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S.B.M. Bosma
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A novel multiscale method for discrete fracture modeling on unstructured grids (MS-DFM) is developed. To this end, the DFM fine-scale discrete system is constructed using unstructured conforming cells for the matrix with lower-dimensional fracture elements placed at their interfaces. On this unstructured fine grid, MS-DFM imposes independent unstructured coarse grids for the fracture and matrix domains. While the conservative coarse-scale system is solved over these coarse-grid cells, overlapping dual-coarse blocks are also formed in order to provide local supports for the multiscale basis functions. To increase the accuracy, but maintaining the computational efficiency, fracture-matrix coupling is considered only for the basis functions inside the matrix domain. This results in additional (enriching) fracture basis functions in the matrix. By construction, basis functions form the partition of unity for both fracture and matrix sub-domains. Furthermore, to enable error reduction to any desired level, a convergent iterative strategy is developed, where MS-DFM is employed along with a fine-scale smoother in order to resolve low- and high-frequency modes in the error. The performance of MS-DFM is assessed for several 2D and 3D test cases. The proposed method achieves accurate results for several test cases even without iterations, and for challenging ones with only a few iterations. MS-DFM is the first of its kind, and thus extends the application of multiscale methods to unstructured discrete fracture models. As such, it provides a promising framework for real-field application of unstructured DFM.
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A novel multiscale method for discrete fracture modeling on unstructured grids (MS-DFM) is developed. To this end, the DFM fine-scale discrete system is constructed using unstructured conforming cells for the matrix with lower-dimensional fracture elements placed at their interfaces. On this unstructured fine grid, MS-DFM imposes independent unstructured coarse grids for the fracture and matrix domains. While the conservative coarse-scale system is solved over these coarse-grid cells, overlapping dual-coarse blocks are also formed in order to provide local supports for the multiscale basis functions. To increase the accuracy, but maintaining the computational efficiency, fracture-matrix coupling is considered only for the basis functions inside the matrix domain. This results in additional (enriching) fracture basis functions in the matrix. By construction, basis functions form the partition of unity for both fracture and matrix sub-domains. Furthermore, to enable error reduction to any desired level, a convergent iterative strategy is developed, where MS-DFM is employed along with a fine-scale smoother in order to resolve low- and high-frequency modes in the error. The performance of MS-DFM is assessed for several 2D and 3D test cases. The proposed method achieves accurate results for several test cases even without iterations, and for challenging ones with only a few iterations. MS-DFM is the first of its kind, and thus extends the application of multiscale methods to unstructured discrete fracture models. As such, it provides a promising framework for real-field application of unstructured DFM.
A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.
...
A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.
A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.
...
A multiscale method for Discrete Fracture Modeling (DFM) using unstructured grids is developed. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) shaped grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarseand dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. By construction, the basis functions are a partition of unity. For 2D and 3D test cases, the performance of the multiscale method is systematically assessed. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The presented multiscale method is a promising framework for real-field application of DFM models.
Bachelor thesis
(2013)
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S.B.M. Bosma, A.A.L.A.X.A.V. Eggermont, R. Heuijerjans, F. Kruijssen, S.A. Leest, M.A. Meijburg, K.L.L. Morias, F.S.C. van den Oudenalder, B. Peerlings, K.B. van Zomeren, A. Gangoli Rao, P. Lv, S. Pröbsting