Dimension reduction method for ODE fluid models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Tartakovsky, Alexandre M.¹  Panchenko, Alexander²  Ferris, Kim F.¹ 

[1] Pacific NW Natl Lab, Richland, WA 99352 USA

[2] Washington State Univ, Dept Math, Pullman, WA 99164 USA

关键词: Model reduction;    ODEs;    Multiscale modeling;    Coarse integration;    Upscaling;    Closure problem;    Deconvolution;   

DOI  :  10.1016/j.jcp.2011.08.004

来源: Elsevier

【 摘 要 】

We develop a new dimension reduction method for large size systems of ordinary differential equations (ODEs) obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large-size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of smoothed particle hydrodynamic ODEs describing single-phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single-phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single-phase flow driven by the periodic body force and for the two-phase flows, the higher-order (the first- and second-order) deconvolutions were necessary to obtain a sufficiently accurate solution. (C) 2011 Published by Elsevier Inc.

【 授权许可】

Free