References
- Lake , LW , Schmidt , RL and Venuto , PB . 1992 . A niche for enhanced oil recovery in the 1990s . Oilfield Rev. , 88 ( 17 ) : 55 – 61 .
- Hill , S . 1952 . Channeling in packed columns . Chem. Eng. Sci. , 1 ( 6 ) : 247 – 253 .
- Chouke , RL , van Meurs , P and van der Poel , C . 1959 . The instability of slow immiscible, viscous liquidliquid displacements in permeable media . Petrol. Trans. AIME , 216 : 188 – 194 .
- Helmig , R , Weiss , A and Wohlmuth , BJ . 2007 . Dynamic capillary effects in heterogeneous porous media . Comput. Geosci. , 11 : 261 – 274 .
- Peaceman , D . 1977 . Fundamentals of Numerical Reservoir Simulation , Amsterdam , NY : Elsevier Scientific .
- van Duijn , CJ , Peletier , LA and Pop , IS . 2007 . A new class of entropy solutions of the Buckley–Leverett equation . SIAM J. Math. Anal. , 39 ( 2 ) : 507 – 536 .
- Saffman , PG and Taylor , GI . 1958 . The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid . Proc. R. Soc. Lond. Ser. A , 245 : 312 – 329 .
- Buckley , SE and Leverett , MC . 1942 . Mechanism of fluid displacement in sands . Trans. Am. Inst. Mining Metal. Eng. Petrol. Develop. Technol. Petrol. Div. , 146 : 107 – 116 .
- Hassanizadeh , SM and Gray , WG . 1990 . Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries . Adv. Water Res. , 13 : 169 – 186 .
- Hassanizadeh , SM and Gray , WG . 1993 . Thermodynamic basis of capillary pressure in porous media . Water Resour. Res. , 29 : 3389 – 3405 .
- Bertozzi , AL and Brenner , MP . 1997 . Linear instability and transient growth in driven contact lines . Phys. Fluids , 9 ( 3 ) : 530 – 539 .
- Yortsos , YC and Hickernell , FJ . 1989 . Linear stability of immiscible displacement in porous media . SIAM J. Appl. Math. , 49 ( 3 ) : 730 – 748 .
- Riaz , A and Tchelepi , HA . 2007 . Numerical simulation of immiscible two-phase flow in porous media . Phys. Fluids , 19 ( 7 ) : 072103
- Kim , JS , Kang , K and Lowengrub , JS . 2004 . Conservative multigrid methods for Cahn–Hilliard fluids . J. Comput. Phys. , 193 ( 2 ) : 511 – 543 .
- Trottenberg , U , Schuller , A and Oosterlee , C . 2005 . Multigrid, Academic Press New York
- Wise , S , Kim , J and Lowengrub , JS . 2007 . Solving the regularized, strongly anisotropic Cahn–Hilliard equation by an adaptive nonlinear multigrid method . J. Comput. Phys. , 226 ( 1 ) : 414 – 446 .