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Abstract: As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes. [Copyright &y& Elsevier]

A physically-based, spatially-distributed model is presented for simulation of surface/subsurface flow and the interactions between these domains. The model is designed for practical application to a wide variety of hydrologic evaluations, at various scales of simulation. The system is represented by the three-dimensional saturated–unsaturated flow equation for the subsurface, coupled with the diffusion wave equation for areal overland flow, both of which are coupled with the diffusion wave equation for flow through a network of streams and channels, including hydraulic structures. Ground surface unevenness at the grid scale is incorporated via the concept of detention storage, and thick vegetation or urban features are included via an obstruction storage exclusion term. Evapotranspiration from the surface and subsurface are modeled using land cover and climatic factors to define the complete water budget using a physically-based formulation. The system of equations is discretized using a fully implicit procedure, with the Newton–Raphson method to handle non-linearities efficiently. Robustness, stability and accuracy of solution are obtained for a wide variety of cases including dry systems and large surface/subsurface interaction fluxes. Adaptive time-stepping schemes and under-relaxation formulas further alleviate the computational burden. Verification and application examples demonstrate the need for a rigorous, fully-coupled solution to the set of equations, for complete hydrologic-cycle analysis. [Copyright &y& Elsevier]

A sub-time stepping method is described for computational fluid dynamics problems that utilize implicit-type time marching procedures to resolve transients. In this method, small time-step sizes are used in portions of a domain where interest and activity is high, with larger time-step sizes being applied in other locations. The sub-time step is an integral portion of a larger time step––i.e., multiple sub-time steps over a sub-timed part of a domain add up to the time interval of the full time step used over the remainder of the domain. The technique is particularly suitable for extensive simulations where large portions of a domain are temporally over-discretized. The principles underlying implementation of the implicit sub-timing procedure, the computational effort in relation to conventional implicit time-stepping methods, and an analysis of the effects of sub-timing on the matrix structure are presented. Feasibility and applicability of the implicit sub-timing method is demonstrated through three proof-of-the-concept example problems. These examples include implementation of implicit sub-timing to one-dimensional as well as two-dimensional flow and solute transport problems. [Copyright &y& Elsevier]