The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
Abstract
A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper [SIAM J. Numer. Anal., 31(1994), pp. 1019--1044]. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used.
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Cites
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
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An Introduction to Fluid Dynamics
Batchelor, G. K. (2000) · doi:10.1017/cbo9780511800955 · Cited by 12,360
Modeling of swirl in turbulent flow systems
Sloan, D. G., Smith, P. J., & Smoot, L. D. (1986) · Progress in Energy and Combustion Science · doi:10.1016/0360-1285(86)90016-x · Cited by 5,246
Numerical analysis of blood flow in the heart
Peskin, C. S. (1977) · Journal of Computational Physics · doi:10.1016/0021-9991(77)90100-0 · Cited by 3,084
A front-tracking method for viscous, incompressible, multi-fluid flows
Unverdi, S. O., & Tryggvason, G. (1992) · Journal of Computational Physics · doi:10.1016/0021-9991(92)90307-k · Cited by 2,387
LeVeque, R. J., & Li, Z. (1994) · SIAM Journal on Numerical Analysis · doi:10.1137/0731054 · Cited by 1,501
Self-citationDynamics of Drop Deformation and Breakup in Viscous Fluids
Stone, H. A. (1994) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fl.26.010194.000433 · Cited by 1,156
Improved Volume Conservation in the Computation of Flows with Immersed Elastic Boundaries
Peskin, C. S., & Printz, B. F. (1993) · Journal of Computational Physics · doi:10.1006/jcph.1993.1051 · Cited by 291
Quirk, J. J. (1994) · Computers & Fluids · doi:10.1016/0045-7930(94)90031-0 · Cited by 248
Analysis of a One-Dimensional Model for the Immersed Boundary Method
Beyer, R. P., & LeVeque, R. J. (1992) · SIAM Journal on Numerical Analysis · doi:10.1137/0729022 · Cited by 246
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Cited by
Peskin, C. S. (2002) · Acta Numerica · doi:10.1017/s0962492902000077 · Cited by 4,603
Griffith, B. E., & Peskin, C. S. (2005) · Journal of Computational Physics · doi:10.1016/j.jcp.2005.02.011 · Cited by 299
Metadata
- Authors
- LeVeque, R. J., & Li, Z.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 1997-05
- Volume
- 18
- Issue
- 3
- Pages
- 709-735
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W1982396064
- Cited by
- 494
- References
- 17
- FWCI
- 9.72
- Type
- journal article
- Language
- en
- Open access
- closed
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