TY - JOUR
T1 - Boundary Integral Methods for Multicomponent Fluids and Multiphase Materials
AU - Hou, T. Y.
AU - Lowengrub, J. S.
AU - Shelley, M. J.
N1 - Funding Information:
The authors thank R. Almgren, N. Akaiwa, P. H. Leo, D. Meiron, Q. Nie, D. Thompson, K. Thornton, and P. Voorhees, who provided us with figures from their recent results. T.Y.H. acknowledges support from NSF Grant DMS-9704976 and ARO Grant DAAD19-99-1-0141 (ARO). J.L. acknowledges support from NSF Grant DMS-9706931 and from the Minnesota Supercomputer Institute. M.J.S. acknowledges support from NSF Grant DMS-9707494 and DOE Grant DE-FG02-88ER25053.
PY - 2001/5/20
Y1 - 2001/5/20
N2 - We present a brief review of the application of boundary integral methods in two dimensions to multicomponent fluid flows and multiphase problems in materials science. We focus on the recent development and outcomes of methods which accurately and efficiently include surface tension. In fluid flows, we examine the effects of surface tension on the Kelvin-Helmholtz and Rayleigh-Taylor instabilities in inviscid fluids, the generation of capillary waves on the free surface, and problems in Hele-Shaw flows involving pattern formation through the Saffman-Taylor instability, pattern selection, and singularity formation. In materials science, we discuss microstructure evolution in diffusional phase transformations, and the effects of the competition between surface and elastic energies on microstructure morphology. A common link between these different physical phenomena is the utility of an analysis of the appropriate equations of motion at small spatial scales to develop accurate and efficient time-stepping methods.
AB - We present a brief review of the application of boundary integral methods in two dimensions to multicomponent fluid flows and multiphase problems in materials science. We focus on the recent development and outcomes of methods which accurately and efficiently include surface tension. In fluid flows, we examine the effects of surface tension on the Kelvin-Helmholtz and Rayleigh-Taylor instabilities in inviscid fluids, the generation of capillary waves on the free surface, and problems in Hele-Shaw flows involving pattern formation through the Saffman-Taylor instability, pattern selection, and singularity formation. In materials science, we discuss microstructure evolution in diffusional phase transformations, and the effects of the competition between surface and elastic energies on microstructure morphology. A common link between these different physical phenomena is the utility of an analysis of the appropriate equations of motion at small spatial scales to develop accurate and efficient time-stepping methods.
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U2 - 10.1006/jcph.2000.6626
DO - 10.1006/jcph.2000.6626
M3 - Article
AN - SCOPUS:0000968412
SN - 0021-9991
VL - 169
SP - 302
EP - 362
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -