Multiscale Hybridizable Discontinuous Galerkin Method for Flow Simulations in Highly Heterogeneous Media
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We propose a multiscale hybridizable discontinuous Galerkin method for Darcy flow and two phase flow simulations in highly heterogeneous media. The multiscale space consists of offline and online multiscale basis functions. The offline basis functions are constructed by solving appropriate local spectral problem, and thus contain important local media information. The online basis functions are computed iteratively with the residuals of previous multiscale solution on selected local regions. Typically, the offline basis provides initial multiscale solution for constructing online basis. For the two phase flow simulations, we only compute the basis space for the initial permeability field and keep it fixed as time advancing. Numerical experiments show the multiscale solution can approximate the fine scale solution accurately for both types of flow simulations.
KeywordsMultiscale finite element method Hybridizable discontinuous Galerkin Two-phase flow simulation Heterogeneous media
Yanfang Yang’s work is supported by the National Natural Science Foundation of China (Grant No. 11901129).
- 11.Durfolsky, L. J.: Numerical calculation of equivalent grid block permeability tensors of heterogeneous porous media: Water Resour. Res. vol. 27, no. 5, May 1991, pp. 299–708. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol. 28, p. A350. Pergamon (1991)Google Scholar
- 17.Fabien, M.S., Knepley, M.G., Riviere, B.M.: A hybridizable discontinuous galerkin method for two-phase flow in heterogeneous porous media (2018). arXiv preprint arXiv:1802.06013
- 28.Xiao, H: Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media. PhD thesis (2013)Google Scholar