A two-level aggregation-based newton-Krylov-Schwarz method for hydrology

Publisher Summary This chapter discusses the design and implementation of a Newton-Krylov-Schwarz solver for the implicit temporal integration on an unstructured three-dimensional spatial mesh of time-dependent partial differential equations. The novel feature of this approach is the formation of a coarse mesh problem using aggregation methods from algebraic mutt\grid. The solver was tested within the Adaptive Hydrology (ADH) Model, a finite element code being developed by the U. S. Army Corps of Engineers, Engineer Research and Development Center (ERDC) that is designed to solve a variety of hydrology problems including surface water flow. This approach is applied to the solution of Richards' equation for groundwater flow in the unsaturated zone while also discussing an application to surfacewater-groundwater interaction. This chapter discusses the performance of the method in a Navier-Stokes simulation. The weak formulation of the Navier-Stokes equations leads to implicit temporal integration. The discretization of the weak formulation leads to a system of nonlinear equations that must be solved at each time step. These equations are solved via Newton-Krylov-Schwarz (NKS) methods.