References
References
- Constantin , P and Pugh , M . 1993 . Global solutions for small data to the Hele-Shaw problem . Nonlinearity , 6 : 393 – 415 .
- Almgren , R . 1996 . Singularity formation in Hele-Shaw bubbles . Phys. Fluids , 8 : 344 – 52 .
- Goldstein , R E , Pesci , A and Shelley , M J . 1998 . Instabilities and singularities in Hele—Shaw flow . Phys. Fluids , 10 : 2701 – 23 .
- Howison , S D . 1986 . Cusp development in a Hele—Shaw flow with a free surface . SIAM J. Appl. Math. , 46 : 20 – 6 .
- DiBenedetto , E and Friedman , A . 1984 . The ill-posed Hele—Shaw model and the Stefan problem for supercooled water . Trans. Am. Math. Soc. , 282 : 183 – 204 .
- Howison , S D , Ockendon , J R and Lacey , A A . 1985 . Singularity development in moving-boundary problems . Q. J. Mech. Appl. Math. , 38 : 343 – 60 .
- DeGregoria , A J and Schwartz , L W . 1986 . A boundary-integral method for two-phase displacement in Hele—Shaw cells . J. Fluid Mech. , 164 : 383 – 400 .
- Meiburg , E and Homsy , G M . 1988 . Nonlinear unstable viscous fingers in Hele—Shaw flows: 2. Numerical simulation . Phys. Fluids , 31 : 429 – 39 .
- Ceniceros , H D , Hou , T Y and Si , H . 1999 . Numerical study of Hele—Shaw flow with suction . Phys. Fluids , 11 : 2471 – 86 .
- Hou , T Y , Lowengrub , J and Shelley , M . 1994 . Removing the stiffness from interfacial flow with surface tension . J. Comput. Phys. , 114 : 312 – 38 .
- Tryggvason , G and Aref , H . 1983 . Numerical experiments in Hele—Shaw flows with a sharp interface . J. Fluid Mech. , 136 : 1 – 30 .
- Ascher , U M , Ruuth , S J and Wetton , B . 1995 . Implicit—explicit methods for time-dependent pde's . SIAM J. Numer. Anal. , 32 : 797 – 823 .
- Shelley , M J . 1992 . A study of singularity formation in vortex sheet motion by a spectrally accurate vortex method . J. Fluid. Mech. , 244 : 493 – 526 .
- Tanveer , S . 1993 . Evolution of Hele—Shaw interface for small surface tension . Phil. Trans. R. Soc. , A 343 : 155 – 204 .
- Siegel , M , Tanveer , S and Dai , W . 1996 . Singular effects of surface tension in evolving Hele—Shaw flows . J. Fluid Mech. , 323 : 201 – 36 .
- Baker , G R and Shelley , M J . 1986 . Boundary integral techniques for multi-connected domains . J. Comput. Phys. , 64 : 112 – 32 .
- Zimmerman , W B and Homsy , G M . 1992 . Viscous fingering in miscible displacements: unification of effects of viscosity contrast, anisotropic dispersion, and velocity dependence of dispersion on nonlinear finger propagation . Phys. Fluids , A 4 : 2348 – 59 .
- Petitjeans , P , Chen , C-Y , Meiburg , E and Maxworthy , T . 1999 . Miscible quarter five-spot displacements in Hele—Shaw cell and the role of flow-induced dispersion . Phys. Fluids , 11 : 1705 – 16 .