Multiblock numerical methods for multiphase flow and transport in porous media

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The main objective of this research is to develop accurate, efficient, and robust numerical methods for modeling subsurface flow and transport. The research approach is based on a recently developed multiblock domain decomposition methodology. The equations hold with their usual meaning on the subdomains, with physically meaningful boundary conditions imposed on the interfaces via mortar finite elements. The formulation provides great flexibility for multiphysics and multinumerics couplings and treatment of irregular geometries and internal boundaries. It is very suitable for efficient parallel implementations. This research will study discretization issues - multiblock schemes for advection dominated problems and multilevel adaptive techniques, efficient solvers - parallel domain decomposition-Newton-Krylov-multigrid methods, and modeling issues - multiphysics couplings.Computer modeling of fluid flow and transport in the subsurface has a major economic impact on environmental and energy industries. It can provide dependable and cost-effective solutions to global problems like contaminant groundwater remediation and enhanced oil recovery. Groundwater supplies are often contaminated by organic, inorganic, and radioactive sources due to improper disposal. Remediation costs at U.S. government sites alone range into the hundreds of billions of dollars. 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. Current computer simulators are limited in their ability to incorporate fine scale geological data and to resolve the physical processes occurring on a wide range of spatial (microns to kilometers) and temporal (microseconds to thousands of years) scales. The goal of this research is to develop new and efficient computational methods for modeling multiphase flow and transport in porous media on multiprocessor computers. These new methods will allow for more accurate resolution of the underlying multiscale phenomena and thus improve the dependability of the computer simulators.