Physical and Computational Domain Decompositions for Modeling Subsurface Flows

Modeling of multiphase flow in permeable media plays a central role in subsurface environmental remediation as well as in problems associated with production of hydrocarbon energy from existing oil and gas fields. Numerical simulation is essential for risk assessment, cost reduction, and rational and efficient use of resources. The contamination of groundwater is one of the most serious environmental problems facing the world. For example, more than 50% of drinking water in the Unites States comes from groundwater. More than 10,000 active military installations and over 6,200 closed installations in the United States require subsurface remediation. The process is difficult and extremely expensive and only now is technology emerging to cope with this severe and widespread problem. Hydrocarbons contribute almost two-thirds of the nation’s energy supply. Moreover, recoverable reserves are being increased twice as fast by enhanced oil recovery techniques as by exploration. Features that make the above problems difficult for numerical simulation include: multiple phases and chemical components, multi-scale heterogeneities, stiff gradients, irregular geometries with internal boundaries such as faults and layers, and multi-physics. Because of the uncertainty in the data, one frequently assumes stochastic coefficients and thus is forced to multiple realizations; therefore both computational efficiency and accuracy are crucial in the simulations. For efficiency, the future lies in developing parallel simulators which utilize domain decomposition algorithms. One may ask what are the important aspects of parallel computation for these complex physical models. First, in all cases, one must be able to partition dynamically the geological domain based upon the physics of the model. Second, efficient distribution of the computations must be performed. Critical issues here are load balancing and minimal communication overhead. It is important to note that the two decompositions may be different.