Abstract
We develop a hybrid finite volume—finite element method for solving a coupled system of advection-diffusion equations in a bulk domain and on an embedded surface. The method is applied for modeling of flow and transport in fractured porous medium. Fractures in a porous medium are considered as sharp interfaces between the surrounding bulk subdomains. We take into account interaction between fracture and bulk domain. The method is based on a monotone nonlinear finite volume scheme for equations posed in the bulk and a trace finite element method for equations posed on the surface. The surface of fracture is not fitted by the mesh and can cut through the background mesh in an arbitrary way. The background mesh is an octree grid with cubic cells and we get a polyhedral octree mesh with cut-cells after grid-surface intersection. The numerical properties of the hybrid approach are illustrated in a series of numerical experiments.
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Acknowledgements
This work has been supported by the Russian Science Foundation Grant 17-71-10173.
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Chernyshenko, A., Olshanskii, M. (2019). Modeling Flow and Transport in Fractured Media by a Hybrid Finite Volume: Finite Element Method. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_13
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DOI: https://doi.org/10.1007/978-3-319-96415-7_13
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