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arXiv · 1707.04038

An arbitrary order scheme on generic meshes for miscible displacements in porous media

Daniel Anderson·Jerome Droniou
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Abstract

We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the Hybrid-High-Order (HHO) method due to Di Pietro et al. [Computational Methods in Applied Mathematics, 14(4), (2014)]. The equation governing the pressure is discretised using an adaptation of the HHO method for variable diffusion, while the discrete concentration equation is based on the HHO method for advection-diffusion-reaction problems combined with numerically stable flux reconstructions for the advective velocity that we have derived using the results of Cockburn et al. [ESAIM: Mathematical Modelling and Numerical Analysis, 50(3), (2016)]. We perform some rigorous analysis of the method to demonstrate its $L^2$ stability under the irregular data often presented by reservoir engineering problems and present several numerical tests to demonstrate the quality of the results that are produced by the proposed scheme.

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Daniel Anderson, Jerome Droniou. 2017-07-13. An arbitrary order scheme on generic meshes for miscible displacements in porous media. https://doi.org/10.1137/17m1138807

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