Improved numerical solvers for implicit coupling of subsurface and overland flow

Due to complex dynamics inherent in the physical models, numerical formulation of subsurface and overland flow coupling can be challenging to solve. ParFlow is a subsurface flow code that utilizes a structured grid discretization in order to benefit from fast and efficient structured solvers. Implicit coupling between subsurface and overland flow modes in ParFlow is obtained by prescribing an overland boundary condition at the top surface of the computational domain. This form of implicit coupling leads to the activation and deactivation of the overland boundary condition during simulations where ponding or drying events occur. This results in a discontinuity in the discrete system that can be challenging to resolve. Furthermore, the coupling relies on unstructured connectivities between the subsurface and surface components of the discrete system, which makes it challenging to use structured solvers to effectively capture the dynamics of the coupled flow. We present a formulation of the discretized algebraic system that enables the use of an analytic form of the Jacobian for the Newton-Krylov solver, while preserving the structured properties of the discretization. An effective multigrid preconditioner is extracted from the analytic Jacobian and used to precondition the Jacobian linear system solver. We compare the performance of the new solver against one that uses a finite difference approximation to the Jacobian within the Newton-Krylov approach, previously used in the literature. Numerical results explores the effectiveness of using the analytic Jacobian for the Newton-Krylov solver, and highlights the performance of the new preconditioner and its cost. The results indicate that the new solver is robust and generally outperforms the solver that is based on the finite difference approximation to the Jacobian, for problems where the overland boundary condition is activated and deactivated during the simulation. A parallel weak scaling study highlights the efficiency of the new solver.