Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics

Weiqing Ren; E. Weinan

doi:https://doi.org/10.1016/j.jcp.2004.10.001

Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics

Weiqing Ren, E. Weinan

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

146 Scopus citations

Abstract

The framework of the heterogeneous multiscale method (HMM) is used to develop numerical methods for the study of macroscale dynamics of fluids in situations, where either the constitutive relation or the boundary conditions are not explicitly available and have to be inferred from microscopic models such as molecular dynamics. Continuum hydrodynamics is used as the macroscopic model, while molecular dynamics serves as the microscopic model and is used to supply the necessary data, e.g., the stress or the boundary condition, for the macroscopic model. Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains. This naturally decouples the micro and macrospatial and temporal scales whenever possible. Applications are presented for models of complex fluids, contact line dynamics, and a simple model of non-trivial fluid - solid interactions.

Original language	American English
Pages (from-to)	1-26
Number of pages	26
Journal	Journal of Computational Physics
Volume	204
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2004.10.001
State	Published - Mar 20 2005

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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title = "Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics",

abstract = "The framework of the heterogeneous multiscale method (HMM) is used to develop numerical methods for the study of macroscale dynamics of fluids in situations, where either the constitutive relation or the boundary conditions are not explicitly available and have to be inferred from microscopic models such as molecular dynamics. Continuum hydrodynamics is used as the macroscopic model, while molecular dynamics serves as the microscopic model and is used to supply the necessary data, e.g., the stress or the boundary condition, for the macroscopic model. Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains. This naturally decouples the micro and macrospatial and temporal scales whenever possible. Applications are presented for models of complex fluids, contact line dynamics, and a simple model of non-trivial fluid - solid interactions.",

author = "Weiqing Ren and E. Weinan",

note = "Funding Information: The authors would like to thank B. Engquist, X. Li, T. Qian and X. P. Wang for helpful discussions. The work of E is supported by ONR grant N00014-01-1-0674 and National Science Foundation of China through a Class B Award for Distinguished Young Scholars 10128102.",

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doi = "https://doi.org/10.1016/j.jcp.2004.10.001",

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N2 - The framework of the heterogeneous multiscale method (HMM) is used to develop numerical methods for the study of macroscale dynamics of fluids in situations, where either the constitutive relation or the boundary conditions are not explicitly available and have to be inferred from microscopic models such as molecular dynamics. Continuum hydrodynamics is used as the macroscopic model, while molecular dynamics serves as the microscopic model and is used to supply the necessary data, e.g., the stress or the boundary condition, for the macroscopic model. Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains. This naturally decouples the micro and macrospatial and temporal scales whenever possible. Applications are presented for models of complex fluids, contact line dynamics, and a simple model of non-trivial fluid - solid interactions.

AB - The framework of the heterogeneous multiscale method (HMM) is used to develop numerical methods for the study of macroscale dynamics of fluids in situations, where either the constitutive relation or the boundary conditions are not explicitly available and have to be inferred from microscopic models such as molecular dynamics. Continuum hydrodynamics is used as the macroscopic model, while molecular dynamics serves as the microscopic model and is used to supply the necessary data, e.g., the stress or the boundary condition, for the macroscopic model. Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains. This naturally decouples the micro and macrospatial and temporal scales whenever possible. Applications are presented for models of complex fluids, contact line dynamics, and a simple model of non-trivial fluid - solid interactions.

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Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics

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