G. K. Batchelor, An Introduction to Fluid Dynamics, Dynamics of Fluids in Porous Media, 1972.
DOI : 10.1017/CBO9780511800955

G. S. Beavers and D. D. Joseph, Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, vol.none, issue.01, pp.197-207, 1967.
DOI : 10.1017/S0022112067001375

C. Beckermann, H. Diepers, I. Steinbach, A. Karma, and X. Tong, Modeling Melt Convection in Phase-Field Simulations of Solidification, Journal of Computational Physics, vol.154, issue.2, pp.468-496, 1999.
DOI : 10.1006/jcph.1999.6323

C. Beckermann and R. Viskanta, Natural convection solid/liquid phase change in porous media, International Journal of Heat and Mass Transfer, vol.31, issue.1, pp.35-46, 1988.
DOI : 10.1016/0017-9310(88)90220-7

W. D. Bennon and F. P. Incropera, A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems???I. Model formulation, International Journal of Heat and Mass Transfer, vol.30, issue.10, pp.2161-2171, 1987.
DOI : 10.1016/0017-9310(87)90094-9

H. C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, vol.15, issue.1, pp.27-34
DOI : 10.1002/andp.19063240204

C. A. Chung and M. G. Worster, Steady-state chimneys in a mushy layer, Journal of Fluid Mechanics, vol.455, pp.387-411, 2002.
DOI : 10.1017/S0022112001007558

&. Beavers and . Joseph, interfacial conditions with ? = 1 (dashed line) for the solidification of a binary alloy in a corner flow (V pull = 1, V = 10, C? ? Ce) = ?7, 1967.

M. Cieszko and J. Kubik, Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid, Transport in Porous Media, pp.319-336, 1999.
DOI : 10.1007/978-94-011-4579-4_20

S. D. Felicelli, J. C. Heinrich, and D. R. Poirier, Simulation of freckles during vertical solidification of binary alloys, Metallurgical Transactions B, vol.10, issue.6, pp.847-859, 1991.
DOI : 10.1007/BF02651162

W. G. Gray, A derivation of the equations for multi-phase transport, Chemical Engineering Science, vol.30, issue.2, pp.229-233
DOI : 10.1016/0009-2509(75)80010-8

J. Gu and C. Beckermann, Simulation of convection and macrosegregation in a large steel ingot, Metallurgical and Materials Transactions A, vol.15, issue.5, pp.1357-1366, 1999.
DOI : 10.1007/s11661-999-0284-5

R. N. Hills, D. E. Loper, and P. H. Roberts, A THERMODYNAMICALLY CONSISTENT MODEL OF A MUSHY ZONE, The Quarterly Journal of Mechanics and Applied Mathematics, vol.36, issue.4, pp.505-539
DOI : 10.1093/qjmam/36.4.505

T. U. Kaempfer and M. Rappaz, Modelling of macrosegregation during solidification processes using an adaptive domain decomposition method, Modelling and Simulation in Materials Science and Engineering, vol.11, issue.4, pp.575-597, 2003.
DOI : 10.1088/0965-0393/11/4/310

M. Lesieur, Numerical simulations of turbulence in shear flows Advances in turbulence IV, In Applied Scientific Research, pp.345-351, 1993.

T. Levy and E. Sanchez-palencia, On boundary conditions for fluid flow in porous media, International Journal of Engineering Science, vol.13, issue.11, pp.923-940, 1975.
DOI : 10.1016/0020-7225(75)90054-3

P. Moin, K. Squires, W. Cabot, and S. Lee, A dynamic subgrid???scale model for compressible turbulence and scalar transport, Physics of Fluids A: Fluid Dynamics, vol.3, issue.11, pp.2746-2757, 1991.
DOI : 10.1063/1.858164

G. H. Neale and W. K. Nader, Prediction of transport processes within porous media: Creeping flow relative to a fixed swarm of spherical particles, AIChE Journal, vol.20, issue.3, pp.530-538, 1974.
DOI : 10.1002/aic.690200314

J. Ochoa-tapia and S. Whitaker, Momentum transfer at the boundary between a porous medium and a homogeneous fluid???I. Theoretical development, International Journal of Heat and Mass Transfer, vol.38, issue.14, pp.2635-2646, 1995.
DOI : 10.1016/0017-9310(94)00346-W

J. Ochoa-tapia and S. Whitaker, Momentum transfer at the boundary between a porous medium and a homogeneous fluid???II. Comparison with experiment, International Journal of Heat and Mass Transfer, vol.38, issue.14, pp.2647-2655, 1995.
DOI : 10.1016/0017-9310(94)00347-X

P. G. Saffman, On the Boundary Condition at the Surface of a Porous Medium, Studies in Applied Mathematics, vol.30, issue.2, pp.93-101, 1971.
DOI : 10.1002/sapm197150293

T. P. Schulze and M. G. Worster, Weak convection, liquid inclusions and the formation of chimneys in mushy layers, Journal of Fluid Mechanics, vol.388, pp.197-215, 1999.
DOI : 10.1017/S0022112099004589

S. Whitaker, The method of volume averaging, 1999.
DOI : 10.1007/978-94-017-3389-2

M. G. Worster, CONVECTION IN MUSHY LAYERS, Annual Review of Fluid Mechanics, vol.29, issue.1, pp.91-122, 1997.
DOI : 10.1146/annurev.fluid.29.1.91

M. G. Worster, Solidification of fluids, Perspectives in Fluid Dynamics, pp.393-446, 2000.

P. Zhao and C. F. Chen, Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model, International Journal of Heat and Mass Transfer, vol.44, issue.24, pp.4625-4633, 2001.
DOI : 10.1016/S0017-9310(01)00102-8