Adaptive Multiscale Simulation Framework for Reduced-Order Modeling in Perforated Domains

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Processes in perforated domains occur in many important applications. These include complex processes in soil, membranes, and filters. With current imaging techniques, detailed microscale geometries of these perforated materials can be constructed. However, it is prohibitively expensive to solve complex processes in these perforated domains due to a rich hierarchy of scales. For this reason, some types of reduced-order computational techniques are needed. The goal of this project is to develop and analyze novel computational techniques for solving challenging multiscale problems in perforated domains. The new approaches will bring the information from the detailed geometries to large-scale simulations and will improve the predictions in the simulations. This will further allow deigning new materials and optimize processes. Many current approaches for multiscale methods for problems in perforated domains have been restricted to homogenization, which is applicable when the media has scale separation. However, in many realistic perforated media, there is no scale separation, i.e., pore sizes can have a wide variety of scales. The multiscale methods of this project develop a general framework that allows rigorous and systematic reduction. The PI's goals are: (1) to develop systematic local model reduction tools for computing multiscale basis functions; (2) to develop and analyze new finite element techniques using these basis functions; (3) to study the interplay between localization of the basis functions and the global coupling mechanism; (4) to apply the developed methods to a wide variety of flows with nonlinearities and multiphysics in 3D; (5) to test and demonstrate their capabilities for solving problems in engineering and geosciences.