10.4122/1.1000000301
Yotov, Ivan
Ivan
Yotov
yotov@math.pitt.edu
Yotov, Ivan
Ivan
Yotov
yotov@math.pitt.edu
Domain decomposition algorithms for coupling ground water and surface
water flows
XVI International Conference on Computational Methods in Water Resources
2006
2006
We present a mathematical and numerical model for coupled subsurface
and surface flows based on coupling the Stokes and the Darcy equations
through the Beavers-Joseph-Saffman interface conditions. Optimal order
error estimates are established for a finite element discretization
based on conforming Stokes elements in the surface flow domain and
mixed finite elements in the porous media domain. The formulation
utilizes a Lagrange multiplier to impose the interface conditions. A
non-overlapping domain decomposition algorithm is developed which
reduces the coupled algebraic system to an interface problem for the
normal stress. Each interface iteration requires solving Stokes and
Darcy subdomain problems. It is shown that the interface problem is
symmetric and positive definite and that its condition number is
$O(1/h)$, where $h$ is the discretization parameter. Numerical results
and parallel scalability studies are presented.