10.4122/1.1000000295
Pereira, Felipe
Felipe
Pereira
felipe-pereira@uol.com.br
Abreu, Eduardo
Eduardo
Abreu
eabreu@iprj.uerj.br
Ribeiro, Simone
Simone
Ribeiro
sribeiro@iprj.uerj.br
Furtado, Frederico
Frederico
Furtado
furtado@uwyo.edu
Pereira, Felipe
Felipe
Pereira
felipe-pereira@uol.com.br
CENTRAL SCHEMES FOR POROUS MEDIA FLOW
XVI International Conference on Computational Methods in Water Resources
2006
2006
We are concerned with numerical schemes for solving scalar hyperbolic conservation
laws arising
in the simulation of multiphase flows in heterogeneous porous media. These schemes
are non-oscillatory and enjoy the main advantage of Godunov-type central schemes:
simplicity, i.e.,
they employ neither characteristic decomposition nor pproximate Riemann solvers. This
makes them universal methods
that can be applied to a wide variety of physical problems, including hyperbolic systems.
We compare the Kurganov-Tadmor (KT) [1] semi-discrete central scheme with the
Nessyahu-Tadmor (NT) [2]
central scheme. The KT scheme uses more precise information about the local speeds
of propagation
together with integration over nonuniform control volumes, which contain the Riemann
fans.
The numerical dissipation in the (KT) scheme is smaller than in the original NT
scheme, however
the NT scheme can use larger time steps.
Numerical simulations are presented for two-phase flow problems in very heterogeneous
formations.
We find the KT scheme to be considerably less diffusive, particularly in the presence of
viscous fingers, which lead to strong restrictions on the time step selection.
REFERENCES
[1] Kurganov, A. & Tadmor, E., 2000. New high-resolution central schemes for
nonlinear conser-
vation laws and convection-diffusion equations. Journal of Computational Physics,
vol. 160,
pp. 241282.
[2] Nessayahu, H. & Tadmor, E., 1990. Non-oscillatory central differencing for
hyperbolic conser-
vation laws. Journal of Computational Physics, vol. 87, n. 2, pp. 408463.