Our approach for parallel multiphysics and multiscale simulation uses two levels of domain decomposition: physical and computational. First, the physical domain is decomposed into subdomains or blocks according to the geometry, geology, and physics/chemistry/biology. Each subdomain represents a single physical system, on a reasonable range of scales, such as a black oil region, a compositional region, a region to one side of a fault, or a near-wellbore region. Second, the computations are decomposed on a parallel machine for efficiency. That is, we use a multiblock or macro-hybrid approach, in which we describe a domain as a union of regions or blocks, and employ an appropriate hierarchical model on each block.

This approach allows one to define grids and computations independently on each block. This local grid structure has many advantages. It allows the most efficient and accurate discretization techniques to be employed in each block. The multiblock structure of the algebraic systems allows for the design and use of efficient domain decomposition solvers and preconditioners. Decomposition into independent blocks offers great flexibility in accommodating the shape of the external boundary, the presence of internal features such as faults and wells, and the need to refine a region of the domain in space or time (by treating it as a distinct block); interfacing structured and unstructured grids; and accommodating various models of multiscale and multiphysical phenomena. The resulting grid is not suited to direct application of discretization methods. We use mortar space techniques to impose physically meaningful, mass conservative, fluxmatching conditions on the interfaces between blocks.

We present numerical simulations to illustrate several of these decomposition strategies, including the coupling of IMPES and fully implicit models and upscaling by varying the number of degrees of freedom on the block interfaces.

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