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.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - May 1 2016|
Bibliographical notePublisher Copyright:
© 2016 World Scientific Publishing Company.
- discrete dynamical system
- porous media
- turbulence modeling
ASJC Scopus subject areas
- Modeling and Simulation
- Engineering (miscellaneous)
- Applied Mathematics