A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS
DOI10.1017/S144618112100033XzbMath1482.76043arXiv2101.07447OpenAlexW3204957104MaRDI QIDQ5164390
Liam C. Morrow, Michael Charles Dallaston, Scott W. McCue, Timothy J. Moroney
Publication date: 11 November 2021
Published in: The ANZIAM Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.07447
conformal mappingboundary integral methodviscous fingeringSaffman-Taylor instabilityfinite difference level-set methodmoving boundary Hele-Shaw problem
Interfacial stability and instability in hydrodynamic stability (76E17) Impact in solid mechanics (74M20) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02) Complex variables methods applied to problems in fluid mechanics (76M40) Basic methods in fluid mechanics (76M99) Other free boundary flows; Hele-Shaw flows (76D27)
Related Items (5)
Cites Work
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- Finite-difference ghost-point multigrid methods on Cartesian grids for elliptic problems in arbitrary domains
- The effect of finiteness in the Saffman-Taylor viscous fingering problem
- From the Hele-Shaw experiment to integrable systems: a historical overview
- Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I: Velocity selection
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Removing the stiffness from interfacial flows with surface tension
- A simple level set method for solving Stefan problems
- A hybrid method for moving interface problems with application to the Hele-Shaw flow
- The selection of Saffman-Taylor fingers by kinetic undercooling
- A level set approach for the numerical simulation of dendritic growth
- A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
- Hele-Shaw flows with nonlinear kinetic undercooling regularization
- Extending fields in a level set method by solving a biharmonic equation
- A review of level-set methods and some recent applications
- Radial fingering in a Hele-Shaw cell: A weakly nonlinear analysis
- Level set methods and dynamic implicit surfaces
- A hybrid particle level set method for improved interface capturing
- Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell
- The stability of immiscible viscous fingering in Hele-Shaw cells with spatially varying permeability
- A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell
- A boundary element study of the effect of surface dissolution on the evolution of immiscible viscous fingering within a Hele-Shaw cell
- Conformal and potential analysis in Hele-Shaw cells.
- Exact solutions for steady bubbles in a Hele-Shaw cell with rectangular geometry
- Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularization
- Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells
- The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells
- Principal warps: thin-plate splines and the decomposition of deformations
- Contracting bubbles in Hele-Shaw cells with a power-law fluid
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
- The motion of long bubbles in tubes
- Modelling finger propagation in elasto-rigid channels
- Stability results for multi-layer radial Hele-Shaw and porous media flows
- Numerical study of Hele-Shaw flow with suction
- Coriolis effects in a rotating Hele-Shaw cell
- Stretch flow of thin layers of Newtonian liquids: Fingering patterns and lifting forces
- Pattern formation in non-Newtonian Hele–Shaw flow
- Two-phase displacement in Hele Shaw cells: theory
- A boundary-integral method for two-phase displacement in Hele-Shaw cells
- SINGULARITY DEVELOPMENT IN MOVING-BOUNDARY PROBLEMS
- Cusp Development in Hele–Shaw Flow with a Free Surface
- Fingering in Hele-Shaw cells
- Bubble growth in porous media and Hele–Shaw cells
- Viscous fingering in Hele-Shaw cells
- Stability of bubbles in a Hele–Shaw cell
- Analytic theory for the selection of a symmetric Saffman–Taylor finger in a Hele–Shaw cell
- Hele - Shaw flow and pattern formation in a time-dependent gap
- The effect of surface tension on the shape of fingers in a Hele Shaw cell
- Moving boundary problems in the flow of liquid through porous media
- A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble
- A MODEL FOR NON-SMOOTH FREE BOUNDARIES IN HELE-SHAW FLOWS
- On the classification of solutions to the zero-surface-tension model for Hele-Shaw free boundary flows
- Singularities in Hele--Shaw Flows
- Numerical simulations of sink flow in the Hele-Shaw cell with small surface tension
- L<scp>EVEL</scp> S<scp>ET</scp> M<scp>ETHODS FOR</scp> F<scp>LUID</scp> I<scp>NTERFACES</scp>
- On the rôle of Stokes lines in the selection of Saffman–Taylor fingers with small surface tension
- Two-dimensional Stokes and Hele-Shaw flows with free surfaces
- The singular perturbation of surface tension in Hele-Shaw flows
- Surprises in viscous fingering
- Viscous fingering in a radial elastic-walled Hele-Shaw cell
- Computation of a Shrinking Interface in a Hele-Shaw Cell
- Rigorous results in existence and selection of Saffman–Taylor fingers by kinetic undercooling
- The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell
- Hele–Shaw flow with a point sink: generic solution breakdown
- On nonlinear interface dynamics in Hele-Shaw flows
- Control of viscous instability by variation of injection rate in a fluid with time-dependent rheology
- Sensitivity of Saffman–Taylor fingers to channel-depth perturbations
- Stability results on radial porous media and Hele-Shaw flows with variable viscosity between two moving interfaces
- Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell
- Dynamics of front propagation in a compliant channel
- Selection of a Hele-Shaw Bubble via Exponential Asymptotics
- Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
- Moving Boundary Problems for Quasi-Steady Conduction Limited Melting
- New exact solutions for Hele-Shaw flow in doubly connected regions
- On Hele–Shaw flow of power-law fluids
- Resonance-like dynamics in radial cyclic injection flows of immiscible fluids in homogeneous porous media
- Convective Stabilization of a Laplacian Moving Boundary Problem with Kinetic Undercooling
- Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation
- Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
- Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges
- Boundary integral methods for multicomponent fluids and multiphase materials.
- Level set methods: An overview and some recent results
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