The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow

DOI10.1016/j.amc.2015.03.131zbMath1410.76302OpenAlexW302697133WikidataQ57436786 ScholiaQ57436786MaRDI QIDQ1659641

Juan Ruiz Álvarez, Zhilin Li

Publication date: 22 August 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.03.131

zbMATH Keywords

finite difference methoddiscontinuous coefficientslevel set methodimmersed interface methodHele-Shaw flowaxis-symmetric interface problem

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for boundary value problems involving PDEs (65N06) Other free boundary flows; Hele-Shaw flows (76D27)

Uses Software

• IIMPACK

Cites Work

• The IIM in polar coordinates and its application to electro capacitance tomography problems
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Removing the stiffness from interfacial flows with surface tension
• A hybrid method for moving interface problems with application to the Hele-Shaw flow
• On the geometry of Hele-Shaw flows with small surface tension
• Level set methods and dynamic implicit surfaces
• A variational level set approach to multiphase motion
• Conformal and potential analysis in Hele-Shaw cells.
• Singularities in Hele--Shaw Flows Driven by a Multipole
• Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Numerical study of Hele-Shaw flow with suction
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Singularities in Hele--Shaw Flows
• A Fast Iterative Algorithm for Elliptic Interface Problems
• Singularity formation in Hele–Shaw bubbles
• The singular perturbation of surface tension in Hele-Shaw flows
• Miscible displacement in a Hele-Shaw cell at high rates
• A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube
• The Immersed Interface Method
• Instabilities and singularities in Hele–Shaw flow
• Computation of axisymmetric suction flow through porous media in the presence of surface tension

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