An adaptive moving mesh method for thin film flow equations with surface tension

Article English OPEN
Abdulghani, A ; Naire, S (2017)
  • Publisher: Elsevier BV
  • Related identifiers: doi: 10.1016/j.cam.2017.01.019
  • Subject: QA
    acm: ComputingMethodologies_COMPUTERGRAPHICS
    arxiv: Mathematics::Numerical Analysis | Physics::Fluid Dynamics

We present an adaptive moving mesh method for the numerical solution of thin liquid film spreading flows with surface tension. We follow the r-adaptive moving mesh technique which utilises a mesh density function and moving mesh partial differential equations (MMPDEs) to adapt and move the mesh coupled to the PDE(s) describing the thin film flow problem. Numerical experiments are performed on two one dimensional thin film flow equations to test the accuracy and efficiency of the method. This technique accurately resolves the multiple one-dimensional structures observed in these test problems. Moreover, it reduces the computational effort in comparison to the numerical solution using the finite difference scheme on a fixed uniform mesh.
  • References (12)
    12 references, page 1 of 2

    [6] A. Oron, S. H. Davis, S. G. Bankoff, Long-scale evolution of thin liq uid films, Rev. Mod. Phy. 69 (1997) 931-980.

    [7] R. Craster, O. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81 (2009) 1131-1198.

    [8] A. L. Bertozzi, The mathematics of moving contact lines in thin liquid films, Notices Amer. Math. Soc. 45 (6) (1998) 689 - 697.

    [9] S. Troian, E. Herbolzheimer, S. Safran, Model for the fingering instability of the spreading surfactant drops, Phys. Rev. Lett. 65 (1990) 333- 336.

    [10] A. L. Bertozzi, M. P. Brenner, Linear stability and transient growth in driven contact lines, Phys. Fluids 9 (1997) 530-539.

    [11] L. Kondic, Instabilities in gravity driven flow of thin fluid films, SIAM Rev. 45 (1) (2003) 95-115.

    [12] M. R. E. Warner, R. V. Craster, O. K. Matar, Fingering phenomena associated with insoluble surfactant spreading on thin liquid films, Fluid Mech. 510 (2004) 169-200.

    [13] B. Edmonstone, O. Matar, R. Craster, Surfactant-induced fingering phenomena in thin film flow down an inclined plane, Physica D: Nonlinear Phenomena 209 (2005) 62-79.

    [14] O. E. Jensen, S. Naire, The spreading and stability of a surfactant-laden drop on a prewetted substrate, J. Fluid Mech. 554 (2006) 5-24.

    [29] J. Verwer, J. Blom, J. M. Sanz-Serna, An adaptive moving grid m ethod for one-dimensional systems of partial differential equations, J. Comp. Phys. 82 (1989) 454-486.

  • Similar Research Results (1)
  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    11
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    Keele Research Repository - IRUS-UK 0 11
Share - Bookmark