MODEL COUPLING WITH CONTROL VOLUME FINITE ELEMENTS Mingjie Chen, George Zyvoloski Los Alamos National Laboratory, mchen@lanl.gov, gaz@lanl.gov, Los Alamos, NM, USA ABSTRACT Model coupling has become increasing important in recent years because of the need for more quantitative and realistic models. Major motivating factors include the need to simulate the complete water cycle, the necessity for high resolution grids to minimize numerical dispersion in contaminant transport calculations, the need to have fine grids for accuracy near production wells, and the requirement to use high resolution grids with resolution sufficient to capture correlation lengths in stochastic models. Model coupling also can be very important for situations where a relatively coarse basin model has been developed with a large investment in data collection and numerical model development. In this situation, it is easily conceived that a high resolution submodel might be required a posteriori for the simulation of a new water well, simulation of the flow and transport near a newly discovered contaminant source or a detailed analysis of aquifer stream interaction. The ability to include submodels with different flow physics is important. Because of the computational burden associated with large-scale coupled models, implementation in a parallel computing environment is desirable. Different numerical methods can dictate different coupling approaches for linking an outer or parent model to an inner or child model. Traditional finite difference methods require alternate flux and head mapping on the parent and child model respectively (Mehl and Hill, 2002a, 2004). By using a flux mapping/head interpolation scheme (with model iteration), Mehl and Hill could minimize the errors associated with the abrupt jump in grid size from a coarse grid parent region to a fine grid child region. Control volume finite elements and traditional finite elements use inherently flexible grids to handle without iteration the transition from the coarse to fine grids. However, this flexibility comes with an additional computational cost. While the finite element methods can represent a model with different grid scales without iteration, it is important to investigate iterative model coupling with finite elements because of situations where a “patch” of fine grid is added to an existing model, where the child region has different physics, where computer memory limitations require the model to be divided, and where multiple models exist in a parallel environment. We will present results for a variety of locally refined (called hybrid in this paper) and iteratively coupled control volume finite element models. In addition we compare the coupling algorithms for models with different physics. Error analysis will include comparisons to finite difference methods, non-iterative finite element methods, and fine grid solutions. Example simulations will include coupled models with different flow physics. Discussion of iteration algorithms, strategies in choosing child regions and transition zones, and computational challenges presented in a parallel computing environment will be given. 1. INTRODUCTION Model coupling are required for hydrologists to simulate the complete water cycle, to minimize numerical dispersion in contaminant transport calculations, and to use high-resolution grids to capture correlation lengths to produce stochastically relevant models. Vanderkwaak et al. (1997) showed the usefulness of incorporating several components on the water cycle in the modeling of catchments. While that work was isothermal, a similar effort at Los Alamos (Winter et. al, 2004) seeks to extend that field by incorporating additional components into the water cycle. These components, including overland flow and evapotranspiration, have large differences in fluid travel times and physics, necessitating some type of coupling between the component models. In some situation, a high-resolution submodel is required to incorporated into a developed large-scale coarse model to simulate a new water well, or a newly discovered contaminant source or a detailed analysis of aquifer stream interaction. Research on coupled models has been carried out by a number of researchers. These models have used finite difference (FD), finite element (FEM), and control volume finite element (CVFE) numerical discretization techniques. While FD and FEM methods are well understood and many textbooks are available, descriptions of CVFE techniques are not widely available. The method is described in some detail in Forsyth (1989). In simplistic terms, The CVFE method can be described as a block-centered finite difference method on