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Center for Nonlinear Studies |
Modeling flow and transport in fractured porous media is challenging because of the disparity in length and time scales between processes in the porous matrix and embedded fracture networks. To model both domains simultaneously, it is necessary to capture dramatically different physical behavior defined by extreme gradients in parameters, such as permeability. The model space is further complicated by the geometry of the problem, where fractures are effectively 2-dimensional surfaces in a 3-dimensional matrix, which must be captured in any explicit modeling scheme. To avoid these complications, we havedeveloped a computational geometry algorithm to represent the fracture-matrix system as a uniform-dimension continuum mesh, which contains the underlying fracture properties as upscaled cell- or node-based attributes. The fractures themselves are not explicitly represented in this formulation, but the meshes are adaptively refinedin the area of the fractures, which preserves the underlying network topology, as well as captures gradients between the fracture network andsurrounding matrix. This approach avoids the complicated numerical methods needed to represent the true multidimensional fracture-matrixsystem and is portable to many pre-existing computational tools. To date, we have successfully tested various continuum meshes in flow, transport, and heat simulations. In this talk, I will give an overview of the computational geometry algorithm we have developed to make thesemeshes, as well as the upscaling techniques that are needed to perform multiphysics simulations on them.
Host: David Métivier