Numerical Investigation of the "poor Man's Navier-Stokes Equations" with Darcy and Forchheimer Terms

Tingting Tang, Zhiyong Li, J. M. McDonough, P. D. Hislop

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, a discrete dynamical system (DDS) is derived from the generalized Navier-Stokes equations for incompressible flow in porous media via a Galerkin procedure. The main difference from the previously studied poor man's Navier-Stokes equations is the addition of forcing terms accounting for linear and nonlinear drag forces of the medium - Darcy and Forchheimer terms. A detailed numerical investigation focusing on the bifurcation parameters due to these additional terms is provided in the form of regime maps, time series, power spectra, phase portraits and basins of attraction, which indicate system behaviors in agreement with expected physical fluid flow through porous media. As concluded from the previous studies, this DDS can be employed in subgrid-scale models of synthetic-velocity form for large-eddy simulation of turbulent flow through porous media.

Original languageEnglish
Article number1650086
JournalInternational Journal of Bifurcation and Chaos
Issue number5
StatePublished - May 1 2016

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.


  • Bifurcation
  • discrete dynamical system
  • porous media
  • turbulence modeling

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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