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Statistical field estimators for multiscale simulations

Jacob Eapen1, Ju Li2, and Sidney Yip1

  • 1Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Materials Science and Engineering, Ohio State University, Columbus, Ohio 43210, USA

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Phys. Rev. E 72, 056712 – Published 30 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056712

Abstract

We present a systematic approach for generating smooth and accurate fields from particle simulation data using the notions of statistical inference. As an extension to a parametric representation based on the maximum likelihood technique previously developed for velocity and temperature fields, a nonparametric estimator based on the principle of maximum entropy is proposed for particle density and stress fields. Both estimators are applied to represent molecular dynamics data on shear-driven flow in an enclosure which exhibits a high degree of nonlinear characteristics. We show that the present density estimator is a significant improvement over ad hoc bin averaging and is also free of systematic boundary artifacts that appear in the method of smoothing kernel estimates. Similarly, the velocity fields generated by the maximum likelihood estimator do not show any edge effects that can be erroneously interpreted as slip at the wall. For low Reynolds numbers, the velocity fields and streamlines generated by the present estimator are benchmarked against Newtonian continuum calculations. For shear velocities that are a significant fraction of the thermal speed, we observe a form of shear localization that is induced by the confining boundary.

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Phys. Rev. E 72, 056712– Published 30 November, 2005
  • Received 13 June 2005

© 2005 American Physical Society

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