Implicit Subtime Stepping for Solving Nonlinear Flow Equations in an Integrated Surface–Subsurface System

A diverse group of problems requires quantification of the entire hydrologic cycle by the integrated simulation of water flow in the surface and subsurface regimes. In a transient integrated simulation of the water cycle, the time step size is a key factor in controlling the solution accuracy and the simulation efficiency for a given spatial discretization. In general, if the time step size is sufficiently small, the resulting solution becomes more accurate but with higher computational cost. Thus, to maintain an acceptable level of solution accuracy in the entire simulation domain, the time step size is restricted by the relatively rapid responses in the surface flow regime. As the relatively rapid responses are typically limited to a small portion of the surface domain compared with the groundwater system, a large portion of the domain tends to be temporally overdiscretized. The implicit subtime stepping approach described here can apply smaller subtime steps only to the subdomain where the accuracy requirements are needed. In this work, generalized formulations for implicit subtime stepping in the numerical solution of the nonlinear coupled surface–subsurface equations were derived and implemented into the integrated model HydroGeoSphere. Application to several problems showed that implicit subtime stepping can significantly improve the simulation efficiency with minimal loss in accuracy. The methodology was successfully applied to enhance the computational efficiency of an integrated flow simulation in the San Joaquin Valley, California, where the characteristic response time near surface drainage streams is orders of magnitude shorter than in the groundwater regime.