Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection
Tóm tắt
This paper presents three-dimensional finite element simulations to evaluate diffusion and dispersion tensors in periodic porous media in the presence of an advective velocity field. These tensors are evaluated in the framework of the double-scale expansion technique. Two problems, a Newtonian flow and a vector-valued advection–diffusion equation, have to be sequentially solved at the pore scale. Finite element techniques to approximate these problems are proposed and analyzed. Numerical results in three-dimensional networks of spheres are presented to quantitatively assess the impact of the pore morphology and of the advection velocity on the diffusion and dispersion tensors.
Tài liệu tham khảo
Allaire, G.: Homogenization of the Stokes flow in a connected porous medium. Asymptot. Anal. 2(3), 203–222 (1989)
Atkins, P.W.: Physical Chemistry. Oxford University Press, Oxford (1992)
Auriault, J.-L.: Transport in porous media; upscaling by multiscale asymptotic expansions. In: Dormieux, L., Ulm, F.-J. (eds.) Applied micromechanics of porous materials, CISM Courses and Lectures n. 480. Springer, Berlin Heidelberg New York (2005)
Auriault, J.-L., Lewandowska, Y.: Diffusion/adsorption/advection macrotransport in soils. Eur. J. Mech. A/Solids, 15, 681–704 (1996)
Bastian, P., Rivière, B.: Superconvergence and H(div) projection for discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 42(10), 1043–1057 (2003)
Bear, J., Bachmat, Y.: Introduction to the Modelling of Transport Phenomena in Porous Media. Kluwer Academic Publishers, Dordrecht (1990)
Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic analysis for periodic structures, vol. 5 of Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam (1978)
Brezzi, F., Douglas, J. Jr., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47(2), 217–235 (1985)
Crouzeix, M., Raviart, P.-A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO. Anal. Num. 3, 33–75 (1973)
Dormieux, L., Kondo, D.: Diffusive transport in disordered media. Application to the determination of the tortuosity and the permeability of cracked material. In: Dormieux, L., Ulm, F.-J. (eds.) Applied micromechanics of porous materials, CISM Courses and Lectures n. 480. Springer, Berlin Heidelberg New York (2005)
Ene, H., Sanchez-Palencia, E.: Equations et phénomènes de surface pour l’écoulement dans un modèle de milieu poreux. J. Méc. 73–108 (1975)
Ern, A., Guermond, J.-L.: Theory and Practice of Finite Elements, vol. 159 of Applied Mathematical Sciences. Springer, Berlin Heidelberg New York (2004)
Whitaker, S.: Flow in porous media I: A theoretical derivation of Darcy’s law. Transp. Porous Media 1, 3–25 (1986)