Evaluating linear and nonlinear solvers for density driven flow

• We investigate different non-linear solvers for density driven flow.
• Iterative solvers of decoupling and fully coupled type are compared.
• For the fully coupled Newton iteration, we develop a transformation mimicking a local decoupling of the unknowns (pressure/salt mass fraction).
• Based on this transformation, we tailor an algebraic multigrid method for density driven flow.

This study investigates properties of different solvers for density driven flow problems. The focus is on both non-linear and linear solvers. For the non-linear part, we compare fully coupled method using a Newton linearization and iteratively coupled versions of Jacobi and Gauss–Seidel type. Fully coupled methods require effective preconditioners for the Jacobian. To that end we present a transformation eliminating some couplings and present a strategy for employing algebraic multigrid to the transformed system as well. The work covers theoretical aspects, and provides numerical experiments. Although the primary focus is on density driven flow, we believe that the analysis may well be extended beyond to similar equations with coupled phenomena, such as geomechanics.