10.4122/1.1000000457
Natvig, Jostein R.
Jostein R.
Natvig
jrn@sintef.no
Lie, Knut-Andreas
Knut-Andreas
Lie
knl@sintef.no
Aarnes, Jørg
Jørg
Aarnes
jaa@sintef.no
Natvig, Jostein R.
Jostein R.
Natvig
jrn@sintef.no
An efficient domain decomposition method for transport in porous media.
XVI International Conference on Computational Methods in Water Resources
2006
2006
Convection dominated transport of fluids in a porous media is governed
by a nonlinear equation. Explicit time discretisations of this
equation are subject to a very restrictive stability condition on the
time step, due to variable background velocity and porosity fields. It
is therefore common to resort to implicit time discretisation. This
results in better stability, but one has to solve large systems of
nonlinear equations for each time step.
We present an efficient solver for hyperbolic transport equations with
positive characteristics. Our solver is based on an implicit discretisation
combined with overlapping domain decomposition. By applying an optimal
ordering algorithm for each subdomain, the discrete system of nonlinear
equations can be solved in one grid block at a time. This way, we avoid assembly
in each subdomain of a full nonlinear system. Our approach allows us to handle
large numbers of grid blocks with modest requirements on memory. Physical terms
violating our assumptions of positive characteristics (e.g., gravity and
capillary forces) can be treated by a standard operator splitting.