Abstract
This work is devoted to the new hybrid method for solving a coupled system of advection–diffusion equations posed in a bulk domain and on an embedded surface. Systems of this kind arise in many engineering and natural science applications, but we consider the modeling of contaminant transport in fractured porous media as an example of an application. Fractures in a porous medium are considered as sharp interfaces between the surrounding bulk subdomains. 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 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. The surface intersects an octree grid and we get a polyhedral octree mesh with cut-cells. The numerical properties of the hybrid approach are illustrated in a series of numerical experiments with different embedded geometries. The method demonstrates great flexibility in handling curvilinear or branching embedded structures.
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Acknowledgements
This work has been supported by RFBR through the grant 16-31-00527 and by NSF through the Division of Mathematical Sciences grant 1522252.
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Chernyshenko, A., Olshahskii, M., Vassilevski, Y. (2017). A Hybrid Finite Volume—Finite Element Method for Modeling Flows in Fractured Media . In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_55
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DOI: https://doi.org/10.1007/978-3-319-57394-6_55
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