HMM-GEM scheme for generic meshes in 2D
Acknowledgement: This research was supported by the Australian Government through the Australian Research Council's Discovery Projects funding scheme (project number DP170100605).
meshes: Different mesh types are given in meshes_HMM_GEM
Problems:
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Diffusion model (found in HMM_diffusion_with_postprocessing)
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Advection-reaction model for solenoidal fields (found in ELLAM_MMOC_advection_reaction)
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Miscible flow model (found in HMM-GEM_miscible_flow)
Some references:
[1] J. Droniou, R. Eymard, T. Gallouet, and R. Herbin. A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods. Math. Models Methods Appl. Sci., 20(2):265-295, 2010. https://arxiv.org/abs/0812.2097
[2] H. M. Cheng and J. Droniou. An HMM-ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media. Journal of Petroleum Science and Engineering, 172:707-723, 2019. https://arxiv.org/abs/1706.02452
[3] H. M. Cheng, J. Droniou, and K.-N. Le. A combined GDM-ELLAM-MMOC scheme for advection dominated PDEs. ArXiv e-prints, May 2018. https://arxiv.org/abs/1805.05585
Notes:
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For a detailed discussion of the HMM, see [1].
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The full HMM--ELLAM scheme for the miscible flow model can be found in ([2] Chapter 2).
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The post-processing of the HMM solutions used for velocity reconstructions can be found in ([2] Section 2.3)
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Discussion on how to perform characteristic tracking using the reconstructed RT0 velocities is found in ([2] Section 2.4).
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The HMM--GEM scheme for the miscible flow model is presented in ([3] Chapter 5).
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The combined ELLAM-MMOC scheme for advection PDEs is presented in ([3] Chapter 4).
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The local volume adjustments can be found in ([3] Section 2.5).