A hybrid method for moving interface problems with application to the Hele-Shaw flow
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Publication:1368637
DOI10.1006/jcph.1997.5689zbMath0888.76067OpenAlexW2123584617MaRDI QIDQ1368637
Zhilin Li, Thomas Yizhao Hou, Stanley J. Osher, Hong-Kai Zhao
Publication date: 4 June 1998
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jcph.1997.5689
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- A continuum method for modeling surface tension
- A front-tracking method for viscous, incompressible multi-fluid flows
- Numerical analysis of blood flow in the heart
- The immersed interface method for acoustic wave equations with discontinuous coefficients
- Some numerical methods for the Hele-Shaw equations
- A level set approach for computing solutions to incompressible two-phase flow
- Removing the stiffness from interfacial flows with surface tension
- A note on immersed interface method for three-dimensional elliptic equations
- A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
- An Eulerian approach for vortex motion using a level set regularization procedure
- A variational level set approach to multiphase motion
- Numerical experiments on Hele Shaw flow with a sharp interface
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
- Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation
- A boundary-integral method for two-phase displacement in Hele-Shaw cells
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- A study of singularity formation in a vortex sheet by the point-vortex approximation
- Interface conditions for two-phase displacement in Hele-Shaw cells
- High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
- Regularization of Ill-Posed Problems Via the Level Set Approach
- A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
- A Fast Iterative Algorithm for Elliptic Interface Problems
- A fast algorithm for particle simulations