  We study a method based on Balancing Domain Decomposition by Constraints
(BDDC) for a numerical solution of a single-phase flow in heterogenous porous
media. The method solves for both flux and pressure variables. The fluxes are
resolved in three steps: the coarse solve is followed by subdomain solves and
last we look for a divergence-free flux correction and pressures using
conjugate gradients with the BDDC preconditioner. Our main contribution is an
application of the adaptive algorithm for selection of flux constraints.
Performance of the method is illustrated on the benchmark problem from the 10th
SPE Comparative Solution Project (SPE 10). Numerical experiments in both 2D and
3D demonstrate that the first two steps of the method exhibit some numerical
upscaling properties, and the adaptive preconditioner in the last step allows a
significant decrease in number of iterations of conjugate gradients at a small
additional cost.
