L.-L. Liu, D. E. Keyes, and S.-Y. Sun
SPE Reservoir Characterization and Simulation Conference and Exhibition, 16-18 September, Abu Dhabi, UAE , (2013)
The fully implicit approach is attractive in reservoir simulation for
reasons of numerical stability and the avoidance of splitting errors
when solving multiphase flow problems, but a large nonlinear system must
be solved at each time step, so efficient and robust numerical methods
are required to treat the nonlinearity. The Additive Schwarz
Preconditioned Inexact Newton (ASPIN) framework, as an option for the
outermost solver, successfully handles strong nonlinearities in
computational fluid dynamics, but is barely explored for the highly
nonlinear models of complex multiphase flow with capillarity,
heterogeneity, and complex geometry. In this paper, the fully implicit
ASPIN method is demonstrated for a finite volume discretization based on
incompressible two-phase reservoir simulators in the presence of
capillary forces and gravity. Numerical experiments show that the number
of global nonlinear iterations is not only scalable with respect to the
number of processors, but also significantly reduced compared with the
standard inexact Newton method with a backtracking technique. Moreover,
the ASPIN method, in contrast with the IMPES method, saves overall
execution time because of the savings in timestep size.