Measurement bias of fluid velocity in molecular simulations

Tysanner, Martin W.; Garcia, Alejandro L.

doi:10.1016/j.jcp.2003.10.021

Cited by 22 publications

(25 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simulations were of a nonequilibrium state, specifically a temperature gradient produced by parallel thermal walls at different temperatures. Similar simulations in [26] verified the predicted bias in the instantaneous center-of-mass fluid velocity (see equation (39)). …”

Section: Appendix D: Non-equilibrium Simulationssupporting

confidence: 74%

“…Worse still, the inclusion of such terms may violate the necessary conservation laws." Such a violation is demonstrated in [26] and is discussed here in Section 4.1.…”

Section: Mean Valuesmentioning

confidence: 70%

“…Finally, since δρ δu ∝ V −1 , the quantity û ∞ is not an intensive variable. This bias of the center-of-mass fluid velocity is studied at length in [26] where it is shown that the nonequilibrium correlation δρ δu leads to an anomalous flow, as measured by û s , in closed systems. 1 …”

Section: 1mentioning

confidence: 99%

“…1 In [26] the quantity u * s is referred to as the Cumulative-Averaged-Measurement (CAM) of fluid velocity and û s is called the Sample-Averaged-Measurement (SAM) of velocity. By direct evaluation (see (73), (76)), we find that T * ∞ = T 1 ∞ = T at equilibrium, while Figure 2 confirms these results, showing the fractional error in the sample mean of temperature (relative to T ) versus the mean number N of particles.…”

Section: 2mentioning

confidence: 99%

See 3 more Smart Citations

Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Garcia

2006

CAMCoS

View full text Add to dashboard Cite

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical simulations, both at thermodynamic equilibrium and at a nonequilibrium steady state.

show abstract

Section: Appendix D: Non-equilibrium Simulationssupporting

confidence: 74%

“…Worse still, the inclusion of such terms may violate the necessary conservation laws." Such a violation is demonstrated in [26] and is discussed here in Section 4.1.…”

Section: Mean Valuesmentioning

confidence: 70%

Section: 1mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

See 2 more Smart Citations

Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Garcia

2006

CAMCoS

View full text Add to dashboard Cite

show abstract

“…The mean velocity can be obtained from any of the several averaging methods like SAM (Tysanner and Garcia, 2004), CAM (Tysanner and Garcia, 2005) or SMC (Karimian et al, 2011) that reduces statistical errors in its calculation. In this paper, the SMC method is used to calculate the mean velocity.…”

Section: Pressure Formulamentioning

confidence: 99%

Analysis of pressure behavior in a temperature controlled molecular dynamic flow

Najafi¹,

Karimian²

2016

jtam

View full text Add to dashboard Cite

Thermo-fluid properties are required for numerical modeling of nano/micro devices. These properties are mostly obtained from results of molecular dynamics (MD) simulations. Therefore, efforts have been put in developing methods for numerical evaluation of fluid properties, such as pressure. In this paper, the pressure behavior in a controllable nanochannel flow is investigated. The nanoflow field is created by imposing a gradient of a macroscopic property such as temperature. Details of the pressure calculation method in a molecular system and its sensitivity to the approximations made are described first. The effect of temperature rise in a uniform flow on the pressure field is studied next. Then, in the flow under a fixed mean velocity condition, the effect of temperature gradient as a controllable property on the pressure field of nanoflow is studied. Velocity, pressure and molecular density of nanoflows with various temperature gradients and different temperature levels are investigated as well. It has been found that the temperature level at which the temperature gradient is imposed, is important. A fixed temperature gradient will not always lead to the same pressure gradient at different temperature levels. Furthermore, quite interestingly, it is observed that at a fixed temperature gradient, with the variation of mean velocity the pressure field also varies.

show abstract

A study on the measurement of mean velocity and its convergence in molecular dynamics simulations

Karimian

Izadi

Farimani

2010

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYIn many particle-based simulations, measurement of local mean flow velocity and other continuum-based properties are of utmost importance. Macroscopic quantities, such as mean flow velocity, temperature, and density, can be estimated by averaging the corresponding microscopic behavior of the particles. The two main subjects that should be considered in the averaging over the particles in a specific problem are spatial and temporal behaviors of them. In this paper, we study the latter. Because of the chaotic nature of the collisions among the molecules and consequently their random path, extracted macroscopic values fluctuate about their average values causing statistical errors. In this paper, an averaging method called SAM-Modified-CAM (SMC) will be proposed for the measurement of mean velocity that reduces statistical errors in its calculation. This proposal is based on the study conducted here on the implementations of two common averaging methods, sample-averaged measurement (SAM) and cumulative average measurement (CAM) in molecular dynamics. In addition, convergence of mean flow velocity measurement is thoroughly discussed, and a convergence criterion is proposed for this purpose. Implementation of the proposed method in different test cases has approved its reliable performance.

show abstract

Measurement bias of fluid velocity in molecular simulations

Cited by 22 publications

References 15 publications

Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Analysis of pressure behavior in a temperature controlled molecular dynamic flow

A study on the measurement of mean velocity and its convergence in molecular dynamics simulations

Contact Info

Product

Resources

About