to the DSMC region. Converged hybrid flow solutions are obtained in about five iterations and the hybrid DSMC-NS solutions show good agreement with the exact solutions in the entire domain considered. An investigation on the impact of the size of the overlap region on the convergence behavior of the Schwarz method indicates that the hybrid coupling by the Schwarz method is weakly dependent on the size of the overlap region. However, the use of a finite overlap region will facilitate the exchange of boundary conditions as the hybrid solution has been found to diverge in the absence of an overlap region for coupling the two models.

show abstract

Non-equilibrium behaviour of equilibrium reservoirs in molecular simulations

Cited by 33 publications

References 19 publications

Relaxation of internal temperature and volume viscosity

Relaxation of internal temperature and volume viscosity

Algorithm refinement for the stochastic Burgers’ equation

Computation of head–disk interface gap micro flowfields using DSMC and continuum–atomistic hybrid methods

Contact Info

Product

Resources

About