More Web Proxy on the site http://driver.im/

article

An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows

Authors:

M. OhtaAuthors Info & Claims

Journal of Scientific Computing, Volume 35, Issue 1

Pages 43 - 61

https://doi.org/10.1007/s10915-007-9173-5

Published: 01 April 2008 Publication History

Abstract

We introduce a robust method for computing viscous and viscoelastic two-phase bubble and drop motions. Our method utilizes a coupled level-set and volume-of-fluid technique for updating and representing the air-water interface. Our method introduces a novel approach for treating the viscous coupling terms at the air-water interface; these improvements result in improved stability for computing two-phase bubble formation solutions. We also present an improved, "positive-preserving" discretization technique for updating the configuration tensor for viscoelastic flows, in the context of computing two-phase bubble and drop motion.

References

[1]

Sussman, M., Smith, K.M., Hussaini, M.Y., Ohta, M., Zhi-Wei, R.: A sharp interface method for incompressible two-phase flows. J. Comput. Phys. 221(2), 469-505 (2007).

Digital Library

[2]

Jimenez, E., Sussman, M., Ohta, M.: A computational study of bubble motion in Newtonian and viscoelastic fluids. Fluid Dyn. Mater. Process. 1(2), 97-108 (2005).

[3]

Sussman, M., Ohta, M.: Improvements for calculating two-phase bubble and drop motion using an adaptive sharp interface method. Fluid Dyn. Mater. Process. 3(1), 21-36 (2007).

[4]

Kang, M., Fedkiw, R., Liu, X.-D.: A boundary condition capturing method formultiphase incompressible flow. J. Sci. Comput. 15 (2000).

[5]

Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost fluid method). J. Comput. Phys. 152(2), 457-492 (1999).

Digital Library

[6]

Liu, X.-D., Fedkiw, R.P., Kang, M.: A boundary condition capturing method for Poisson's equation on irregular domains. J. Comput. Phys. 160(1), 151-178 (2000).

Digital Library

[7]

Li, J., Renardy, Y.Y., Renardy, M.: Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Phys. Fluids 12(2), 269-282 (2000).

[8]

Hong, J.-M., Shinar, T., Kang, M., Fedkiw, R.: On boundary condition capturing for multiphase interfaces. J. Sci. Comput. 31, 99-125 (2007).

Digital Library

[9]

Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., Fedkiw, R.: Directable photorealistic liquids. In: Eurographics/ACM SIGGRAPH Symposium on Computer Animation, 2004.

[10]

Yu, J.-D., Sakai, S., Sethian, J.A.: Two-phase viscoelastic jetting. J. Comput. Phys. 220(2), 568-585 (2007).

Digital Library

[11]

Pillapakkam, S.B., Singh, P.: A level-set method for computing solutions to viscoelastic two-phase flow. J. Comput. Phys. 174(2), 552-578 (2001).

Digital Library

[12]

Goktekin, T.G., Bargteil, A.W., O'Brien, J.F.: Method for animating viscoelastic fluids. ACM Trans. Graph. 23(3), 463-468 (2004).

Digital Library

[13]

Losasso, F., Shinar, T., Selle, A., Fedkiw, R.: Multiple interacting fluids. In: SIGGRAPH 2006. ACM TOG 25, pp. 812-819 (2006).

[14]

Irving, G.: Methods for the physically based simulation of solids and fluids. Department of Computer Science, Stanford, Palo Alto (2007).

[15]

Chilcott, M.D., Rallison, J.M.: Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newton. Fluid Mech. 29, 381-432 (1988).

[16]

Singh, P., Leal, L.G.: Finite-element simulation of the start-up problem for a viscoelastic fluid in an eccentric rotating cylinder geometry using a third-order upwind scheme. Theor. Comput. Fluid Dyn. V5(2), 107-137 (1993).

[17]

Khismatullin, D., Renardy, Y., Renardy, M.: Development and implementation of VOF-PROST for 3D viscoelastic liquid-liquid simulations. J. Non-Newton. Fluid Mech. 140(1-3), 120-131 (2006).

[18]

Trebotich, D., Colella, P., Miller, G.H.: A stable and convergent scheme for viscoelastic flow in contraction channels. J. Comput. Phys. 205(1), 315-342 (2005).

Digital Library

[19]

Chang, Y., Hou, T., Merriman, B., Osher, S.: Eulerian capturing methods based on a level set formulation for incompressible fluid interfaces. J. Comput. Phys. 124, 449-464 (1996).

Digital Library

[20]

Sussman, M., Puckett, E.G.: A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301-337 (2000).

Digital Library

[21]

Tatebe, O.: The multigrid preconditioned conjugate gradient method. In: 6th Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, 1993.

[22]

Briggs, W.L., Henson, V.E., McCormick, S.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000).

[23]

van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 100, 25-37 (1979).

[24]

Sussman, M.: A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. J. Comput. Phys. 187(1), 110-136 (2003).

Digital Library

[25]

Sussman, M.: A parallelized, adaptive algorithm for multiphase flows in general geometries. Comput. Struct. 83, 435-444 (2005).

Digital Library

[26]

Hadamard, J.: Movement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris 152, 1735-1738 (1911).

[27]

Rybczynski, W.: Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium. Bull. Int. Acad. Sci. Cracovia Cl. Sci. Math. Natur, 40-46 (1911).

[28]

Bhaga, D., Weber, M.E.: Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech. Digit. Arch. 105(1), 61-85 (2006).

[29]

Bright, A.: Minimum drop volume in liquid jet breakup. Chem. Eng. Res. Des. 63, 59-66 (1985).

[30]

Richards, J.R., Lenhoff, A.M., Beris, A.N.: Dynamic breakup of liquid-liquid jets. Phys. Fluids 6, 2640- 2655 (1994).

[31]

Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201-225 (1981).

[32]

Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335-354 (1992).

Digital Library

[33]

Johnson, J.R.E., Dettre, R.H.: The wettability of low-energy liquid surfaces. J. Colloid Interface Sci. 21(6), 610-622 (1966).

[34]

Noh, D.S., Kang, I.S., Leal, L.G.: Numerical solutions for the deformation of a bubble rising in dilute polymeric fluids. Phys. Fluids A 5, 1315 (1993).

Cited By

Heryudono ARaessi M(2023)Adaptive partition of unity interpolation method with moving patchesMathematics and Computers in Simulation10.1016/j.matcom.2023.03.006210:C(49-65)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.matcom.2023.03.006
Ma MOuyang JWang X(2023)A high-order SRCR-DG method for simulating viscoelastic flows at high Weissenberg numbersEngineering with Computers10.1007/s00366-022-01707-539:5(3041-3059)Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1007/s00366-022-01707-5
Pathak ARaessi M(2019)A 3D, fully Eulerian, VOF-based solver to study the interaction between two fluids and moving rigid bodies using the fictitious domain methodJournal of Computational Physics10.1016/j.jcp.2016.01.025311:C(87-113)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.jcp.2016.01.025
Show More Cited By

Index Terms

An Improved Sharp Interface Method for Viscoelastic and Viscous Two-Phase Flows
1. Applied computing
  1. Physical sciences and engineering
    1. Physics
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations

Recommendations

A level-set continuum method for two-phase flows with insoluble surfactant

A level-set continuum surface force method is presented to compute two-phase flows with insoluble surfactant. Our method recasts the Navier-Stokes equations for a two-phase flow with insoluble surfactant as ''one-fluid'' formulation. Interfacial ...
A level-set method for two-phase flows with moving contact line and insoluble surfactant

A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, ...
Sharp interface immersed-boundary/level-set method for wave-body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost-fluid method ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 35, Issue 1

April 2008

71 pages

ISSN:0885-7474

Issue’s Table of Contents

Copyright © Copyright © 2008 Springer Science+Business Media, LLC.

Publisher

Plenum Press

United States

Publication History

Published: 01 April 2008

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 30 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Heryudono ARaessi M(2023)Adaptive partition of unity interpolation method with moving patchesMathematics and Computers in Simulation10.1016/j.matcom.2023.03.006210:C(49-65)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.matcom.2023.03.006
Ma MOuyang JWang X(2023)A high-order SRCR-DG method for simulating viscoelastic flows at high Weissenberg numbersEngineering with Computers10.1007/s00366-022-01707-539:5(3041-3059)Online publication date: 1-Oct-2023
https://dl.acm.org/doi/10.1007/s00366-022-01707-5
Pathak ARaessi M(2019)A 3D, fully Eulerian, VOF-based solver to study the interaction between two fluids and moving rigid bodies using the fictitious domain methodJournal of Computational Physics10.1016/j.jcp.2016.01.025311:C(87-113)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.jcp.2016.01.025
Jemison MLoch ESussman MShashkov MArienti MOhta MWang Y(2018)A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase FlowsJournal of Scientific Computing10.1007/s10915-012-9614-754:2-3(454-491)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1007/s10915-012-9614-7

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents