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Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments (2015)
Journal Article
Muljadi, B. P., Narski, J., Lozinski, A., & Degond, P. (in press). Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 13(4), https://doi.org/10.1137/14096428X

The multiscale finite element method (MsFEM) is developed in the vein of the Crouzeix--Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at multiple... Read More about Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments.

The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation (2015)
Journal Article
Muljadi, B. P., Blunt, M. J., Raeini, A. Q., & Bijeljic, B. (2016). The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation. Advances in Water Resources, 95, https://doi.org/10.1016/j.advwatres.2015.05.019

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation... Read More about The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation.

Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media (2015)
Journal Article
Degond, P., Lozinski, A., Muljadi, B. P., & Narski, J. (in press). Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media. Communications in Computational Physics, 17(4), https://doi.org/10.4208/cicp.2014.m299

The adaptation of Crouzeix-Raviart finite element in the context of multi-scale finite element method (MsFEM) is studied and implemented on diffusion and advection-diffusion problems in perforated media. It is known that the approximation of boundary... Read More about Crouzeix-Raviart MsFEM with bubble functions for diffusion and advection-diffusion in perforated media.