On Some Probability Density Function Based Moment Closure Approximations of Micro–Macro Models for Viscoelastic Polymeric Fluids

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In this paper we will discuss several issues related to the moment-closure approximation of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability density function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro–macro models which consist of the coupled incompressible Navier-Stokes equations and the Fokker-Planck equations. We present the exact energy law of the resulting closure systems and introduce a post-modification scheme to preserve the positivity of PDF. The scheme not only reduces the region of negative PDF values but also preserves the structure of the induced stress tensor resulting from the molecular behaviors such as stretching and rotation. Numerical verifications are provided for the moment-closure system with some standard external flows. We also explore the relation of the maximum entropy principle (MEP) and the moment-closure approach.
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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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