CIMOLIN, F. and DISCACCIATI, M., 2013. Navier-Stokes/Forchheimer models for filtration through porous media. Applied Numerical Mathematics, 72, pp. 205 - 224.
Modeling the filtration of incompressible fluids through porous media requires dealing
with different types of partial differential equations in the fluid and porous subregions of
the computational domain. Such equations must be coupled through physically significant
continuity conditions at the interface separating the two subdomains. To avoid the
difficulties of this heterogeneous approach, a widely used strategy is to consider the
Navier–Stokes equations in the whole domain and to correct them introducing suitable
terms that mimic the presence of the porous medium. In this paper we discuss these two
different methodologies and we compare them numerically on a sample test case after
proposing an iterative algorithm to solve a Navier–Stokes/Forchheimer problem. Finally, we
apply these strategies to a problem of internal ventilation of motorbike helmets.
This article was published in the journal Applied Numerical Mathematics and the definitive version is available at: http://dx.doi.org/10.1016/j.apnum.2013.07.001
The second author acknowledges the partial support of the Marie Curie Career Integration Grant 2011-294229 within
the 7th European Community Framework Programme.