Dimension reduction method for ODE fluid models

  • Authors:

  • Alexandre M. Tartakovsky;Alexander Panchenko;Kim F. Ferris

  • Affiliations:

  • Pacific Northwest National Laboratory, Richland, WA 99352, United States;Department of Mathematics, Washington State University, Pullman, WA 99164, United States;Pacific Northwest National Laboratory, Richland, WA 99352, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

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.