Dimension reduction method for ODE fluid models

Alexandre M. Tartakovsky, Alexander Panchenko, Kim F. Ferris

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)8554-8572
Number of pages19
JournalJournal of Computational Physics
Issue number23
StatePublished - Sep 20 2011
Externally publishedYes


  • Closure problem
  • Coarse integration
  • Deconvolution
  • Model reduction
  • Multiscale modeling
  • ODEs
  • Upscaling

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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